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Class 12 • Physics
Electrostats & Capacitance
Chapter-1
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1
Medium
Identify the correct statements:\\A.Electrostatic field lines form closed loops.\\B. The electric field lines point radially outward when charge is greater than zero (q > 0).\\C. The Gauss Law is valid only for inverse-square force.\\D. The work done in moving a charged particle in a static electric field around a closed path is zero (\oint \vec{E} \cdot d\vec{l} = 0).\\E. The motion of a particle under Coulomb's force must take place in a plane.
Options:
A) A, C, E Only
B) A, B, D, E Only
C) B, C, D, E Only
D) A, B, C, D Only
2
MediumAiims2019
In the given circuit, find charge on capacitor after 1s of opening the switch at $t=\infty$.
Options:
A) 20~ e^{-10} \mu \mathrm{C}
B) 25 ~e^{-10} \mu \mathrm{C}
C) 30 ~e^{-10} \mu \mathrm{C}
D) 35 ~e^{-10} \mu \mathrm{C}
3
MediumAiims2018
A half ring of radius $R has a charge of \lambda per unit length. The electric force on 1 \mathrm{C}$ charged placed at the centre is
Options:
A) zero
B) \frac{k \lambda}{R}
C) \frac{2 k \lambda}{R}
D) \frac{k \pi \lambda}{R}
4
Medium
Two point charges of 1\text{ nC} and 2\text{ nC} are placed at the two corners of an equilateral triangle of side 3\text{ cm}. The work done in bringing a charge of 3\text{ nC} from infinity to the third corner of the triangle is ______ \mu\text{J}.\\Take \frac{1}{4\pi\epsilon_0} = 9 \times 10^9\text{ N} \cdot \text{m}^2/\text{C}^2
Options:
A) A. 3.3
B) B. 27
C) C. 2.7
D) D. 5.4
5
MediumAiims2019
A capacitor of capacitance $15 \mu \mathrm{F} having dielectric slab of \varepsilon_r=2.5, dielectric strength 30 \mathrm{~MV} / \mathrm{m} and potential difference =30 \mathrm{~V}$. Calculate the area of the plate.
Options:
A) 6.7 \times 10^{-4} \mathrm{~m}^2
B) 4.2 \times 10^{-4} \mathrm{~m}^2
C) 8.0 \times 10^{-4} \mathrm{~m}^2
D) 9.85 \times 10^{-4} \mathrm{~m}^2
6
MediumAiims2018
Positive charge $Q is distributed uniformly over a circular ring of radius R. A point particle having a mass (m) and a negative charge -q is placed on its axis at a distance x from the centre. Assuming x < R$, find the time period of oscillation of the particle, if it is released from there [neglect gravity].
Options:
A) \left[\frac{16 \pi^3 \varepsilon_0 R^3 m}{Q q}\right]^{1 / 2}
B) \left[\frac{8 \pi^2 \varepsilon_0 R^3}{q}\right]^{1 / 2}
C) \left[\frac{2 \pi^3 \varepsilon_0 R^3}{3 q}\right]^{1 / 2}
D) None of these
7
Medium
The electrostatic potential in a charged spherical region of radius r varies as V = ar^3 + b, where a and b are constants. The total charge in the sphere of unit radius is \alpha \times \pi a \epsilon_0. The value of \alpha is ______.(permittivity of vacuum is \epsilon_0)
Options:
A) A. -12
B) B. -8
C) C. -9
D) D. -6
8
MediumAiims2018
An infinite number of identical capacitors each of capacitance 1 $\mu$F are connected as shown in the figure. Then, the equivalent capacitance between A and B is
Options:
A) 1 \mu \mathrm{F}
B) 2 \mu \mathrm{F}
C) \frac{1}{2} \mu \mathrm{F}
D) \infty
9
MediumAiims2018
Assertion Mass of a body decreases slightly when it is negatively charged. Reason Charging is due to transfer of electrons.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
10
Medium
There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charge q1, q2 and q3 respectively. The potentials of the spheres A, B and C respectively, are:
Options:
A) \frac{1}{4\pi\epsilon_0} \left( \frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{b} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{c} \right)
B) \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{a} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{b} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{c} \right)
C) \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{a} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2}{b} + \frac{q_3}{c} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c} \right)
D) \frac{1}{4\pi\epsilon_0} \left( \frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2}{b} + \frac{q_3}{c} \right), \frac{1}{4\pi\epsilon_0} \left( \frac{q_1+q_2+q_3}{c} \right)
11
MediumAiims2018
Assertion A dielectric slab is inserted between plates of an isolated charged capacitor which remain same. Reason Charge on an isolated system is conserved.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
12
MediumAiims2017
Charges $+q and -q are placed at points A and B respectively which are a distance 2 L apart, C is the mid-point between A and B. The work done in moving a charge +Q along the semicircle C R D$ is
Options:
A) \frac{q Q}{4 \pi \varepsilon_0 L}
B) \frac{q Q}{2 \pi \varepsilon_0 L}
C) \frac{q Q}{6 \pi \varepsilon_0 L}
D) \frac{-q Q}{6 \pi \varepsilon_0 L}
13
MediumAiims2017
Two capacitors $C and \frac{C}{2} are connected to a battery of V$ volts, as shown below The work done in charging both the capacitors fully is
Options:
A) 2 C V^2
B) \frac{3}{4} C V^2
C) \frac{1}{2} C V^2
D) \frac{1}{4} C V^2
14
Medium
Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin is ______.
Options:
A) A. 2qa(7\hat{i} - 3\hat{j})
B) B. 2qa(3\hat{j} - 7\hat{i})
C) C. 2qa(3\hat{i} - 7\hat{j})
D) D. 2qa(3\hat{j} - \hat{i})
15
MediumAiims2017
Assertion : The electric field due to a dipole on its axis line at a distance $r is E. Then, electric field due to the same dipole on the equatorial line and at the same distance will be E / 2$. Reason : Electric field due to dipole varies inversely as the square of the distance.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
16
MediumAiims2017
A parallel plate capacitor has an electric field of $10^5 \mathrm{~Vm}^{-1} between the plates. If the charge on the capacitor plates is 1 \mu \mathrm{C}$, the force on each capacitor plate is
Options:
A) 0.5 N
B) 0.05 N
C) 0.005 N
D) None of these
17
Medium
Two short dipoles (A, B), A having charges \pm 2\mu\text{C} and length 1\text{ cm} and B having charges \pm 4\mu\text{C} and length 1\text{ cm} are placed with their centres 80\text{ cm} apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is ______ \text{N/C}.
Options:
A) A. \frac{9}{16} \sqrt{2} \times 10^5
B) B. \frac{9}{16} \sqrt{2} \times 10^4
C) C. 9\sqrt{2} \times 10^4
D) D. 4.5\sqrt{2} \times 10^4
18
MediumBITSAT2024
An oil drop of radius 1 \mu \mathrm{~m} is held stationary under a constant electric field of 3.65 \times 10^{4} \mathrm{~N} / \mathrm{C} due to some excess electrons presence on it. If the density of oil drop is 1.26 \mathrm{~g} / \mathrm{cm}^{3} , then number of excess electrons on the oil drop approximately are [Take, g=10 \mathrm{~ms}^{-2} ]
Options:
A) 7
B) 12
C) 9
D) 8
19
Medium
Two charges 7\mu\text{C} and -2\mu\text{C} are placed at (-9, 0, 0)\text{ cm} and (9, 0, 0)\text{ cm} respectively in an external field E = \frac{A}{r^2}\hat{r}, where A = 9 \times 10^5\text{ N/C}\cdot\text{m}^2. Considering the potential at infinity is 0, the electrostatic energy of the configuration is ______ \text{J}.
Options:
A) A. 49.3
B) B. 1.4
C) C. 24.3
D) D. -90.7
20
MediumBITSAT2024
A parallel plate capacitor consists of two circular plates of radius R=0.1 \mathrm{~m} . They are separated by a short distance. If electric field between the capacitor plates changes as \frac{d E}{d t}=6 \times 10^{13} \frac{\mathrm{~V}}{\mathrm{~m} \times \mathrm{s}} , then the value of displacement current is
Options:
A) 15.25 A
B) 6.25 A
C) 16.67 A
D) 4.69 A
21
MediumBITSAT2024
The potential of a large liquid drop when eight liquid drops are combined is 20 V , then the potential of each single drop was
Options:
A) 10 V
B) 7.5 V
C) 5 V
D) 2.5 V
22
Medium
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is:
Options:
A) A. \frac{3q}{2\epsilon_0}
B) B. \frac{3q}{4\epsilon_0}
C) C. \frac{q}{\epsilon_0}
D) D. \frac{3q}{\epsilon_0}
23
MediumBITSAT2021
The separation between two parallel plates of capacitor is 1 mm. What is the electric potential generates between the plates of capacitor, when electric field of 2000 N/C is applied on it?
Options:
A) 2 V
B) 2000 V
C) 0.2 V
D) 200 V
24
MediumBITSAT2024
A dust particle of mass 4 \times 10^{-12} \mathrm{mg} in suspended in air under the influence of an electric field of 50 \mathrm{~N} / \mathrm{C} directed vertically upwards. How many electrons were removed from the neutral dust particle? [Take, g=10 \mathrm{~m} / \mathrm{s} { }^{2} ]
Options:
A) 15
B) 8
C) 5
D) 4
25
Medium
Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field (\vec{E}) at the center O of the pentagon due to these five positive charges are :
Options:
A) A. V = \frac{5q}{4\pi\epsilon_o r} and \vec{E} = \frac{5\sqrt{3}q}{8\pi\epsilon_o r^2} \hat{r}
B) B. V = \frac{5q}{4\pi\epsilon_o r} and \vec{E} = 0
C) C. V = 0 and \vec{E} = 0
D) D. V = \frac{5q}{4\pi\epsilon_o r} and \vec{E} = \frac{5q}{4\pi\epsilon_o r^2} \hat{r}
26
MediumBITSAT2020
Three capacitors C1, C2 and C3 are connected as shown in the figure below. If capacitor C3 breaks down electrically, the change in total charge on the combination of capacitors is
Options:
A) ({C_1} + {C_2})V\left[ {1 - \left( {{{{C_3}} \over {{C_1} + {C_2} + {C_3}}}} \right)} \right]
B) ({C_3} + {C_2})V\left[ {1 - \left( {{{{C_1}} \over {{C_1} + {C_2} + {C_3}}}} \right)} \right]
C) ({C_1} + {C_2})V\left[ {1 - \left( {{{{C_2} + {C_1}} \over {{C_1} + {C_3}}}} \right)} \right]
D) ({C_1} + {C_2})V\left[ {1 - \left( {{{{C_2}} \over {{C_1} + {C_3}}}} \right)} \right]
27
MediumBITSAT2024
Electric field at point (30,30,0) due to a charge of 0.008 \mu \mathrm{C} placed at origin will be, (coordinates are in cm )
Options:
A) 8000 \mathrm{NC}^{-1}
B) 4000(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \mathrm{NC}^{-1}
C) 200 \sqrt{2}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \mathrm{NC}^{-1}
D) 400 \sqrt{2}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \mathrm{NC}^{-1}
28
Medium
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
Options:
A) A. 1 : 3^{2/3}
B) B. 3^{2/3} : 1
C) C. 1 : 3^{1/3}
D) D. 1 : 2^{2/3}
29
MediumCOMEDK2025
A network of capacitors is as shown below. If the voltage supply is 100 V , find the energy stored in the 6 \mu \mathrm{~F} capacitor. C_1=3 \mu F, C_2=6 \mu F, C_3=3 \mu F and C_4=4 \mu F
Options:
A) 1.2 mJ
B) 12 mJ
C) 2.2 mJ
D) 4.2 mJ
30
MediumBITSAT2022
Which one of the following graphs represents the variation of electric potential with distance r from the centre of a non-conducting charged sphere of radius R?
Options:
A)
B)
C)
D)
31
Medium
Electric field in a region is given by \vec{E} = Ax\hat{i} + By\hat{j}, where A = 10\text{ V/m}^2 and B = 5\text{ V/m}^2. If the electric potential at a point (10, 20) is 500\text{ V}, then the electric potential at origin is ______ \text{V}.
Options:
A) A. 1000
B) B. 0
C) C. 2000
D) D. 500
32
MediumCOMEDK2025
A capacitor of capacitance 4 \mu \mathrm{~F} is charged to a potential of 24 V and then connected in parallel to an uncharged capacitor of capacitance 6 \mu \mathrm{~F}. The final potential difference across each capacitor will be:
Options:
A) 6.9 V
B) 8.2 V
C) 9.6 V
D) 7.4 V
33
MediumBITSAT2021
Four charges equal to + Q are placed at the four corners of a square and a charge ($-q) is at its centre. If the system is in equilibrium, then the value of -$q is
Options:
A) - {Q \over 4}(1 + 2\sqrt 2 )
B) {Q \over 2}(2\sqrt 2 + 1)
C) {Q \over 4}(1 + 2\sqrt 2 )
D) {Q \over 4}(1 + \sqrt 2 )
34
Medium
A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \vec{E} is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______
Options:
A) A. mg - qE
B) B. \sqrt{m^2g^2 + q^2E^2}
C) C. m \text{ g} + qE
D) D. \sqrt{m^2g^2 - q^2E^2}
35
MediumCOMEDK2025
When a dielectric slab of dielectric constant \mathrm{k}=2 is used to fill the space between the plates of a parallel plate capacitor, the capacitance of the capacitor is found to be 20 \mu \mathrm{~F}. What will be the capacitance when the slab is replaced with air?
Options:
A) 10 \mu F
B) 40 \mu F
C) 20 \mu F
D) 5 \mu F
36
MediumBITSAT2021
An electric dipole is placed at an angle of 30$^\circ$ in a non-uniform electric field. The dipole will experience
Options:
A) torque only
B) translational force only in the direction of the field
C) translational force only in a direction normal to the direction of the field
D) torque as well as a translational force
37
Medium
Six point charges are kept 60^\circ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is _____. (\varepsilon_0 \text{ is permittivity of free space})
Options:
A) A. -\left(\dfrac{5Q}{8\pi\varepsilon_0 R^2}\right)(\hat{i} - 3\hat{j})
B)
B. \dfrac{Q}{4\pi\varepsilon_0 R^2}(\sqrt{3}\hat{i} - \hat{j})
C)
C. -\dfrac{Q}{4\pi\varepsilon_0 R^2}(\sqrt{3}\hat{i} - \hat{j})
D)
D. -\dfrac{5Q}{8\pi\varepsilon_0 R^2}(\hat{i} + \sqrt{3}\hat{j})
38
MediumCOMEDK2025
By connecting two given capacitors, a technician was able to make two new capacitors having the effective capacitance 12.5 \mu \mathbf{F} and 2 \mu \mathbf{F}. What would be the capacitance of the given capacitors?
Options:
A) 8.5 \mu \mathrm{~F} and 4 \mu \mathrm{~F}
B) 10 \mu \mathrm{~F} and 2.5 \mu \mathrm{~F}
C) 6.5 \mu \mathrm{~F} and 6 \mu \mathrm{~F}
D) 10.5 \mu \mathrm{~F} and 2 \mu \mathrm{~F}
39
MediumBITSAT2020
A charge +q is placed at the origin O of XY-axes as shown in the figure. The work done in taking a charge Q from A to B along the straight line AB is
Options:
A) {{qQ} \over {4\pi {\varepsilon _0}}}\left( {{{a - b} \over {ab}}} \right)
B) {{qQ} \over {4\pi {\varepsilon _0}}}\left( {{{b - a} \over {ab}}} \right)
C) {{qQ} \over {4\pi {\varepsilon _0}}}\left( {{b \over {{a^2}}} - {1 \over b}} \right)
D) {{qQ} \over {4\pi {\varepsilon _0}}}\left( {{a \over {{b^2}}} - {1 \over b}} \right)
40
Medium
Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is: \\ (\text{Take } k = \dfrac{1}{4\pi \varepsilon_0} \text{ and assume } kQ^2 > Gm^2 \text{ where } G \text{ is the Gravitational constant})
Options:
A) A. \sqrt{\dfrac{kQ^2}{4mR}\left(1 + \dfrac{Gm^2}{kQ^2}\right)}
B)
B. \sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{2kQ^2}\right)}
C)
C. \sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}
D)
D. \sqrt{\dfrac{kQ^2}{4mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}
41
MediumCOMEDK2025
Two capacitors \mathrm{C}_1 and \mathrm{C}_2 are charged to 100 V and 120 V respectively. It is found that upon connecting them together in parallel, the potential on each one of them is zero. Therefore
Options:
A) \mathrm{C}_1+3 \mathrm{C}_2=0
B) 5 \mathrm{C}_1=3 \mathrm{C}_2
C) 5 \mathrm{C}_1+6 \mathrm{C}_2=0
D) 5 \mathrm{C}_1=6 \mathrm{C}_2
42
MediumBITSAT2020
Two small conducting spheres of equal radius have charges +20 $\mu C and -40 \mu$C respectively and placed at a distance R from each other experience for F1. If they are brought in contact and separated to the same distance, they experience force F2. The ratio of F1 to F2 is
Options:
A) 1 : 4
B) +8 : 1
C) -$8 : 1
D) 1 : 8
43
Medium
A point charge of 10^{-8}\text{ C} is placed at origin. The work done in moving a point charge 2\mu\text{C} from point A(4, 4, 2)\text{ m} to B(2, 2, 1)\text{ m} is ____ J. \\\left( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ in SI units} \right)
Options:
A) A. 30 \times 10^{-6}
B)
B. 0
C)
C. 15 \times 10^{-6}
D)
D. 45 \times 10^{-6}
44
MediumCOMEDK2024
Figure below shows a network of resistors, cells, and a capacitor at steady state. What is the current through the resistance 4 $\Omega$ ?
Options:
A) 1.0 A
B) 0.2 A
C) Zero
D) 0.5 A
45
MediumCOMEDK2025
A bob of a simple pendulum has a mass of 4 g and a charge of 20 \mu \mathrm{C}. If it is at rest in a uniform horizontal electric field of intensity 1000 \mathrm{Vm}^{-1}, the angle that the pendulum makes with the vertical at equilibrium is:
Options:
A) \tan ^{-1} \frac{1}{2}
B) 60^{\circ}
C) 30^{\circ}
D) \tan ^{-1} 2
46
Medium
Two metal spheres of radius R and 3R have same surface charge density \sigma. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes \sigma_1 and \sigma_2, respectively. The ratio \frac{\sigma_1}{\sigma_2} is
Options:
A) A. \frac{1}{3}
B)
B. \frac{1}{9}
C)
C. 9
D) D. 3
47
MediumCOMEDK2024
A parallel plate capacitor having a dielectric constant 5 and dielectric strength $10^6 \mathrm{~V} \mathrm{~m}^{-1} is to be designed with voltage rating of 2 \mathrm{~kV}. The field should never exceed 10 \% of its dielectric strength. To have the capacitance of 60 \mathrm{~pF}$ the minimum area of the plates should be
Options:
A) 27.1 \times 10^{-4} \mathrm{~m}^2
B) 2.7 \times 10^{-2} \mathrm{~m}^2
C) 2.71 \times 10^{-4} \mathrm{~m}^2
D) 27.1 \times 10^{-2} \mathrm{~m}^2
48
MediumCOMEDK2025
Three charges, Q,-q and 2 q are placed at the vertices of a right-angled isosceles triangle. What is the value of q for the net electrostatic energy of the configuration to be zero?
Options:
A) Q\left[\frac{1}{2 \sqrt{2}}-1\right]
B) Q\left[1-\frac{1}{2 \sqrt{2}}\right]
C) Q\left[1+\frac{1}{2 \sqrt{2}}\right]
D) Q\left[\frac{2 \sqrt{2}+1}{2}\right]
49
Medium
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R \\ Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. \\ \\.\\ Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. \\ In the light of the above statements, choose the correct answer from the options given below.
Options:
A) A. A is true but R is false
B)
B. Both A and R are true and R is the correct explanation of A
C)
C. Both A and R are true but R is NOT the correct explanation of A
D)
D. A is false but R is true
50
MediumCOMEDK2024
The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 $\mu$F capacitor.
Options:
A) 2 \times 10^{-4} \mathrm{C}
B) 4 \times 10^{-4} \mathrm{C}
C) 6 \times 10^{-4} \mathrm{C}
D) 1 \times 10^{-4} \mathrm{C}
51
MediumCOMEDK2025
A particle of mass 3 g and charge 60 \mu \mathrm{C} is released from rest in a uniform electric field of intensity 10^5 N C^{-1}. If the value of kinetic energy attained by the particle after moving through a distance of 2 cm is m \times 10^{-2} J, then the value of m is:
Options:
A) 12
B) 6
C) 5
D) 4
52
MediumCOMEDK2024
A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as $\epsilon=2 U. A similar capacitor with no dielectric is charged to U_0=78 \mathrm{~V}$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.
Options:
A) 6V
B) 8V
C) 2V
D) 4V
53
MediumCOMEDK2025
A uniformly charged conducting sphere of 0.2 m diameter has a surface charge density of 70 \mu \mathrm{Cm}^{-2}. The electric flux leaving the surface of the sphere is:
Options:
A) 9.9 \times 10^5 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^2
B) 9.9 \times 10^6 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^2
C) 8.9 \times 10^5 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^2
D) 8.9 \times 10^6 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^2
54
MediumCOMEDK2023
A capacitor of capacity $2 ~\mu \mathrm{F} is charged upto a potential 14 \mathrm{~V} and then connected in parallel to an uncharged capacitor of capacity 5 ~\mu \mathrm{F}$. The final potential difference across each capacitor will be
Options:
A) 6 V
B) 4 V
C) 8 V
D) 14 V
55
MediumCOMEDK2025
Two electric dipoles of dipole moments 3.9 \times 10^{-30} \mathrm{Cm} and 5.2 \times 10^{-30} \mathrm{Cm} are placed in two different uniform electric fields of strengths 16 \times 10^4 \mathrm{NC}^{-1} and 4 \times 10^4 \mathrm{NC}^{-1} respectively. What is the ratio of maximum torque experienced by the electric dipoles?
Options:
A) 12: 1
B) 9: 1
C) 1:9
D) 3: 1
56
MediumCOMEDK2023
A dielectric of dielectric constant $K is introduced such that half of its area of a capacitor of capacitance C$ is occupied by it. The new capacity is
Options:
A) 2 C
B) \frac{C}{2}
C) \frac{(1+K) C}{2}
D) 2 C(1+K)
57
MediumCOMEDK2025
A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' v '. Then the mass ' m ' of the charged particle is
Options:
A) M=\frac{Q^2}{\left[16 \pi^3 \varepsilon_0 R^3 v^2\right]}
B) M=\frac{Q^2}{\left[16 \pi^2 \varepsilon_0 R v^2\right]}
C) M=\frac{Q^2}{\left[16 \pi^2 \varepsilon_0 R^3 v^2\right]}
D) M=\frac{Q^2}{\left[16 \pi^3 \varepsilon_0 R^2 v^2\right]}
58
MediumCOMEDK2023
In the figure below, the capacitance of each capacitor is $3 \mu \mathrm{F}. The effective capacitance between A and B$ is
Options:
A) \frac{3}{4} \mu \mathrm{F}
B) 3 \mu \mathrm{F}
C) 6 \mu \mathrm{F}
D) 5 \mu \mathrm{F}
59
MediumCOMEDK2025
Three point charges -1 C,+1 C,+1 C are placed at points A, B, C respectively of a triangle A B C. What is the total potential energy of the system? [given \mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm} and \mathrm{BC}=3 \mathrm{~cm} ]
Options:
A) 0 J (Zero joule)
B) 4.5 \times 10^{13} \mathrm{~J}
C) 6 \times 10^{13} J
D) 3 \times 10^{13} J
60
MediumCOMEDK2023
If $C be the capacitance and V be the electric potential, then the dimensional formula of \mathrm{CV}^2$ is
Options:
A) \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^0\right]
B) \left[\mathrm{MLT}^{-2} \mathrm{~A}^{-1}\right]
C) \left[\mathrm{M}^0 \mathrm{LT}^{-2} \mathrm{~A}^0\right]
D) \left[\mathrm{ML}^{-3} \mathrm{TA}\right]
61
MediumCOMEDK2025
The electric field versus distance graph is shown as given. Select the correct statement from the following. E- electric field R-radius r - distance from the centre
Options:
A) The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged conducting ring of radius R.
B) The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged non conducting solid sphere of radius R.
C) The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged conducting solid sphere of radius R.
D) The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged non conducting cylinder of radius R.
62
MediumCOMEDK2023
In the figure, first the capacitors are fully charged by closing the key $\mathrm{K}. Then after opening the Key a dielectric material with dielectric constant 2 is filled in the space between the plates of both the capacitor. At this state the ratio of the Charge on the capacitor C_1 to that of C_2$ is:
Options:
A) 1 : 1
B) 3 : 2
C) 2 : 1
D) 1 : 2
63
MediumCOMEDK2025
What is the dimensional formula for electric flux?
Options:
A) \left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]
B) \left[\mathrm{M}^2 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]
C) \left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]
D) \left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]
64
MediumCOMEDK2022
If R and C denote resistance and capacitance of a material, then the dimension of CR will be :
Options:
A) [ML$^0$T]
B) [M$^0L^0$T]
C) [M$^0L^0T^2$]
D) [M$^2L^0$T]
65
MediumCOMEDK2025
When a metallic spherical shell of radius 20 cm is charged, the potential on its surface is found to be 5 V . The potential at a point 10 cm from the centre of the spherical shell is :
Options:
A) 10 V
B) 2.5 V
C) 1.25 V
D) 5 V
66
MediumCOMEDK2022
In the network shown in figure, the equivalent capacitance between points P and Q is
Options:
A) 1 $\mu$F
B) 2 $\mu$F
C) 3 $\mu$F
D) 4 $\mu$F
67
MediumCOMEDK2025
Point charges -3 Q,-q, 2 q and 2 Q are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is
Options:
A) Q=\frac{1}{q}
B) Q=-q
C) Q=\frac{-1}{q}
D) Q=q
68
MediumCOMEDK2020
Two capacitors $C_1 and C_2$ are charged to 120 V and 200 V, respectively. When they are connected in parallel, it is found that potential on each one of them is zero. Therefore,
Options:
A) 5C_1=3C_2
B) 3C_1=5C_2
C) 3C_1+5C_2=0
D) 9C_1=4C_2
69
MediumCOMEDK2025
For the charge configuration shown here, which of the following is not true?
Options:
A) \frac{q_1}{q_2}=1
B) \left|q_1\right|=\left|q_2\right|
C) \left|q_1\right|>\left|q_2\right|
D) q_1 and q_2 are negative
70
HardJee Advance2024
Four identical thin, square metal sheets, S_1, S_2, S_3 and S_4, each of side a are kept parallel to each other with equal distance d(\ll a) between them, as shown in the figure. Let ${C_0} = {{{\varepsilon _0}{a^2}} \over d}, where \varepsilon_0 is the permittivity of free space. Match the quantities mentioned in List-I with their values in List-II and choose the correct option. List-I List-II (P) The capacitance between S_1 and S_4, with S_2 and S_3 not connected, is (1) 3C_0 (Q) The capacitance between S_1 and S_4, with S_2 shorted to S_3, is (2) \frac{C_0}{2} (R) The capacitance between S_1 and S_3, with S_2 shorted to S_4, is (3) \frac{C_0}{3} (S) The capacitance between S_1 and S_2, with S_3 shorted to S_1, and S_2 shorted to S_4, is (4) \frac{2C_0}{3} (5) 2C_0$
Options:
A) \mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 5
B) \mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 1
C) \mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 1
D) \mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5
71
MediumCOMEDK2025
Two identical conducting balls having positive charges q_1 and q_2 are separated by a distance r. If they are made to touch each other and then separated to the same distance, the force between them will be
Options:
A) Same as before
B) zero
C) Less than before
D) More than before
72
MediumJee Advance2023
A container has a base of 50 \mathrm{~cm} \times 5 \mathrm{~cm} and height 50 \mathrm{~cm}, as shown in the figure. It has two parallel electrically conducting walls each of area 50 \mathrm{~cm} \times 50 \mathrm{~cm}. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250 \mathrm{~cm}^3 \mathrm{~s}^{-1}. What is the value of the capacitance of the container after 10 seconds? [Given: Permittivity of free space \epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}, the effects of the non-conducting walls on the capacitance are negligible]
Options:
A) 27 ~\mathrm{pF}
B) 63 ~\mathrm{pF}
C) 81 ~\mathrm{pF}
D) 135 ~\mathrm{pF}
73
MediumCOMEDK2024
A neutral water molecule is placed in an electric field $E=2.5 \times 10^4 \mathrm{NC}^{-1}. The work done to rotate it by 180^{\circ} is 5 \times 10^{-25} \mathrm{~J}$. Find the approximate separation of centre of charges.
Options:
A) 1.25 \times 10^{-10} \mathrm{~m}
B) 0.625 \times 10^{-10} \mathrm{~m}
C) 0.625 \times 10^{-9} \mathrm{~m}
D) 0.998 \times 10^{-10} \mathrm{~m}
74
EasyJee Advance2017
Consider a simple RC circuit as shown in Figure 1.Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.Process 2 : In a different process the voltage is first set to ${{{V_0}} \over 3} and maintained for a charging time T >> RC. Then, the voltage is raised to {{2{V_0}} \over 3}$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.These two processes are depicted in Figure 2.
Options:
A) EC = ED ln2
B) EC = ED
C) EC = 2ED
D) EC = ${1 \over 2}$ED
75
MediumCOMEDK2024
Two point charges $\mathrm{M} and \mathrm{N} having charges +q and -q respectively are placed at a distance apart. Force acting between them is \mathrm{F}. If 30 \% of charge of \mathrm{N} is transferred to \mathrm{M}$, then the force between the charges becomes:
Options:
A) F
B)
\frac{100}{49} F
C)
\frac{49}{100} F
D)
\frac{9}{16} F
76
MediumJee Advance2017
Consider a simple RC circuit as shown in Figure 1.Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.Process 2 : In a different process the voltage is first set to ${{{V_0}} \over 3} and maintained for a charging time T >> RC. Then, the voltage is raised to {{2{V_0}} \over 3}$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.These two processes are depicted in Figure 2.
Options:
A) {E_D} = {1 \over 3}\left( {{1 \over 2}CV_0^2} \right)
B) {E_D} = 3\left( {{1 \over 2}CV_0^2} \right)
C) {E_D} = 3CV_0^2
D) {E_D} = {1 \over 2}CV_0^2
77
MediumCOMEDK2024
If 216 drops of the same size are charged at $200 \mathrm{~V}$ each and they combine to form a bigger drop, the potential of the bigger drop will be
Options:
A) 2400 V
B) 7200 V
C) 1200 V
D) 8200 V
78
MediumJee Advance2012
In the given circuit, a charge of $+80 \mu C is given to the upper plate of the 4 \mu F capacitor. Then in the steady state, the charge on the upper plate of the 3 \mu F$ capacitor is
Options:
A) + \,32\,\mu C
B) + \,40\,\mu C
C) + \,48\,\mu C
D) + \,80\,\mu C
79
MediumCOMEDK2024
Three point charges are located on a circular arc at $\mathrm{A}, \mathrm{B} and \mathrm{C} as shown in the figure below. The total electric field at the centre of the \operatorname{arc}(\mathrm{C})$ is
Options:
A) 15000 \mathrm{~NC}^{-1}
B) 10000 \mathrm{~N} \mathrm{C}^{-1}
C) 20000 \mathrm{~NC}^{-1}
D) 5000 \mathrm{~NC}^{-1}
80
MediumJee Advance2011
A $2 \mu F capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position 2$ is
Options:
A) 0\%
B) 20\%
C) 75\%
D) 80\%
81
MediumCOMEDK2024
A tiny ball of mass $\mathrm{m} and charge \mathrm{q} is suspended from the fixed support using an insulating string of length 1 \mathrm{~m}. The horizontal uniform electric field \mathrm{E} is switched on. The angle made by the string with vertical when the ball is in equilibrium is 45^{\circ}$. The magnitude of uniform electric field is
Options:
A)
E=\frac{m g}{q} \quad N C^{-1}
B)
\mathrm{E}=\frac{\sqrt{2} \mathrm{mg}}{\mathrm{q}} \mathrm{NC}^{-1}
C)
E=\frac{m g}{\sqrt{2} q} \quad N C^{-1}
D)
\mathrm{E}=0 \quad \mathrm{NC}^{-1}
82
MediumJee Advance2007
A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is
Options:
A) 0
B) 54 $\mu$C
C) 27 $\mu$C
D) 81 $\mu$C
83
MediumCOMEDK2024
Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point $\mathrm{P} and then accelerated through point \mathrm{Q} by the electric field. Points \mathrm{P} and \mathrm{Q} have equal separations in the three arrangements. If p_1 p_2 and p_3 are linear momentum of the proton at point \mathrm{Q}$ in the three arrangement respectively, then
Options:
A)
p_3>p_2>p_1
B)
p_1=p_2=p_3
C)
p_1< p_2=p_3
D)
p_1< p_2>p_3
84
MediumJee Advance2007
Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 $\times$ 4 matrix given in the ORS. Column I Column II (A) A charged capacitor is connected to the ends of the wire (P) A constant current flows through the wire (B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion (Q) Thermal energy is generated in the wire (C) The wire is placed in a constant electric field that has a direction along the length of the wire. (R) A constant potential difference develops between the ends of the wire (D) A battery of constant emf is connected to the ends of the wire (S) Charges of constant magnitude appear at the ends of the wire
Options:
A) A $\to (Q); B \to (R); C \to (R, S); D \to$ (P, Q)
B) A $\to (Q); B \to (R, S); C \to (R, S); D \to$ (P, Q, R)
C) A $\to (Q); B \to (R, S); C \to (R); D \to$ (Q, R)
D) A $\to (Q, R); B \to (R, S); C \to (R); D \to$ (P, Q, R)
85
MediumCOMEDK2024
3 point charges each of $-\mathrm{q} are placed on the circumference of a circle of diameter 2 \mathrm{a} at \mathrm{A}, \mathrm{B} and \mathrm{C} respectively as shown in figure. The electric field at \mathrm{O}$ is
Options:
A) Zero
B) \frac{\mathrm{Kq}}{2 \mathrm{a}} towards \mathrm{OC}
C) \frac{\mathrm{Kq}}{\mathrm{a}} towards \mathrm{OB}
D) \frac{\mathrm{Kq}}{\mathrm{a}} towards \mathrm{OA}
86
MediumJee Advance2006
In the following circuits, it is given that \mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F} and \mathrm{C}_2=4 \mu \mathrm{~F}.The time constants (in \mu \mathrm{s} ) for the circuits I, II, III are, rcspectively.
Options:
A) 18,8 / 9,4
B) 18,4,8 / 9
C) 4,8 / 9,18
D) 8 / 9,18,4
87
MediumCOMEDK2024
A uniformly charged solid sphere of radius $\mathrm{R} has potential \mathrm{V}_0 (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials \frac{3 \mathrm{~V}_0}{2}, \frac{\mathrm{V}_0}{1}, \frac{3 \mathrm{~V}_0}{4} and \frac{\mathrm{V}_0}{4} have radius \mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_3 and \mathrm{R}_4$ and respectively, then
Options:
A)
R_1 \neq 0 \text { and }\left(R_2-R_1\right)>\left(R_4-R_3\right)
B)
R _2< R_4
C)
R_1=0 \text { and } R_2>\left(R_4-R_3\right)
D)
R_1=0 \text { and } R_2<\left(R_4-R_3\right)
88
MediumJee Advance2005
In the given circuit, the switch S is closed at time $t=0. The charge Q on the capacitor at any instant t is given by Q(t)=Q_0(1-e^{-\alpha t}). Find the value of Q_0 and \alpha$ in terms of given parameters shown in the circuit.
Options:
A) \mathrm{Q_0=\frac{2CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{CR_1R_2}}
B) \mathrm{Q_0=\frac{CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{3CR_1R_2}}
C) \mathrm{Q_0=\frac{CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{CR_1R_2}}
D) \mathrm{Q_0=\frac{2CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{3CR_1R_2}}
89
MediumCOMEDK2024
A square shaped aluminium coin weighs $0.75 \mathrm{~g} and its diagonal measures 14 \mathrm{~mm}. It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges (+Q and -Q)$ that are separated by a distance equal to the side of the coin, the dipole moment of the dipole is
Options:
A) 34.8 \mathrm{~Cm}
B) 3.48 \mathrm{~Cm}
C) 3480 \mathrm{~Cm}
D) 348 \mathrm{~Cm}
90
HardJee Advance2023
In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 \mathrm{~A} flows through the 1 \Omega resistor. The key is closed at time t=t_0. Which of the following statement(s) is(are) correct? [Given: e^{-1}=0.36 ]
Options:
A) The value of the resistance R is 3 \Omega.
B) For t < t_0 , the value of current I_1 is 2 \mathrm{~A}.
C) At t=t_0+7.2 \mu \mathrm{s}, the current in the capacitor is 0.6 \mathrm{~A}.
D) For t \rightarrow \infty, the charge on the capacitor is 12 \mu \mathrm{C}.
91
MediumCOMEDK2024
If potential (in volt) in a region is expressed as $\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathrm{y}+2 \mathrm{yz}, the electric field (in N C^{-1}) at point (1,0,1)$ is
Options:
A) \mathrm{-7 j}
B) +7 \mathrm{j}
C) \mathrm{-6 i+7 j}
D) \mathrm{6 i-7 j}
92
HardJee Advance2022
A medium having dielectric constant K>1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d. The capacitor is connected to a battery of voltage V, as shown in Figure (a). Now, both the plates are moved by a distance of \frac{d}{2} from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?
Options:
A) The electric field inside the dielectric material is reduced by a factor of 2 K.
B) The capacitance is decreased by a factor of \frac{1}{K+1}.
C) The voltage between the capacitor plates is increased by a factor of (K+1).
D) The work done in the process DOES NOT depend on the presence of the dielectric material.
93
MediumCOMEDK2024
Five charges, '$q' each are placed at the comers of a regular pentagon of side 'a' as shown in figure. First, charge from 'A' is removed with other charges intact, then charge at 'A' is replaced with an equal opposite charge. The ratio of magnitudes of electric fields at \mathrm{O}, without charge at A and that with equal and opposite charge at A$ is
Options:
A) 4 : 1
B) 2 : 1
C) 1 : 4
D) 1 : 2
94
MediumJee Advance2015
A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities ($\varepsilon 1 = 2 and \varepsilon 2 = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio {{{C_2}} \over {{C_1}}}$ is
Options:
A) {6 \over 5}
B) {5 \over 3}
C) {7 \over 5}
D) {7 \over 3}
95
MediumCOMEDK2024
Two charges '$-q' each are fixed, separated by distance '2 d'. A third charge 'q' of mass 'm' placed at the mid-point is displaced slightly by 'x' (x< < d) perpendicular to the line joining the two fixed charges as shown in Fig. The time period of oscillation of 'q$' will be
Options:
A)
\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^2 \mathrm{~d}^3}{\mathrm{q}^2}}
B)
\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^3}}
C)
\mathrm{T}=\sqrt{\frac{4 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^2}}
D)
\mathrm{T}=\sqrt{\frac{8 \varepsilon_0 \mathrm{~m} \pi^3 \mathrm{~d}^3}{\mathrm{q}^2}}
96
MediumJee Advance2014
A parallel plate capacitor has a dielectric slab of dielectric constant $K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is {C_1}. When the capacitor is charged, the plate area covered by the dielectric gets charge {Q_1} and the rest of the area gets charge {Q_2}. The electric field in the dielectric is {E_1} and that in the other portion is {E_2}.$ Choose the correct option/ options, ignoring edge effects.
Options:
A) {{{E_1}} \over {{E_2}}} = 1
B) {{{E_1}} \over {{E_2}}} = {1 \over K}
C) {{{Q_1}} \over {{Q_2}}} = {3 \over K}
D) {C \over {{C_1}}} = {{2 + K} \over K}
97
MediumCOMEDK2024
Two metal spheres, one of radius $\frac{R}{2} and the other of radius 2 \mathrm{R}$ respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is
Options:
A) 2: 1
B) 4: 1
C) 1: 4
D) 1: 2
98
MediumJee Advance2013
In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C. The switch {S_1} is pressed first to fully charge the capacitor {C_1} and then released. The switch {S_2} is then pressed to charge the capacitor {C_2}. After some time, {S_2} is released and then {S_3}$ is pressed. After some time
Options:
A) The charge on the upper plate of ${C_1} is 2C{V_0}
B) The charge on the upper plate of ${C_1} is C{V_0}
C) The charge on the upper plate of ${C_2} is 0
D) The charge on the upper plate of ${C_2} is - C{V_0}
99
MediumCOMEDK2023
When $10^{19}$ electrons are removed from a neutral metal plate, the electric charge on it is
Options:
A) -1.6 \mathrm{~C}
B) +1.6 \mathrm{~C}
C) 10^{+19} \mathrm{~C}
D) 10^{-19} \mathrm{~C}
100
EasyJee Advance2021
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 $\muC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \mu$C.The magnitude of q1 is ________________.
Options:
101
MediumCOMEDK2023
Two point charges $20 \mu \mathrm{C} and -10 \mu \mathrm{C} are separated by a distance of 1 \mathrm{~m}$ in air. At what point on the line joining the two charges, the electric potential is zero.
Options:
A) 0.5 \mathrm{~m} from the charge 10 \mu \mathrm{C}
B) 0.76 \mathrm{~m} from the charge 20 \mu \mathrm{C}
C) 0.67 \mathrm{~m} from the charge 20 \mu \mathrm{C}
D) 0.25 \mathrm{~m} from the charge 10 \mu \mathrm{C}
102
MediumJee Advance2021
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 $\muC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \mu$C.The magnitude of q2 is ________________.
Options:
103
MediumCOMEDK2023
A spherical metal ball of density '$\rho' and radius 'r' is immersed in a liquid of density '\sigma$'. When an electric field is applied in the upward direction the metal ball remains just suspended in the liquid. Then the expression for the charge on the metal ball is :
Options:
A) q=\frac{\left[\frac{4}{3} \pi r^3 \rho g\right]}{\sigma E}
B) q=\frac{\left[4 \pi r^3(\rho-\sigma) g\right]}{3 E}
C) q=\frac{\left[4 \pi r^2 \rho g\right]}{\sigma E}
D) q=\frac{\left[4 \pi r^2(\rho-\sigma) g\right]}{E}
104
MediumJee Advance2020
Two capacitors with capacitance values C1 = 2000 $ \pm 10 pF and C2 = 3000 \pm 15 pF are connected in series. The voltage applied across this combination is V = 5.00 \pm $ 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is ________.
Options:
105
MediumCOMEDK2023
PQRS is square of side $1 \mathrm{~m}. A charge of 100 \mu \mathrm{C} is placed at the centre of the square. Then the work done to take 3 \mu \mathrm{C} charge from the corner \mathrm{P} to the corner \mathrm{R}$.
Options:
A) 9 \sqrt{2} \times 10^5 \mathrm{~J}
B) 4.5 \times 10^5 \mathrm{~J}
C) Zero
D) 1.8 \times 10^5 \mathrm{~J}
106
MediumJee Advance2019
A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness, $\delta = {d \over N}. The dielectric constant of the mth layer is {K_m} = K\left( {1 + {m \over N}} \right). For a very large N(>103), the capacitance C is \alpha \left( {{{K{\varepsilon _0}A} \over {d\ln 2}}} \right)The value of \alpha will be ..................[ \in $0 is the permittivity of free space.]
Options:
107
MediumCOMEDK2023
An electron and a proton having mass $m_e and m_p respectively, initially at rest, move through the same distance 's' in a uniform electric field 'E'. If the time taken by them to cover that distance is t_e and t_p respectively, then t_e / t_p$ is equal to:
Options:
A)
\sqrt{\left(\frac{m_p}{m_e}\right)}
B)
\sqrt{\left(\frac{m_e}{m_p}\right)}
C)
\frac{\sqrt{\left(m_e\right)}}{m_p}
D)
\frac{m_e}{m_p}
108
MediumJee Advance2018
Three identical capacitors ${C_1},{C_2} and {C_3} have a capacitance of 1.0\,\mu F each and they are unchanged initially. They are connected in a circuit as shown in the figure and {C_1} is then filled completely with a dielectric material of relative permittivity {\varepsilon _r}. The cell electromotive force \left( {emf} \right)\,\,{V_0} = 8V. First the switch {S_1} is closed while the switch {S_2} is kept open. When the capacitor {C_3} is fully charged, {S_1} is opened and {S_2} is closed simultaneously. When all the capacitors reach equilibrium, the charge on {C_3} is found to be 5\,\mu C. The value of {\varepsilon _r} = $ _________________.
Options:
109
MediumCOMEDK2023
The force between two electric point charges at rest in air is $F_1 When the same arrangement is kept inside water, the force between them is F_2$. Which of the following statement is correct?
Options:
A) F_2=0
B) F_2>F_1
C) F_2=F_1
D) F_2< F_1
110
MediumJee Advance2010
At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)
Options:
111
MediumCOMEDK2022
Which of the following diagram represents the variation of the electric field with distance r from the centre of a uniformly charged non-conducting sphere of radius R?
Options:
A)
B)
C)
D)
112
MediumJEE Mains2026
Identify the correct statements :A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.Choose the correct answer from the options given below :
Options:
A) A, C and D Only
B) A, B and C Only
C) B and D Only
D) C and D Only
113
MediumCOMEDK2022
Charge on electron is
Options:
A) 3.2 $\times 10^{-19}$ C
B) 1.6 $\times 10^{-19}$ C
C) -1.6 \times 10^{-19}$ C
D) -3.2 \times 10^{-19}$ C
114
MediumJEE Mains2026
Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( k_1 and k_2 ) in the following fashion. Which of the following is true? $ \left(k_1>k_2\right)
Options:
A) C_C>C_B>C_A
B) C_B>C_C>C_A
C) C_A>C_C>C_B
D) C_C>C_A>C_B
115
MediumCOMEDK2022
Two charged spheres of $-20\muC and 60\mu$C are kept at a certain distance. They are touched and kept again at the same distance. What is the ratio of force experienced before and after?
Options:
A) 1 : 3
B) 3 : 1
C) 2 : 1
D) 1 : 2
116
MediumJEE Mains2026
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25 \% more charge from the battery. The dielectric constant of mica is \_\_\_\_
Options:
A) 1.0
B) 2.5
C) 1.5
D) 2.0
117
MediumCOMEDK2021
Insulators can be charged by which of the following process?
Options:
A) Induction
B) Diverging
C) Friction
D) Heating
118
MediumJEE Mains2026
A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness \left(\frac{1}{3}\right)^{\mathrm{rd}} of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :
Options:
A) \frac{3 C K^2}{(2 K+1)^2}
B) \frac{4 K C}{3 K-1}
C) \frac{C K}{2+K}
D) \frac{3 K C}{2 K+1}
119
MediumCOMEDK2021
Work done in moving a charge of 25C is 50 J. Calculate potential difference, between two points.
Options:
A) 0.5 V
B) 1 V
C) 2 V
D) 2.5 V
120
EasyJEE Mains2025
Three parallel plate capacitors C_1, C_2 and C_3 each of capacitance 5 \mu \mathrm{~F} are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of C_1 capacitor is filled with a dielectric medium having dielectric constant of 4, is :
Options:
A) 9 \mu \mathrm{~F}
B) 30 \mu \mathrm{~F}
C) 7.5 \mu \mathrm{~F}
D) 22.5 \mu \mathrm{~F}
121
MediumCOMEDK2021
What is the electric field near infinite plane sheet of charge density $\sigma$ ?
Options:
A) {\sigma \over {2{\varepsilon _0}}}
B) {{\sigma A} \over {2{\varepsilon _0}}}
C) {\sigma \over {2{\varepsilon _0}A}}
D) {\sigma \over {{\varepsilon _0}}}
122
EasyJEE Mains2025
Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is: (in pF )
Options:
A) 600
B) 100
C) 400
D) 200
123
MediumCOMEDK2020
Consider a thin spherical shell of radius R consisting of uniform surface charge density s. The electric field at a point of distance x from its centre and outside the shell is
Options:
A) inversely proportional to $s
B) directly proportional to $x^2
C) directly proportional to $R
D) inversely proportional to $x^2
124
MediumJEE Mains2025
A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants \varepsilon_1 and \varepsilon_2, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are \mathrm{C}_1 and \mathrm{C}_2 respectively, then \frac{C_1}{C_2} is: First Configuration Second Configuration
Options:
A) \frac{\varepsilon_0\left(\varepsilon_1+\varepsilon_2\right)}{2}
B) \frac{\varepsilon_1 \varepsilon_2^2}{\left(\varepsilon_1+\varepsilon_2\right)^2}
C) \frac{4 \varepsilon_1 \varepsilon_2}{\left(\varepsilon_1+\varepsilon_2\right)^2}
D) \frac{\varepsilon_1 \varepsilon_2}{\varepsilon_1+\varepsilon_2}
125
MediumCOMEDK2020
A charge of 0.8 C is divided into two charges Q$_1 and Q_2. These are kept at a separation of 30 cm. The force on Q_1$ is maximum when
Options:
A) Q_1=Q_2=0.4$ C
B) Q_1 \approx 0.8 C, Q_2$ negligible
C) Q_1 negligible, Q_2 \approx 0.8$ C
D) Q_1=0.2 C, Q_2=0.6$ C
126
EasyJEE Mains2025
A capacitor, C_1 = 6 \mu F is charged to a potential difference of V_0 = 5V using a 5V battery. The battery is removed and another capacitor, C_2 = 12 \mu F is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (q_1 and q_2) on the capacitors C_1 and C_2 when equilibrium condition is reached.
Options:
A) q_1 = 10 \mu C, \ q_2 = 20 \mu C
B) q_1 = 15 \mu C, \ q_2 = 30 \mu C
C) q_1 = 20 \mu C, \ q_2 = 10 \mu C
D) q_1 = 30 \mu C, \ q_2 = 15 \mu C
127
MediumCOMEDK2020
An electric dipole has a pair of equal and opposite point charges $q and -q separated by a distance 2x$. The axis of the dipole is defined as
Options:
A) direction from positive charge to negative charge
B) direction from negative charge to positive charge
C) perpendicular to the line joining the two charges drawn at the centre and pointing upward direction
D) perpendicular to the line joining the two charges at the centre and pointing downward direction
128
EasyJEE Mains2025
A parallel plate capacitor of capacitance 1 µF is charged to a potential difference of 20 V. The distance between plates is 1 µm. The energy density between plates of capacitor is :
Options:
A) 1.8 \times 10^3 J/m3
B) 2 \times 10^2 J/m3
C) 2 \times 10^{-4} J/m3
D) 1.8 \times 10^5 J/m3
129
MediumCOMEDK2020
An electric dipole is placed in a uniform electric field with the dipole axis making an angle $\theta$ with the direction of the electric field. The orientation of the dipole for stable equilibrium is
Options:
A) \frac{\pi}{6}
B) \frac{\pi}{3}
C) 0
D) \frac{\pi}{2}
130
MediumJEE Mains2025
Two capacitors \mathrm{C}_1 and \mathrm{C}_2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \mathrm{U}_1 and \mathrm{U}_2, respectively. Which of the given statements is true?
Options:
A) \mathrm{C}_2>\mathrm{C}_1, \mathrm{U}_2>\mathrm{U}_1
B) \mathrm{C}_1>\mathrm{C}_2, \mathrm{U}_1>\mathrm{U}_2
C) \mathrm{C}_2>\mathrm{C}_1, \mathrm{U}_2<\mathrm{U}_1
D) \mathrm{C}_1>\mathrm{C}_2, \mathrm{U}_1<\mathrm{U}_2
131
MediumCOMEDK2020
Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is
Options:
A) 2.0\times10^{-7}$ J
B) 1.35\times10^{-7}$ J
C) 2.7\times10^{-7}$ J
D) 12.1\times10^{-7}$ J
132
EasyJEE Mains2025
A parallel plate capacitor was made with two rectangular plates, each with a length of l=3 \mathrm{~cm} and breath of \mathrm{b}=1 \mathrm{~cm}. The distance between the plates is 3 \mu \mathrm{~m}. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m} B. l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m} C. l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m} D. l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m} E. l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m} Choose the correct answer from the options given below:
Options:
A) C only
B) A only
C) B and D only
D) C and E only
133
MediumCOMEDK2020
The potential energies associated with four orientations of an electric dipole in an electric field are (i) $-5U_0 (ii) -7U_0 (iii) 3U_0 (iv) 5U_0 where U_0$ is positive. Rank the orientations according to the angle between the electric dipole moment p and electric field E, greatest first
Options:
A) (i), (ii), (iii), (iv)
B) (ii), (iii), (i), (iv)
C) (iv), (iii), (i), (ii)
D) (iv), (i), (iii), (ii)
134
EasyJEE Mains2025
Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor R. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:
Options:
A) A, C Only
B) C, D Only
C) A, B, D Only
D) B, C, D Only
135
HardJee Advance2025
Two co-axial conducting cylinders of same length \ell with radii \sqrt{2}R and 2R are kept, as shown in Fig. 1. The charge on the inner cylinder is Q and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant \kappa=5. Consider an imaginary plane of the same length \ell at a distance R from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is (\epsilon_0 is the permittivity of free space):
Options:
A) \frac{Q}{30\epsilon_0}
B) \frac{Q}{15\epsilon_0}
C) \frac{Q}{60\epsilon_0}
D) \frac{Q}{120\epsilon_0}
136
EasyJEE Mains2025
Which one of the following is the correct dimensional formula for the capacitance in F ? \mathrm{M}, \mathrm{L}, \mathrm{T} and C stand for unit of mass, length, time and charge,
Options:
A) [\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]
B) [\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]
C) [\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]
D) [\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]
137
MediumJee Advance2025
List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude p, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance 2 r apart along the x direction. The midpoint of the line joining the two dipoles is X. The possible resultant electric fields \vec{E} at X are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II. List–I List–II (P) (1) $ \vec{E}=0 (Q) (2) \displaystyle \vec{E} = -\,\frac{p}{2\pi\epsilon_0\,r^3}\,\hat{\jmath} (R) (3) \displaystyle \vec{E} = -\,\frac{p}{4\pi\epsilon_0\,r^3}\,(\hat{\imath} - \hat{\jmath}) (S) (4) \displaystyle \vec{E} = \frac{p}{4\pi\epsilon_0\,r^3}\,(2\hat{\imath} - \hat{\jmath}) (5) \displaystyle \vec{E} = \frac{p}{\pi\epsilon_0\,r^3}\,\hat{\imath}$
Options:
A) \mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4
B) \mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 1
C) \mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5
D) \mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 5
138
EasyJEE Mains2025
An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 10^6 \mathrm{~m} / \mathrm{s}. If the magnitude of the electric field between the plates is 9.1 \mathrm{~V} / \mathrm{cm}, then the vertical component of velocity of electron is (mass of electron =9.1 \times 10^{-31} \mathrm{~kg} and charge of electron =1.6 \times 10^{-19} \mathrm{C} )
Options:
A) 1 \times 10^6 \mathrm{~m} / \mathrm{s}
B) 16 \times 10^6 \mathrm{~m} / \mathrm{s}
C) 16 \times 10^4 \mathrm{~m} / \mathrm{s}
D) 0
139
HardJee Advance2024
Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius a. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ \varepsilon_0 is the permittivity of free space.]
Options:
A) {{{q^2}} \over {4\pi {\varepsilon _0}{a^3}m}}
B) {{{q^2}} \over {32\pi {\varepsilon _0}{a^3}m}}
C) {{{q^2}} \over {8\pi {\varepsilon _0}{a^3}m}}
D) {{{q^2}} \over {16\pi {\varepsilon _0}{a^3}m}}
140
MediumJEE Mains2025
A parallel-plate capacitor of capacitance 40 \mu \mathrm{~F} is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant \mathrm{K}=2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are
Options:
A) 8 mC and 2.0 J
B) 4 mC and 0.2 J
C) 2 mC and 0.2 J
D) 2 mC and 0.4 J
141
MediumJee Advance2023
An electric dipole is formed by two charges +q and -q located in x y-plane at (0,2) \mathrm{mm} and (0,-2) \mathrm{mm}, respectively, as shown in the figure. The electric potential at point P(100,100) \mathrm{mm} due to the dipole is V_0. The charges +q and -q are then moved to the points (-1,2) \mathrm{mm} and (1,-2) \mathrm{mm}, respectively. What is the value of electric potential at P due to the new dipole?
Options:
A) \frac{V_0}{4}
B) \frac{V_0}{2}
C) \frac{V_0}{\sqrt{2}}
D) \frac{3 V_0}{4}
142
MediumJEE Mains2024
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3} and the height is d$, the capacitance of the arrangement is :
Options:
A) \frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{20 \mathrm{~d}}
B) \frac{13 \epsilon_{\mathrm{o}} \mathrm{A}}{17 \mathrm{~d}}
C) \frac{18 \epsilon_{\mathrm{o}} \mathrm{A}}{11 \mathrm{~d}}
D) \frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}
143
MediumJee Advance2019
A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area $\alpha 4\pi R2(\alpha $ << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
Options:
A) The ratio of the potential at the center of the shell of that of the point at ${1 \over 2}R from center towards the hole will be {{1 - \alpha } \over {1 - 2\alpha }}$.
B) The potential at the center of the shell is reduced by 2$\alpha $V0.
C) The magnitude of electric field at the center of the shell is reduced by ${{\alpha {V_0}} \over {2R}}$.
D) The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by ${{\alpha {V_0}} \over {2R}}$.
144
MediumJEE Mains2024
A capacitor has air as dielectric medium and two conducting plates of area $12 \mathrm{~cm}^2 and they are 0.6 \mathrm{~cm} apart. When a slab of dielectric having area 12 \mathrm{~cm}^2 and 0.6 \mathrm{~cm} thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 \mathrm{~cm} to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given \epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}$)
Options:
A) 1.50
B) 0.66
C) 1.33
D) 1
145
MediumJee Advance2018
The electric field $E is measured at a point P(0,0,d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-{\rm I} contains different relations between E and d. List-{\rm II} describes different electric charge distributions, along with their locations. Match the functions in List-{\rm I} with the related charge distributions in List-{\rm II}. LIST - I LIST - II P. E is independent of d 1. A point charge Q at the origin Q. E\, \propto \,1/d 2. A small dipole with point charges Q at \left( {0,0,l} \right) and -Q at \left( {0,0, - l} \right). Take 2l < < d R. E\, \propto \,1/{d^2} 3. An infinite line charge coincident with the x-axis, with uniform linear charge density \lambda S. E\, \propto \,1/{d^3} 4. Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along \left( {y = 0,z = l} \right) has a charge density + \lambda and the one along \left( {y = 0,z = - l} \right) has a charge density Take 5. Infinite plane charge coincident with the xy$-plane with uniform surface charge density
Options:
A) P \to 5;Q \to 3,4;R \to 1;S \to 2
B) P \to 5;Q \to 3;R \to 1,4;S \to 2
C) P \to 4;Q \to 3;R \to 1,2;S \to 4
D) P \to 4;Q \to 2,3;R \to 1;S \to 5
146
MediumJEE Mains2024
A galvanometer (G) of 2 \Omega resistance is connected in the given circuit. The ratio of charge stored in C_1 and C_2 is :
Options:
A) 1
B) \frac{2}{3}
C) \frac{3}{2}
D) \frac{1}{2}
147
MediumJee Advance2016
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $-$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity) Which one of the following statement is correct?
Options:
A) The balls will execute simple harmonic motion between the two plates
B) The balls will bounce back to the bottom plate carrying the same charge they went up with
C) The balls will stick to the top plate and remain there
D) The balls will bounce back to the bottom plate carrying the opposite charge they went up with
148
MediumJEE Mains2024
Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2 \mathrm{~V}. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :
Options:
A) \frac{1}{4} \mathrm{CV}^2
B) \frac{3}{4} \mathrm{CV}^2
C) \frac{1}{2} \mathrm{CV}^2
D) 2 \mathrm{CV}^2
149
MediumJee Advance2016
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $-$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)The average current in the steady state registered by the ammeter in the circuit will be
Options:
A) proportional to $V_0^2
B) proportional to the potential ${V_0}
C) zero
D) proportions to $V_0^{1/2}
150
MediumJEE Mains2023
In the network shown below, the charge accumulated in the capacitor in steady state will be:
Options:
A) 10.3 $\mu$C
B) 7.2 $\mu$C
C) 4.8 $\mu$C
D) 12 $\mu$C
151
HardJee Advance2014
Charges $Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii R/2,R and 2R respectively, as shown in figure. If magnitude of the electric fields at point P at a distance R from the center of sphere 1,2 and 3 are {E_1}, {E_2} and {E_3}$ respectively, then
Options:
A) {E_1} > {E_2} > {E_3}
B) {E_3} > {E_1} > {E_2}
C) {E_2} > {E_1} > {E_3}
D) {E_3} > {E_2} > {E_1}
152
MediumJEE Mains2023
A capacitor of capacitance $\mathrm{C}$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :
Options:
A) Zero
B) \frac{C V}{\varepsilon_{0}}
C) \frac{C V}{2 \varepsilon_{0}}
D) \frac{2 C V}{\varepsilon_{0}}
153
HardJee Advance2014
Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = $-2a, -a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists. List I List II P. Q_1, Q_2, Q_3, Q_4 all positive 1. +x Q. Q_1, Q_2 positive; Q_3, Q_4 negative 2. - x R. Q_1, Q_4 positive; Q_2, Q_3 negative 3. +y S. Q_1, Q_3 positive; Q_2, Q_4 negative 4. - $y
Options:
A) P-3, Q-1, R-4, S-2
B) P-4, Q-2, R-3, S-1
C) P-3, Q-1, R-2, S-4
D) P-4, Q-2, R-1, S-3
154
EasyJEE Mains2023
A parallel plate capacitor of capacitance $2 \mathrm{~F} is charged to a potential \mathrm{V}, The energy stored in the capacitor is E_{1}. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is \mathrm{E}_{2}. The ratio \mathrm{E}_{2} / \mathrm{E}_{1}$ is :
Options:
A) 1 : 2
B) 2 : 3
C) 2 : 1
D) 1 : 4
155
MediumJee Advance2013
Two non-conducting solid spheres of radii $R and 2R, having uniform volume charge densities {\rho _1} and {\rho _2} respectively, touch each other. The net electric field at a distance 2 R from the center of the smaller sphere, along the line joining the centers of the spheres, is zero. The ratio {{{\rho _1}} \over {{\rho _2}}}$ can be
Options:
A) -4
B) - {{32} \over {25}}
C) {{32} \over {25}}
D) 4
156
MediumJEE Mains2023
The distance between two plates of a capacitor is $\mathrm{d} and its capacitance is \mathrm{C}_{1}, when air is the medium between the plates. If a metal sheet of thickness \frac{2 d}{3} and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes \mathrm{C}_{2}. The ratio \frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$ is
Options:
A) 1 : 1
B) 3 : 1
C) 2 : 1
D) 4 : 1
157
MediumJee Advance2012
Consider a thin spherical shell of radius $R with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field \left| {\overrightarrow E \left( r \right)} \right| and the electric potential V(r) with the distance r$ from the center, best represented by which graph?
Options:
A)
B)
C)
D)
158
EasyJEE Mains2023
The equivalent capacitance of the combination shown is :
Options:
A) \frac{C}{2}
B) 4C
C) \frac{5}{3}$C
D) 2C
159
MediumJee Advance2012
Two large vertical and parallel metal plates having a separation of $1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at {45^ \circ } to the vertical JUST after release. Then X$ is nearly
Options:
A) 1 \times {10^{ - 5}}\,\,V
B) 1 \times {10^{ - 7}}\,\,V
C) 1 \times {10^{ - 9}}\,\,V
D) 1 \times {10^{ - 10}}\,\,V
160
MediumJEE Mains2023
In this figure the resistance of the coil of galvanometer G is $2 ~\Omega. The emf of the cell is 4 \mathrm{~V}. The ratio of potential difference across \mathrm{C}_{1} and \mathrm{C}_{2}$ is:
Options:
A) \frac{5}{4}
B) \frac{3}{4}
C) 1
D) \frac{4}{5}
161
MediumJee Advance2011
Consider an electric field $\overrightarrow E = {E_0}\widehat x where {E_0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is
Options:
A) 2{E_0}{a_2}
B) \sqrt 2 {E_0}{a^2}
C) {E_0}\,{a^2}
D) {{{E_0}{a^2}} \over {\sqrt 2 }}
162
EasyJEE Mains2023
Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres In light of the above statements, choose the correct answer from the options given below.
Options:
A) Both $\mathbf{A} and \mathbf{R} are true but \mathbf{R} is not the correct explanation of \mathbf{A}
B) Both $\mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
C) \mathbf{A} is false but \mathbf{R}$ is true
D) \mathbf{A} is true but \mathbf{R}$ is false
163
MediumJee Advance2011
Which of the field patterns given below is valid for electric field as well as for magnetic field ?
Options:
A)
B)
C)
D)
164
EasyJEE Mains2023
A parallel plate capacitor has plate area 40 cm$^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :
Options:
A) \mathrm{10\varepsilon_0~F}
B) \mathrm{24\varepsilon_0~F}
C) \mathrm{\frac{3}{10}\varepsilon_0~F}
D) \mathrm{\frac{10}{3}\varepsilon_0~F}
165
MediumJee Advance2010
A uniformly charged thin spherical shell of radius $R carries uniform surface charge density of \sigma per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F$ is proportional to
Options:
A) {1 \over {{\varepsilon _0}}}{\sigma ^2}{R^2}
B) {1 \over {{\varepsilon _0}}}{\sigma ^2}R
C) {1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over R}
D) {1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over {{R^2}}}
166
MediumJEE Mains2022
Two identical thin metal plates has charge $q_{1} and q_{2} respectively such that q_{1}>q_{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :
Options:
A) \frac{\left(q_{1}+q_{2}\right)}{C}
B) \frac{\left(q_{1}-q_{2}\right)}{C}
C) \frac{\left(q_{1}-q_{2}\right)}{2 C}
D) \frac{2\left(q_{1}-q_{2}\right)}{C}
167
MediumJee Advance2010
A tiny spherical oil drop carrying a net charge $q is balanced in still air with a vertical uniform electric field of strength {{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}. When the field is switched off, the drop is observed to fall with terminal velocity 2 \times {10^{ - 3}}\,\,m{s^{ - 1}}. Given g = 9.8\,m\,{s^{ - 2}}, viscosity of the air = 1.8 \times {10^{ - 5}}\,\,Ns\,{m^{ - 2}} and the density of coil =900 kg {m^{ - 3}}, the magnitude of q$ is
Options:
A) 1.6 \times {10^{ - 19}}C
B) 3.2 \times {10^{ - 19}}C
C) 4.8 \times {10^{ - 19}}C
D) 8.0 \times {10^{ - 19}}C
168
MediumJEE Mains2022
A slab of dielectric constant $\mathrm{K} has the same cross-sectional area as the plates of a parallel plate capacitor and thickness \frac{3}{4} \mathrm{~d}, where \mathrm{d} is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given \mathrm{C}_{0}$ = capacitance of capacitor with air as medium between plates.)
Options:
A) \frac{4 K C_{0}}{3+K}
B) \frac{3 K C_{0}}{3+K}
C) \frac{3+K}{4 K C_{0}}
D) \frac{K}{4+K}
169
MediumJee Advance2009
A disk of radius ${a \over 4} having a uniformly distributed charge 6C is placed in the xy-plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two points charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x=\pm a/2,y=\pm a/2,z=\pm a/2$. The electric flux through this cubical surface is
Options:
A) {{ - 2c} \over {{\varepsilon _0}}}
B) {{2c} \over {{\varepsilon _0}}}
C) {{10c} \over {{\varepsilon _0}}}
D) {{12c} \over {{\varepsilon _0}}}
170
EasyJEE Mains2022
Two capacitors, each having capacitance $40 \,\mu \mathrm{F} are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \mathrm{K} such that the equivalence capacitance of the system became 24 \,\mu \mathrm{F}. The value of \mathrm{K}$ will be :
Options:
A) 1.5
B) 2.5
C) 1.2
D) 3
171
MediumJee Advance2009
Three concentric metallic spherical shells of radii $R,2R,3R are given charges Q_1,Q_2,Q_3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q_1:Q_2:Q_3$, is
Options:
A) 1 : 2 : 3
B) 1 : 3 : 5
C) 1 : 4 : 9
D) 1 : 8 : 18
172
MediumJEE Mains2022
A source of potential difference $V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is E_{1}. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E_{2}. The ratio E_{1} / E_{2}$ will be :
Options:
A) \frac{1}{10}
B) \frac{2}{5}
C) \frac{5}{13}
D) \frac{5}{26}
173
HardJee Advance2009
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and $\mu be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. Column I Column II (A) E=0 (P) Charge are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon. (B) V\ne 0 (Q) Charges are on a line perpendicular to PQ at equal intervals. M is the midpoint between the two innermost charges. (C) B=0 (R) Charges are placed on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings. (D) \mu \ne 0$ (S) Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides. (T) Charges are placed on two coplanar, identical insulating rings are equal intervals. M is the midpoint between the centres of the rings. PQ is perpendicular to the line joining the centres and coplanar to the rings.
Options:
A) \mathrm{(A)\to(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(T),(S)}
B) \mathrm{(A)\to(P),(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(S);(D)\to(R),(S)}
C) \mathrm{(A)\to(P),(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(R),(S)}
D) \mathrm{(A)\to(P),(Q),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(R),(S)}
174
EasyJEE Mains2022
The total charge on the system of capacitors $C_{1}=1 \mu \mathrm{F}, C_{2}=2 \mu \mathrm{F}, \mathrm{C}_{3}=4 \mu \mathrm{F} and \mathrm{C}_{4}=3 \mu \mathrm{F} connected in parallel is : (Assume a battery of 20 \mathrm{~V}$ is connected to the combination)
Options:
A) 200 \,\mu \mathrm{C}
B) 200 C
C) 10 \,\mu \mathrm{C}
D) 10 C
175
MediumJee Advance2008
Consider a system of three charges ${q \over 3},{q \over 3} and - {{2q} \over 3} placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60^\circ
Options:
A) The electric field at point O is ${q \over {8\pi {\varepsilon _0}{R^2}}}$ directed along the negative x-axis
B) The potential energy of the system is zero
C) The magnitude of the force between the charges at C and B is ${{{q^2}} \over {54\pi {\varepsilon _0}{R^2}}}
D) The potential at point O is ${q \over {12\pi {\varepsilon _0}R}}
176
MediumJEE Mains2022
Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii $\left( {{{{R_2}} \over {{R_1}}}} \right)$ is :
Options:
A) {n \over {n - 1}}
B) {{2n} \over {2n + 1}}
C) {{n + 1} \over n}
D) {{2n + 1} \over n}
177
MediumJee Advance2008
A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is $\frac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is:
Options:
A) {{6{\varepsilon _0}R} \over {5d + 3Vt}}
B) {{(15d + 9Vt){\varepsilon _0}R} \over {2{d^2} - 3dVt - 9{V^2}{t^2}}}
C) {{6{\varepsilon _0}R} \over {5d - 3Vt}}
D) {{(15d - 9Vt){\varepsilon _0}R} \over {2{d^2} + 3dVt - 9{V^2}{t^2}}}
178
EasyJEE Mains2022
A condenser of $2 \,\mu \mathrm{F} capacitance is charged steadily from 0 to 5 \,\mathrm{C}. Which of the following graph represents correctly the variation of potential difference (\mathrm{V}) across it's plates with respect to the charge (Q)$ on the condenser?
Options:
A)
B)
C)
D)
179
EasyJee Advance2008
STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by ${Q \over {4\pi {\varepsilon _0}R}}
Options:
A) Statement 1 is True, Statement 2 is True; Statement 2 is a CORRECT explanation for Statement 1
B) Statement 1 is True, Statement 2 is True; Statement 2 is a NOT CORRECT explanation for Statement 1
C) Statement 1 is True, Statement 2 is False
D) Statement 1 is False, Statement 2 is True
180
MediumJEE Mains2022
Co is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\varepsilon $r (as shown in Fig. 2), the new capacitance of the capacitor will be :
Options:
A) {{{C_o}} \over 2}(1 + {\varepsilon _r})
B) {C_o} + {\varepsilon _r}
C) {{{C_o}{\varepsilon _r}} \over 2}
D) {C_o}(1 + {\varepsilon _r})
181
EasyJee Advance2008
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
Options:
A) independent of a
B) directly proportional to a
C) directly proportional to a$^2
D) inversely proportional to a
182
MediumJEE Mains2022
A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half of its initial value and in time t2, the charge stored reduces to one eighth of its initial value. The ratio t1/t2 will be
Options:
A) 1/2
B) 1/3
C) 1/4
D) 1/6
183
MediumJee Advance2008
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
Options:
A) {{3Ze} \over {4\pi {R^3}}}
B) {{3Ze} \over {\pi {R^3}}}
C) {{4Ze} \over {3\pi {R^3}}}
D) {{Ze} \over {3\pi {R^3}}}
184
EasyJEE Mains2022
A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :
Options:
A) increase by 50%
B) decrease by 15%
C) increase by 25%
D) increase by 33%
185
HardJee Advance2008
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
Options:
A) a = 0
B) a = {R \over 2}
C) a = R
D) a = {{2R} \over 3}
186
MediumJEE Mains2022
A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.
Options:
A) 5 N
B) 10 N
C) 20 N
D) Zero
187
MediumJee Advance2007
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is
Options:
A) zero everywhere
B) non-zero and uniform
C) non-uniform
D) zero only at its center
188
MediumJEE Mains2022
The charge on capacitor of capacitance 15$\mu$F in the figure given below is :
Options:
A) 60$\mu$c
B) 130$\mu$c
C) 260$\mu$c
D) 585$\mu$c
189
EasyJee Advance2007
Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right) and \left(0,0, \frac{-a}{2}\right), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0,0) to (0, a, 0)$ is
Options:
A) positive
B) negative
C) zero
D) depends on the path connecting the initial and final positions
190
MediumJEE Mains2022
A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 $\mu$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :
Options:
A) 2$\mu$F
B) 32$\mu$F
C) 6$\mu$F
D) 8$\mu$F
191
MediumJee Advance2007
A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinder are initially electrically neutral.
Options:
A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
D) No potential difference appears between the two cylinders when same charge density is given to both the cylinders
192
EasyJEE Mains2022
Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C1 is now connected to uncharged capacitor C2 by closing the switch S. The amount of charge on the capacitor C2, after equilibrium, is :
Options:
A) {{{C_1}{C_2}} \over {({C_1} + {C_2})}}V
B) {{({C_1} + {C_2})} \over {{C_1}{C_2}}}V
C) ({C_1} + {C_2})V
D) ({C_1} - {C_2})V
193
MediumJee Advance2007
Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
Options:
A) negative and distributed uniformly over the surface of the sphere
B) negative and appears only at the point on the sphere closest to the point charge
C) negative and distributed non-uniformly over the entire surface of the sphere
D) zero
194
EasyJEE Mains2022
Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness ${d \over 2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?
Options:
A) 2 : 1
B) 1 : 2
C) 1 : 4
D) 4 : 1
195
MediumJee Advance2005
A conducting liquid bubble of radius $a and thickness t(t < < a)$ is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet.
Options:
A) V{\left[ {{2a \over {3t}}} \right]^{1/3}}
B) V{\left[ {{7a \over {3t}}} \right]^{1/3}}
C) V{\left[ {{a \over {3t}}} \right]^{1/3}}
D) V{\left[ {{5a \over {9t}}} \right]^{1/3}}
196
MediumJEE Mains2022
If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)
Options:
A) 10
B) 20
C) 30
D) 40
197
MediumJee Advance2025
A positive point charge of 10^{-8} C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of 10 cm further away from the center of the sphere along the radial direction. Taking \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 Nm^2/C^2 (where \epsilon_0 is the permittivity of free space), which of the following statements is/are correct:
Options:
A) Before the grounding, the electrostatic potential of the sphere is 450 V.
B) Charge flowing from the sphere to the ground because of grounding is 5 \times 10^{-9} C.
C) After the grounding is removed, the charge on the sphere is -5 \times 10^{-9} C.
D) The final electrostatic potential of the sphere is 300 V.
198
MediumJEE Mains2022
A parallel plate capacitor is formed by two plates each of area 30$\pi cm2 separated by 1 mm. A material of dielectric strength 3.6 \times 107 Vm-1 is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 \times 10-6C, the value of dielectric constant of the material is : [Use {1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9} Nm2 C-$2]
Options:
A) 1.66
B) 1.75
C) 2.25
D) 2.33
199
HardJee Advance2025
Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of \sigma_0. The separation between any two consecutive sheets is 1~\mu \text{m}. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If \sigma_0 = 9~\mu\text{C/m}^2, then which of the following statements is/are correct:(Take permittivity of free space \epsilon_0 = 9 \times 10^{-12} F/m)
Options:
A) In region 4 of the configuration I, the magnitude of the electric field is zero.
B) In region 3 of the configuration II, the magnitude of the electric field is \dfrac{\sigma_0}{\epsilon_0}.
C) Potential difference between the first and the last sheets of the configuration I is 5 V.
D) Potential difference between the first and the last sheets of the configuration II is zero.
200
MediumJEE Mains2021
A capacitor is connected to a 20 V battery through a resistance of 10$\Omega. It is found that the potential difference across the capacitor rises to 2 V in 1 \mus. The capacitance of the capacitor is __________ \muF. Given : \ln \left( {{{10} \over 9}} \right) = 0.105
Options:
A) 9.52
B) 0.95
C) 0.105
D) 1.85
201
HardJee Advance2024
A small electric dipole \vec{p}_0, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density \sigma is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle \theta as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? [ \varepsilon_0 is the permittivity of free space.]
Options:
A) The dipole will undergo small oscillations at any finite value of r.
B) The dipole will undergo small oscillations at any finite value of r>R.
C) The dipole will undergo small oscillations with an angular frequency of \sqrt{\frac{2 \sigma p_0}{\epsilon_0 I}} at r=2 R.
D) The dipole will undergo small oscillations with an angular frequency of \sqrt{\frac{\sigma p_0}{100 \epsilon_0 I}} at r=10 R.
202
MediumJEE Mains2021
Three capacitors C1 = 2$\muF, C2 = 6\muF and C3 = 12\mu$F are connected as shown in figure. Find the ratio of the charges on capacitors C1, C2 and C3 respectively :
Options:
A) 2 : 1 : 1
B) 2 : 3 : 3
C) 1 : 2 : 2
D) 3 : 4 : 4
203
HardJee Advance2022
In the figure, the inner (shaded) region A represents a sphere of radius r_{A}=1, within which the electrostatic charge density varies with the radial distance r from the center as \rho_{A}=k r, where k is positive. In the spherical shell B of outer radius r_{B}, the electrostatic charge density varies as \rho_{B}= \frac{2 k}{r}. Assume that dimensions are taken care of. All physical quantities are in their SI units. Which of the following statement(s) is(are) correct?
Options:
A) If r_{B}=\sqrt{\frac{3}{2}}, then the electric field is zero everywhere outside B.
B) If r_{B}=\frac{3}{2}, then the electric potential just outside B is \frac{k}{\epsilon_{0}}.
C) If r_{B}=2, then the total charge of the configuration is 15 \pi k.
D) If r_{B}=\frac{5}{2}, then the magnitude of the electric field just outside B is \frac{13 \pi k}{\epsilon_{0}}.
204
EasyJEE Mains2021
Calculate the amount of charge on capacitor of 4$\muF. The internal resistance of battery is 1\Omega$ :
Options:
A) 8 $\mu$C
B) zero
C) 16 $\mu$C
D) 4 $\mu$C
205
HardJee Advance2022
A disk of radius \mathrm{R} with uniform positive charge density \sigma is placed on the x y plane with its center at the origin. The Coulomb potential along the z-axis is $ V(z)=\frac{\sigma}{2 \epsilon_{0}}\left(\sqrt{R^{2}+z^{2}}-z\right) . A particle of positive charge q is placed initially at rest at a point on the z axis with z=z_{0} and z_{0}>0. In addition to the Coulomb force, the particle experiences a vertical force \vec{F}=-c \hat{k} with c>0. Let \beta=\frac{2 c \epsilon_{0}}{q \sigma}$. Which of the following statement(s) is(are) correct?
Options:
A) For \beta=\frac{1}{4} and z_{0}=\frac{25}{7} R, the particle reaches the origin.
B) For \beta=\frac{1}{4} and z_{0}=\frac{3}{7} R, the particle reaches the origin.
C) For \beta=\frac{1}{4} and z_{0}=\frac{R}{\sqrt{3}}, the particle returns back to z=z_{0}.
D) For \beta>1 and z_{0}>0, the particle always reaches the origin.
206
MediumJEE Mains2021
A parallel plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:
Options:
A) {{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1}{K_2}} \over {{K_1} + {K_2}}}} \right)
B) {{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1}{K_2}} \over {2({K_1} + {K_2})}}} \right)
C) {{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{{K_1} + {K_2}} \over {{K_1}{K_2}}}} \right)
D) {{{\varepsilon _0}A} \over d}\left( {{1 \over 2} + {{2({K_1} + {K_2})} \over {{K_1}{K_2}}}} \right)
207
HardJee Advance2022
Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge q, and the remaining one has charge x. The perpendicular from each charge to the nearest hexagon side passes through the center 0 of the hexagon and is bisected by the side. Which of the following statement(s) is(are) correct in SI units?
Options:
A) When x=q, the magnitude of the electric field at 0 is zero.
B) When x=-q, the magnitude of the electric field at 0 is \frac{q}{6 \pi \epsilon_{o} a^{2}}.
C) When x=2 q, the potential at 0 is \frac{7 q}{4 \sqrt{3} \pi \epsilon_{o} a}.
D) When x=-3 q, the potential at 0 is -\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}.
208
MediumJEE Mains2021
The material filled between the plates of a parallel plate capacitor has resistivity 200 $\Omega$m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permittivity of material is 50)
Options:
A) 9.0 $\mu$A
B) 9.0 mA
C) 0.9 mA
D) 0.9 $\mu$A
209
MediumJee Advance2020
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha. The spheres are now immersed in a dielectric liquid of density 800 kg m-$3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then
Options:
A) electric force between the spheres remains unchanged
B) electric force between the spheres reduces
C) mass density of the spheres is 840 kg m$-$3
D) the tension in the strings holding the spheres remains unchanged
210
EasyJEE Mains2021
Match List I with List II. List - I List - II (a) Capacitance, C (i) ${M^1}{L^1}{T^{ - 3}}{A^{ - 1}} (b) Permittivity of free space, {\varepsilon _0} (ii) {M^{ - 1}}{L^{ - 3}}{T^4}{A^2} (c) Permeability of free space, {\mu _0} (iii) {M^{ - 1}}{L^{ - 2}}{T^4}{A^2} (d) Electric field, E (iv) {M^1}{L^1}{T^{ - 2}}{A^{ - 2}}$ Choose the correct answer from the options given below
Options:
A) (a) $\to (iii), (b) \to (ii), (c) \to (iv), (d) \to$ (i)
B) (a) $\to (iii), (b) \to (iv), (c) \to (ii), (d) \to$ (i)
C) (a) $\to (iv), (b) \to (ii), (c) \to (iii), (d) \to$ (i)
D) (a) $\to (iv), (b) \to (iii), (c) \to (ii), (d) \to$ (i)
211
HardJee Advance2020
A uniform electric field, $\overrightarrow E = - 400\sqrt 3 \widehat y NC−1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2\sqrt {10} \times 106 ms−1 . This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure. Take {q \over m}$ = 1010 Ckg−1 . Then
Options:
A) the particle will hit T if projected at an angle 45o
from the horizontal
B) the particle will hit T if projected either at an angle 30o or 60o
from the horizontal
C) time taken by the particle to hit T could be $\sqrt {{5 \over 6}} \mu s as well as \sqrt {{5 \over 2}} \mu $s
D) time taken by the particle to hit T is $\sqrt {{5 \over 3}} \mu $s
212
MediumJEE Mains2021
A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be
Options:
A) {\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]
B) {\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]
C) {\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]
D) {\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]
213
HardJee Advance2019
An electric dipole with dipole moment ${{{p_0}} \over {\sqrt 2 }}(\widehat i + \widehat j) is held fixed at the origin O in the presence of a uniform electric field of magnitude E0.If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are, ( \in $0 is the permittivity of the free space, R >> dipole size)
Options:
A) The magnitude of total electric field on any two points of the circle will be same.
B) Total electric field at point B is ${\overrightarrow E _B}$ = 0
C) R = {\left( {{{{p_0}} \over {4\pi { \in _0}{E_0}}}} \right)^{1/3}}
D) Total electric field at point A is${\overrightarrow E _A} = \sqrt 2 {E_0}(\widehat i + \widehat j)
214
EasyJEE Mains2021
A capacitor of capacitance C = 1 $\muF is suddenly connected to a battery of 100 volt through a resistance R = 100 \Omega$. The time taken for the capacitor to be charged to get 50 V is :[Take ln 2 = 0.69]
Options:
A) 1.44 $\times 10-$4 s
B) 3.33 $\times 10-$4 s
C) 0.69 $\times 10-$4 s
D) 0.30 $\times 10-$4 s
215
MediumJee Advance2019
A charged shell of radius R carries a total charge Q. Given $\phi as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct?[ \in $0 is the permittivity of free space]
Options:
A) If h > 2R and r = 4R / 5 then $\phi = Q / 5 \in $0
B) If h > 2R and r = 3R / 5 then $\phi = Q / 5 \in $0
C) If h > 8R /5 and r = 3R / 5 then $\phi $ = 0
D) If h > 2R and r = R then $\phi = Q / \in $0
216
MediumJEE Mains2021
In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :(Given area of plate = A)
Options:
A) {{15} \over {34}}{{K{\varepsilon _0}A} \over d}
B) {{15} \over 6}{{K{\varepsilon _0}A} \over d}
C) {{25} \over 6}{{K{\varepsilon _0}A} \over d}
D) {9 \over 6}{{K{\varepsilon _0}A} \over d}
217
MediumJee Advance2018
An infinitely long thin non-conducting wire is parallel to the $z-axis and carries a uniform line charge density \lambda . It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ subtends an angle {120^ \circ } at the center O of the spherical shell, as shown in the figure. The permittivity of free space is { \in _0}.$ Which of the following statement is (are) true?
Options:
A) The electric flux through the shell is $\sqrt 3 R\lambda /{ \in _0}
B) The $z$-component of the electric field is zero at all the points on the surface of the shell
C) The electric flux through the shell is $\sqrt 2 R\lambda /{ \in _0}
D) The electric field is normal to the surface of the shell at all points
218
MediumJEE Mains2021
Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :
Options:
A) {V \over {K + 2}}
B) {V \over K}
C) {{3V} \over {K + 2}}
D) {{3V} \over K}
219
MediumJee Advance2017
A point charge $+Q is placed just outside an imaginary hemispherical surface of radius R$ as shown in the figure. Which of the following statements is/are correct?
Options:
A) The electric flux passing through the curved surface of the hemisphere is
$ - {Q \over {2{\varepsilon _0}}} \left( {1 - {1 \over {\sqrt 2 }}} \right)
B) Total flux through the curved and the flat surfaces is ${Q \over {{\varepsilon _0}}}
C) The component of the electric field normal to the flat surface is constant over the surface
D) The circumference of the flat surface is an equipotential
220
MediumJEE Mains2021
If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb an be expressed as :
Options:
A) {q_b} = {q_f}\left( {1 - {1 \over {\sqrt k }}} \right)
B) {q_b} = {q_f}\left( {1 - {1 \over k}} \right)
C) {q_b} = {q_f}\left( {1 + {1 \over {\sqrt k }}} \right)
D) {q_b} = {q_f}\left( {1 + {1 \over k}} \right)
221
MediumJee Advance2015
Consider a uniform spherical charge distribution of radius ${R_1} centred at the origin O. In this distribution, a spherical cavity of radius {R_2}, centred at P with distance OP=a = {R_1} - {R_2} (see figure) is made. If the electric field inside the cavity at position \overrightarrow r is \overrightarrow E \overrightarrow {\left( r \right)} ,$ then the correct statement(s) is (are)
Options:
A) \overrightarrow E is uniform, its magnitude is independent of {R_2} but its direction depends on \overrightarrow r .
B) \overrightarrow E is uniform, its magnitude depends on {R_2} and its direction depends on \overrightarrow r .
C) \overrightarrow E is uniform, its magnitude is independent of a but its direction depends on \overrightarrow a
D) \overrightarrow E is uniform and both its magnitude and direction depend on \overrightarrow a
222
MediumJEE Mains2021
A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :$\varepsilon (x) = {\varepsilon _0} + kx, for \left( {0 < x \le {d \over 2}} \right)\varepsilon (x) = {\varepsilon _0} + k(d - x), for \left( {{d \over 2} \le x \le d} \right)
Options:
A) {\left( {{\varepsilon _0} + {{kd} \over 2}} \right)^{2/kA}}
B) {{kA} \over {2\ln \left( {{{2{\varepsilon _0} + kd} \over {2{\varepsilon _0}}}} \right)}}
C) 0
D) {{kA} \over 2}\ln \left( {{{2{\varepsilon _0}} \over {2{\varepsilon _0} - kd}}} \right)
223
MediumJee Advance2015
The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are)
Options:
A) Both charges execute simple harmonic motion
B) Both charges will continue moving in the direction of their displacement
C) Charge $+q executes simple harmonic motion while charge -q$ continues moving in the direction of its displacement
D) Charge $-q executes simple harmonic motion while charge +q$ continues moving in the direction of its displacement
224
MediumJEE Mains2021
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is ${3 \over 4}$d, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C0) is given by the following relation :
Options:
A) C' = {{3 + K} \over {4K}}{C_0}
B) C' = {{4 + K} \over {3}}{C_0}
C) C' = {{4K} \over {K + 3}}{C_0}
D) C' = {{4} \over {3 + K}}{C_0}
225
MediumJee Advance2014
Let ${E_1}\left( r \right),{E_2}\left( r \right) and {E_3}\left( r \right) be the respective electric field at a distance r from a point charge Q, an infinitely long wire with constant linear charge density \lambda , and an infinite plane with uniform surface charge density \sigma . If E{}_1\left( {{r_0}} \right) = {E_2}\left( {{r_0}} \right) = {E_3}\left( {{r_0}} \right) at a given distance {r_0}.$ then
Options:
A) Q = 4\sigma \pi r_0^2
B) {r_0} = {\lambda \over {2\pi \sigma }}
C) {E_1}\left( {{r_0}/2} \right) = 2{E_2}\left( {{r_0}/2} \right)
D) {E_2}\left( {{r_0}/2} \right) = 4{E_3}\left( {{r_0}/2} \right)
226
MediumJEE Mains2021
Consider the combination of 2 capacitors C1 and C2 with C2 > C1, when connected in parallel, the equivalent capacitance is ${{15} \over 4} times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, {{{C_2}} \over {{C_1}}}$.
Options:
A) {{15} \over {11}}
B) No Solutions
C) {{29} \over {15}}
D) {{15} \over {4}}
227
MediumJee Advance2013
Two non-conducting spheres of radii ${R_1} and {R_2} and carrying uniform volume charge densities + \rho and - \rho ,$ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region
Options:
A) The electrostatic field is zero
B) The electrostatic potential is constant
C) The electrostatic field is constant in magnitude
D) The electrostatic field has same direction
228
EasyJEE Mains2021
An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle '$\alpha' with the plates. It leaves the plates at angle '\beta$' with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be :
Options:
A) {{{{\cos }^2}\beta } \over {{{\cos }^2}\alpha }}
B) {{\cos \beta } \over {\cos \alpha }}
C) {{{{\sin }^2}\beta } \over {{{\cos }^2}\alpha }}
D) {{\cos \beta } \over {\sin \alpha }}
229
MediumJee Advance2012
Six point charges are kept at the vertices of a regular hexagon of side $L and center O, as shown in the figure. Given that K = {1 \over {4\pi {\varepsilon _0}}}{q \over {{L^2}}},$ which of the following statement(s) is (are) correct ?
Options:
A) The electric field at $O is 6K along OD
B) The potential at $O$ is zero
C) The potential at all points on the line $PR$ is same
D) The potential at all points on the line $ST$ is same
230
EasyJEE Mains2021
Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :
Options:
A) 4 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 4
231
MediumJee Advance2012
A cubical region of side $a has its center at the origin. It encloses three fixed point charges, -q at \left( {0, - a/4,0} \right), + 3q at \left( {0,0,0} \right) and -q at \left( {0, + a/4,0} \right).$ Choose the correct option(s)
Options:
A) The net electric flux crossing the plane $x=+a/2 is equal to the net electric flux crossing the plane x=-a/2
B) The net electric flux crossing the plane $y=+a/2 is more than the net electric flux crossing the plane y=-a/2.
C) The net electric flux crossing the entire region is ${q \over {{\varepsilon _0}}}
D) The net electric flux crossing the plane $z = + a/2 is equal to the net electric flux crossing the plane x=+a/2.
232
MediumJEE Mains2020
For the given input voltage waveform Vin(t), the output voltage waveform V0(t), across the capacitor is correctly depicted by :
Options:
A)
B)
C)
D)
233
MediumJee Advance2011
A spherical metal shell A of radius ${R_A} and a solid metal sphere B of radius {R_B}\left( { < {R_A}} \right) are kept far apart and each is given charge ' + Q'.$ Now they are connected by a thin metal wire. Then
Options:
A) E_A^{inside} = 0
B) {Q_A} > {Q_B}
C) {{{\sigma _A}} \over {{\sigma _B}}} = {{{R_B}} \over {{R_A}}}
D) E_A^{on\,\,surface} < \,E_B^{on\,\,surface}
234
MediumJEE Mains2020
In the circuit shown, charge on the 5 $\mu $F capacitor is :
Options:
A) 5.45 $\mu $C
B) 18.00 $\mu $C
C) 10.90 $\mu $C
D) 16.36 $\mu $C
235
MediumJee Advance2011
Which of the following statement(s) is/are correct?
Options:
A) If the electric field due to a point charge varies as ${r^{ - 2.5}} instead of {r^{ - 2}},$ then the Gauss law will still be valid.
B) The Gauss law can be used to calculate the field distribution around an electric dipole.
C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
D) The work done by the external force in moving a unit positive charge from point $A at potential {V_A} to point B at potential {V_B} is \left( {{V_B} - {V_A}} \right).
236
MediumJEE Mains2020
A parallel plate capacitor has plate of length 'l', width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?
Options:
A) {l \over 4}
B) {l \over 2}
C) {{2l} \over 3}
D) {l \over 3}
237
MediumJee Advance2010
A few electric field lines for a system of two charges ${Q_1} and {Q_2} fixed at two different points on the x$-axis are shown in the figure. These lines suggest that
Options:
A) \left| {{Q_1}} \right| > \left| {{Q_2}} \right|
B) \left| {{Q_1}} \right| < \left| {{Q_2}} \right|
C) at a finite distance to the left of ${{Q_1}}$ the electric field is zero
D) at a finite distance to the right of ${{Q_2}}$ the electric field is zero
238
MediumJEE Mains2020
Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :
Options:
A) Zero
B) {3 \over 2}C{V^2}
C) {9 \over 2}C{V^2}
D) {{25} \over 6}C{V^2}
239
MediumJee Advance2006
The electrostatic potential \left(\phi_r\right) of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as $ \begin{array}{ll} \phi_r=\frac{q}{4 \pi \epsilon_0 r} & \left(r \geq \mathrm{R}_0\right) \\ \phi_r=\frac{q}{4 \pi \epsilon_0 \mathrm{R}_0} & \left(r \leq \mathrm{R}_0\right) \end{array} $ Which of the following option(s) is/are correct?
Options:
A) For spherical region r \leq \mathrm{R}_0, the total electrostatic energy stored is zero.
B) Within r=2 \mathrm{R}_0, the total charge is q.
C) There will be no charge anywhere except at r=\mathrm{R}_0.
D) Electric field is discontinuous at r=\mathrm{R}_0.
240
MediumJEE Mains2020
A capacitor C is fully charged with voltage V0. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance ${C \over 2}$. The energy loss in the process after the charge is distributed between the two capacitors is :
Options:
A) {1 \over 2}CV_0^2
B) {1 \over 4}CV_0^2
C) {1 \over 3}CV_0^2
D) {1 \over 6}CV_0^2
241
HardJee Advance2024
A charge is kept at the central point \mathrm{P} of a cylindrical region. The two edges subtend a half-angle \theta at \mathrm{P}, as shown in the figure. When \theta=30^{\circ}, then the electric flux through the curved surface of the cylinder is \Phi. If \theta=60^{\circ}, then the electric flux through the curved surface becomes \Phi / \sqrt{n}, where the value of n is ___.
Options:
242
MediumJEE Mains2020
In the circuit shown in the figure, the total charge is 750 $\mu $C and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is :
Options:
A) 160 $\mu $C
B) 450 $\mu $C
C) 590 $\mu $C
D) 650 $\mu $C
243
MediumJee Advance2024
An infinitely long thin wire, having a uniform charge density per unit length of 5 \mathrm{nC} / \mathrm{m}, is passing through a spherical shell of radius 1 \mathrm{~m}, as shown in the figure. A 10 \mathrm{nC} charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points \mathrm{P} and \mathrm{R}, in Volt, is ________. [Given: In SI units \frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7. Ignore the area pierced by the wire.]
Options:
244
MediumJEE Mains2020
A 10 $\mu $F capacitor is fully charged to a potential difference of 50 V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is :
Options:
A) 20 $\mu $F
B) 15 $\mu $F
C) 10 $\mu $F
D) 30 $\mu $F
245
MediumJee Advance2022
A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base radius R, and a hemisphere of radius R as shown in the figure. The electric flux through the conical surface is \frac{n q}{6 \epsilon_{0}} (in SI units). The value of n is _______.
Options:
246
MediumJEE Mains2020
A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha $ between them, as shown in figure. The capacitance will be close to :
Options:
A) {{{\varepsilon _0}{a^2}} \over d}\left( {1 + {{\alpha a} \over {d}}} \right)
B) {{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{\alpha a} \over {4d}}} \right)
C) {{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{\alpha a} \over {2d}}} \right)
D) {{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{3\alpha a} \over {2d}}} \right)
247
MediumJee Advance2021
Two point charges $-Q and +Q/\sqrt 3 $ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.The value of R is __________ meter.
Options:
248
MediumJEE Mains2020
Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be :
Options:
A) 4.2 μF
B) 8.4 μF
C) 1.6 μF
D) 3.2 μF
249
MediumJee Advance2021
Two point charges $-Q and +Q/\sqrt 3 $ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.The value of b is __________ meter.
Options:
250
MediumJEE Mains2020
A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + $\alpha $x) where 'x' is the distance measured from one of the plates. If (ad) << 1, the total capacitance of the system is best given by the expression :
Options:
A) {{A{ \in _0}K} \over d}\left( {1 + {{\left( {{{\alpha d} \over 2}} \right)}^2}} \right)
B) {{A{ \in _0}K} \over d}\left( {1 + {{\alpha d} \over 2}} \right)
C) {{A{ \in _0}K} \over d}\left( {1 + {{{\alpha ^2}{d^2}} \over 2}} \right)
D) {{A{ \in _0}K} \over d}\left( {1 + \alpha d} \right)
251
MediumJee Advance2020
Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m−3 are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8 $ \times 10−7 m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________. (neglect the buoyancy force, take acceleration due to gravity = 10 ms−2 and charge on an electron (e) = 1.6 \times $ 10–19 C)
Options:
252
MediumJEE Mains2019
In the given circuit, the charge on 4 $\mu $F capacitor will be :
Options:
A) 5.4 $\mu $C
B) 9.6 $\mu $C
C) 13.4 $\mu $C
D) 24 $\mu $C
253
MediumJee Advance2020
A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole moment $\overrightarrow p is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is N \times (mgh), where g is the acceleration due to gravity, then the value of N is _________ . (Note that for three coplanar forces keeping a point mass in equilibrium, {F \over {\sin \theta }} is the same for all forces, where F is any one of the forces and \theta $ is the angle between the other two forces)
Options:
254
MediumJEE Mains2019
Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3. The first capacitor is filled as shown in fig.I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E1 refers to capacitor (I) and E2 to capacitor (II)):
Options:
A) {{{E_1}} \over {{E_2}}} = {{\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)} \over {{K_1}{K_2}{K_3}}}
B) {{{E_1}} \over {{E_2}}} = {{{K_1}{K_2}{K_3}} \over {\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)}}
C) {{{E_1}} \over {{E_2}}} = {{\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)} \over {9{K_1}{K_2}{K_3}}}
D) {{{E_1}} \over {{E_2}}} = {{9{K_1}{K_2}{K_3}} \over {\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)}}
255
HardJee Advance2020
One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\overrightarrow p pointing towards the charge q is fixed at the origin, the spring gets stretched to a length l and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by \Delta l << l from its equilibrium position and released, it is found to oscillate at frequency {1 \over \delta }\sqrt {{k \over m}} . The value of \delta $ is ______.
Options:
256
MediumJEE Mains2019
A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :
Options:
A) 2\pi \sqrt {{L \over {\sqrt {{g^2} - {{{q^2}{E^2}} \over {{m^2}}}} }}}
B) 2\pi \sqrt {{L \over {\left( {g + {{qE} \over m}} \right)}}}
C) 2\pi \sqrt {{L \over {\sqrt {{g^2} + {{{q^2}{E^2}} \over {{m^2}}}} }}}
D) 2\pi \sqrt {{L \over {\left( {g - {{qE} \over m}} \right)}}}
257
HardJee Advance2020
A circular disc of radius R carries surface charge density $\sigma \left( r \right) = {\sigma _0}\left( {1 - {r \over R}} \right), where \sigma 0 is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is \phi 0. Electric flux through another spherical surface of radius {R \over 4} and concentric with the disc is \phi . Then the ratio {{{\phi _0}} \over \phi }$ is ________.
Options:
258
MediumJEE Mains2019
Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are :
Options:
A) 40 $\mu F and 10 \mu $F
B) 60 $\mu F and 40 \mu $F
C) 20 $\mu F and 30 \mu $F
D) 50 $\mu F and 30 \mu $F
259
HardJee Advance2018
A particle, of mass ${10^{ - 3}} kg and charge 1.0 C, is initially at rest. At time t=0, the particle comes under the influence of an electric field \overrightarrow E \left( t \right) = {E_0}\sin \,\, \omega t\widehat i, where {E_0} = 1.0\,N{C^{ - 1}} and \omega = 10{}^3\,rad\,{s^{ - 1}}. Consider the effect of only the electrical force on the particle. Then the maximum speed, in m{s^{ - 1}},$ attained by the particle at subsequent times is _______________.
Options:
260
MediumJEE Mains2019
The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-
Options:
A) V
B) {V \over {K + n}}
C) {{(n+1)V} \over {K + n}}
D) {{nV} \over {K + n}}
261
HardJee Advance2015
An infinitely long uniform line charge distribution of charge per unit length $\lambda lies parallel to the y-axis in the y-z plane at z = {{\sqrt 3 } \over 2}a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is {{\lambda L} \over {n{\varepsilon _0}}} ({{\varepsilon _0}}$ = permittivity of free space), then the value of n is
Options:
262
MediumJEE Mains2019
A capacitor with capacitance 5μF is charged to 5μC. If the plates are pulled apart to reduce the capacitance to 2μF, how much work is done ?
Options:
A) 2.16 × 10–6 J
B) 2.55 × 10–6 J
C) 3.75 × 10–6 J
D) 6.25 × 10–6 J
263
MediumJee Advance2012
An infinitely long solid cylinder of radius R has a uniform volume charge density $\rho. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression {{23\rho R} \over {16k{\varepsilon _0}}}$. The value of k is _____________.
Options:
264
MediumJEE Mains2019
Determine the charge on the capacitor in the following circuit :
Options:
A) 200μC
B) 2μC
C) 10μC
D) 60μC
265
MediumJee Advance2011
Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The surface tension of the soap film is $\gamma. The system of charges and planar film are in equilibrium, and a = k{\left[ {{{{q^2}} \over \gamma }} \right]^{1/N}}$, where k is a constant. Then N is __________.
Options:
266
MediumJEE Mains2019
A parallel plate capacitor has 1μF capacitance. One of its two plates is given +2μC charge and the other plate, +4μC charge. The potential difference developed across the capacitor is:-
Options:
A) 1V
B) 5V
C) 2V
D) 3V
267
MediumJee Advance2009
A solid sphere of radius R has a charge Q distributed in its volume with a charge density $\rho = K{r^a}, where K and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times than at r = R, find the value of a$.
Options:
268
MediumJEE Mains2019
Voltage rating of a parallel plate capacitor is 500V. Its dielectric can withstand a maximum electric field of 106 V/m. The plate area is 10–4 m2. What is the dielectric constant is the capacitance is 15 pF? (given $\varepsilon $0 = 8.86 × 10–12 C2/Nm2)
Options:
A) 8.5
B) 4.5
C) 3.8
D) 6.2
269
MediumJEE Mains2026
Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse-square force. D. The work done in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :
Options:
A) A, C, E Only
B) A, B, D, E Only
C) B, C, D, E Only
D) A, B, C, D Only
270
MediumJEE Mains2019
In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $\mu F. All values in the circuit are in \mu $F.
Options:
A) {6 \over 5}\mu F
B) {7 \over 11}\mu F
C) 4$\mu $F
D) {7 \over 10}\mu F
271
EasyJEE Mains2026
Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm . The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is \_\_\_\_ \mu \mathrm{J}. $ \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}^2
Options:
A) 3.3
B) 27
C) 2.7
D) 5.4
272
MediumJEE Mains2019
The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure : When is the value of current at t = 4 s ?
Options:
A) zero
B) 1.5 $\mu $A
C) 2 $\mu $A
D) 3 $\mu $A
273
MediumJEE Mains2026
The electrostatic potential in a charged spherical region of radius r varies as V=a r^3+b, where a and b are constants. The total charge in the sphere of unit radius is \alpha \times \pi a \in_0. The value of \alpha is \_\_\_\_ . (permittivity of vacuum is \epsilon_0 )
Options:
A) -12
B) -8
C) -9
D) -6
274
MediumJEE Mains2019
A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is : (Take $\varepsilon 0 = 8.85 \times 10-12 {{{C^2}} \over {N - {m^2}}}$)
Options:
A) 9.85 $ \times $ 10–10 C
B) 8.85 $ \times $ 10–10 C
C) 6.85 $ \times $ 10–10 C
D) 7.85 × 10–10 C
275
MediumJEE Mains2026
There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively ( c>b>a ) and they are charged with charge q_1, q_2 and q_3 respectively. The potentials of the spheres A, B and C respectively, are :
Options:
A) \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{c}\right)
B) \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{c}\right)
C) \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right)
D) \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_1+q_2+q_3}{c}\right)
276
MediumJEE Mains2019
In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is :
Options:
A) {1 \over 8}{{{Q^2}} \over C}
B) {5 \over 8}{{{Q^2}} \over C}
C) {3 \over 4}{{{Q^2}} \over C}
D) {3 \over 8}{{{Q^2}} \over C}
277
MediumJEE Mains2026
Three charges +2 q,+3 q and -4 q are situated at (0,-3 a),(2 a, 0) and (-2 a, 0) respectively in the x y plane. The resultant dipole moment about origin is \_\_\_\_ .
Options:
A) 2 q a(7 \hat{i}-3 \hat{j})
B) 2 q a(3 \hat{j}-7 \hat{i})
C) 2 q a(3 \hat{i}-7 \hat{j})
D) 2 q a(3 \hat{j}-\hat{i})
278
MediumJEE Mains2019
Seven capacitors, each of capacitance 2 $\mu F, are to be connected in a configuration to obtain an effective capacitance of \left( {{6 \over {13}}} \right)\mu F.$ Which of the combinations, shown in figures below, will achieve the desired value
Options:
A)
B)
C)
D)
279
MediumJEE Mains2026
Two shorts dipoles (A, B), A having charges \pm 2 \mu \mathrm{C} and length 1 cm and B having charges \pm 4 \mu \mathrm{C} and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is \_\_\_\_ N/C.
Options:
A) \frac{9}{16} \sqrt{2} \times 10^5
B) \frac{9}{16} \sqrt{2} \times 10^4
C) 9 \sqrt{2} \times 10^4
D) 4.5 \sqrt{2} \times 10^4
280
MediumJEE Mains2019
In the figure shown below, the charge on the left plate of the 10$\mu F capacitor is –30\mu C. The charge on the right plate of the 6 \mu $F capacitor is :
Options:
A) + 12 $\mu $C
B) + 18 $\mu $C
C) - 18 \mu $C
D) - 12 \mu $C
281
HardJEE Mains2026
Two charges 7 \mu \mathrm{C} and -2 \mu \mathrm{C} are placed at (-9,0,0) \mathrm{cm} and (9,0,0) \mathrm{cm} respectively in an external field E=\frac{\mathrm{A}}{r^2} \hat{r}, where A=9 \times 10^5 \mathrm{~N} / \mathrm{C} . \mathrm{m}^2. Considering the potential at infinity is 0 , the electrostatic energy of the configuration is \_\_\_\_ J.
Options:
A) 49.3
B) 1.4
C) 24.3
D) -90.7
282
MediumJEE Mains2019
A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is :
Options:
A) 508 pJ
B) 692 pJ
C) 560 pJ
D) 600 pJ
283
MediumJEE Mains2026
Two point charges 2 q and q are placed at vertex A and centre of face C D E F of the cube as shown in figure. The electric flux passing through the cube is:
Options:
A) \frac{3 q}{2 \epsilon_0}
B) \frac{3 q}{4 \epsilon_0}
C) \frac{q}{\epsilon_0}
D) \frac{3 q}{\epsilon_0}
284
MediumJEE Mains2019
A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be -
Options:
A) 12
B) 36
C) 14
D) 4
285
MediumJEE Mains2026
Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field (\vec{E}) at the center O of the pentagon due to these five positive charges are :
Options:
A) V=\frac{5 q}{4 \pi \varepsilon_o r} and \vec{E}=\frac{5 \sqrt{3} q}{8 \pi \varepsilon_o r^2} \hat{r}
B) V=\frac{5 q}{4 \pi \varepsilon_o r} and \vec{E}=0
C) V=0 and \vec{E}=0
D) V=\frac{5 q}{4 \pi \varepsilon_0 r} and \vec{E}=\frac{5 q}{4 \pi \varepsilon_{\mathrm{o}} r^2} \hat{r}
286
MediumJEE Mains2019
A parallel plate capacitor with square plates is filled with four dielecytrics of dielectrics constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be :
Options:
A) K = {{{K_1}{K_2}} \over {{K_1} + {K_2}}} + {{{K_3}{K_4}} \over {{K_3} + {K_4}}}
B) K = {{\left( {{K_1} + {K_2}} \right)\left( {{K_3} + {K_4}} \right)} \over {2\left( {{K_1} + {K_2} + {K_3} + {K_4}} \right)}}
C) K = {{\left( {{K_1} + {K_2}} \right)\left( {{K_3} + {K_4}} \right)} \over {{K_1} + {K_2} + {K_3} + {K_4}}}
D) K = {{\left( {{K_1} + {K_4}} \right)\left( {{K_2} + {K_3}} \right)} \over {2\left( {{K_1} + {K_2} + {K_3} + {K_4}} \right)}}
287
MediumJEE Mains2026
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
Options:
A) 1: 3^{2 / 3}
B) 3^{2 / 3}: 1
C) 1: 3^{1 / 3}
D) 1: 2^{2 / 3}
288
MediumJEE Mains2019
A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d < < a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :
Options:
A) {{K{ \in _0}{a^2}} \over {2d(K + 1)}}
B) {{K{ \in _0}{a^2}} \over {d(K - 1)}}\ln K
C) {{K{ \in _0}{a^2}} \over d}\ln K
D) {1 \over 2}{{K{ \in _0}{a^2}} \over d}
289
MediumJEE Mains2026
Electric field in a region is given by \vec{E}=A x \hat{i}+B y \hat{j}, where A=10 \mathrm{~V} / \mathrm{m}^2 and B=5 \mathrm{~V} / \mathrm{m}^2. If the electric potential at a point (10,20) is 500 V , then the electric potential at origin is \_\_\_\_ V.
Options:
A) 1000
B) 0
C) 2000
D) 500
290
MediumJEE Mains2018
In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by $\left( {{C_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)
Options:
A) {C_1}E\left[ {1 - \exp \left( { - tR/{C_1}} \right)} \right]
B) {C_2}E\left[ {1 - \exp \left( { - t/R{C_2}} \right)} \right]
C) {C_{eq}}E\left[ {1 - \exp \left( { - t/R{C_{eq}}} \right)} \right]
D) {C_{eq}}E\,\,\exp \left( { - t/R{C_{eq}}} \right)
291
MediumJEE Mains2026
A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \vec{E} is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is \_\_\_\_ .
Options:
A) m g-q E
B) \sqrt{m^2 g^2+q^2 E^2}
C) m \mathrm{~g}+q E
D) \sqrt{m^2 g^2-q^2 E^2}
292
MediumJEE Mains2018
A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :
Options:
A) 0.9 n C
B) 1.2 n C
C) 0.3 n C
D) 2.4 n C
293
MediumJEE Mains2026
Six point charges are kept 60^{\circ} apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is \_\_\_\_ . ( \epsilon_0 is permittivity of free space)
Options:
A) -\left(\frac{5 Q}{8 \pi \epsilon_0 R^2}\right)(\hat{i}-3 \hat{j})
B) \frac{Q}{4 \pi \in_{\mathrm{o}} R^2}(\sqrt{3} \hat{i}-\hat{j})
C) -\frac{\mathrm{Q}}{4 \pi \in_{\mathrm{o}} R^2}(\sqrt{3} \hat{i}-\hat{j})
D) -\frac{5 Q}{8 \pi \epsilon_{\mathrm{o}} R^2}(\hat{i}+\sqrt{3} \hat{j})
294
MediumJEE Mains2018
A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $25 \times {10^{ - 6}}N, the value of V is approximately : \left( {{ \in _o} = 8.85 \times {{10}^{ - 12}}{{{C^2}} \over {N.{m^2}}}} \right)
Options:
A) 250 V
B) 100 V
C) 300 V
D) 150 V
295
MediumJEE Mains2026
Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is:(Take k = \frac{1}{4 \pi \epsilon_0} and assume kQ^2 > Gm^2 where G is the Gravitational constant)
Options:
A) \sqrt{\frac{kQ^2}{4mR} \left(1 + \frac{Gm^2}{kQ^2} \right)}
B) \sqrt{\frac{kQ^2}{2mR} \left(1 - \frac{Gm^2}{2kQ^2} \right)}
C) \sqrt{\frac{kQ^2}{2mR} \left(1 - \frac{Gm^2}{kQ^2} \right)}
D) \sqrt{\frac{kQ^2}{4mR} \left(1 - \frac{Gm^2}{kQ^2} \right)}
296
MediumJEE Mains2018
A capacitor C1 = 1.0 $\mu F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors {C_2} = 3.0\mu F and C3 = 6.0 \mu $F through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is :
Options:
A) 40 $\mu $C
B) 36 $\mu $C
C) 20 $\mu $C
D) 54 $\mu $C
297
EasyJEE Mains2026
A point charge of 10^{-8} \mathrm{C} is placed at origin. The work done in moving a point charge 2 \mu \mathrm{C} from point A(4,4,2) \mathrm{m} to B(2,2,1) \mathrm{m} is \_\_\_\_ J. \left(\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9\right. in SI units)
Options:
A) 30 \times 10^{-6}
B) 0
C) 15 \times 10^{-6}
D) 45 \times 10^{-6}
298
MediumJEE Mains2018
The equivalent capacitance between $A and B$ in the circuit given below, is :
Options:
A) 2.4\,\mu F
B) 4.9\,\mu F
C) 3.6\,\mu F
D) 5.4\,\mu F
299
MediumJEE Mains2025
Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1 and σ2, respectively. The ratio \frac{\sigma_1}{\sigma_2} is
Options:
A) \frac{1}{3}
B) \frac{1}{9}
C) 9
D) 3
300
MediumJEE Mains2017
A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.
Options:
A) 3
B) 4
C) 5
D) 6
301
EasyJEE Mains2025
Given below are two statements: one is labelled as Assertion \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below.
Options:
A) A is true but R is false
B) Both A and R are true and R is the correct explanation of A
C) Both A and R are true but R is NOT the correct explanation of A
D) A is false but R is true
302
MediumJEE Mains2017
The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $\mu C charge, its radius will be : [ Take : {1 \over {4\,\pi { \in _0}}} = 9 \times 109 N -$ m2/C2 ]
Options:
A) 20 mm
B) 32 mm
C) 28 mm
D) 16 mm
303
MediumJEE Mains2025
Electric charge is transferred to an irregular metallic disk as shown in the figure. If \sigma_1, \sigma_2, \sigma_3 and \sigma_4 are charge densities at given points then, choose the correct answer from the options given below: A. \sigma_1>\sigma_3 ; \sigma_2=\sigma_4 B. \sigma_1>\sigma_2 ; \sigma_3>\sigma_4 C. \sigma_1>\sigma_3>\sigma_2=\sigma_4 D. \sigma_1<\sigma_3<\sigma_2=\sigma_4 E. \sigma_1=\sigma_2=\sigma_3=\sigma_4
Options:
A) B and C Only
B) A and C Only
C) D and E Only
D) A, B and C Only
304
MediumJEE Mains2017
A capacitance of 2 $\mu F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 \mu $F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:
Options:
A) 2
B) 16
C) 32
D) 24
305
MediumJEE Mains2025
An infinitely long wire has uniform linear charge density \lambda = 2 \text{ nC/m}. The net flux through a Gaussian cube of side length \sqrt{3} cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x \text{ Nm}^2\text{C}^{-1}, where x is: [Neglect any edge effects and use \frac{1}{4\pi \epsilon_0} = 9 \times 10^9 SI units]
Options:
A) 6.48 \pi
B) 0.72 \pi
C) 1.44 \pi
D) 2.16 \pi
306
MediumJEE Mains2017
In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:
Options:
A) CE{{{r_1}} \over {({r_1} + r)}}
B) CE
C) CE{{{r_1}} \over {({r_2} + r)}}
D) CE{{{r_2}} \over {(r + {r_2})}}
307
EasyJEE Mains2025
A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:
Options:
A) 2.5×10−9 Nm
B) 2.5×10−12 Nm
C) 5×10−3 Nm
D) 5×10−9 Nm
308
MediumJEE Mains2016
Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $\mu $F is :
Options:
A) {{31} \over {23}}\,\mu F
B) {{32} \over {23}}\,\mu F
C) {{33} \over {23}}\,\mu F
D) {{34} \over {23}}\,\mu F
309
EasyJEE Mains2025
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes. Reason (R) : The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
B) (A) is correct but (R) is not correct
C) Both (A) and (R) are correct and (R) is the correct explanation of (A)
D) (A) is not correct but (R) is correct
310
MediumJEE Mains2016
Three capacitors each of 4 $\mu F are to be connected in such a way that the effective capacitance is 6 \mu $F. This can be done by connecting them :
Options:
A) all in series
B) two in series and one in parallel
C) all in parallel
D) two in parallel and one in series
311
MediumJEE Mains2025
If \epsilon_0 denotes the permittivity of free space and \Phi_E is the flux of the electric field through the area bounded by the closed surface, then dimensions of \left(\epsilon_0 \frac{d \phi_E}{d t}\right) are that of :
Options:
A) electric charge
B) electric field
C) electric current
D) electric potential
312
MediumJEE Mains2016
A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q (having a charge equal to the sum of the charges on the 4 \mu \,F and 9 \mu \,F capacitors), at a point distance 30 m$ from it, would equal :
Options:
A) 420N/C
B) 480N/C
C) 240N/C
D) 360N/C
313
MediumJEE Mains2025
Two charges q_1 and q_2 are separated by a distance of 30 cm . A third charge q_3 initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D . If the difference in potential energy due to movement of q_3 from C to D is given by \frac{q_3 \mathrm{~K}}{4 \pi \epsilon_0}, the value of K is :
Options:
A) 6 \mathrm{q}_2
B) 6 \mathrm{q}_1
C) 8 \mathrm{q}_1
D) \mathrm{8 q_2}
314
MediumJEE Mains2015
In the given circuit, charges ${Q_2} on the 2\mu F capacitor changes as C is varied from 1\,\mu F to 3\mu F. {Q_2} as a function of 'C' is given properly by: \left( {figures\,\,are\,\,drawn\,\,schematically\,\,and\,\,are\,\,not\,\,to\,\,scale} \right)
Options:
A)
B)
C)
D)
315
MediumJEE Mains2025
A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc A B at ' O ' is ' E ' in magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?
Options:
A) 2E
B) Zero
C) E/2
D) \sqrt2E
316
MediumJEE Mains2014
A parallel plate capacitor is made of two circular plates separated by a distance $5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 \times {10^4}\,V/m$ the charge density of the positive plate will be close to:
Options:
A) 6 \times {10^{ - 7}}\,\,C/{m^2}
B) 3 \times {10^{ - 7}}\,\,C/{m^2}
C) 3 \times {10^4}\,\,C/{m^2}
D) 6 \times {10^4}\,\,C/{m^2}
317
MediumJEE Mains2025
Two infinite identical charged sheets and a charged spherical body of charge density ' \rho ' are arranged as shown in figure. Then the correct relation between the electrical fields at \mathrm{A}, \mathrm{B}, \mathrm{C} and D points is:
Options:
A) \left|\vec{E}_A\right|=\left|\vec{E}_B\right| ; \vec{E}_C>\vec{E}_D
B) \vec{E}_A=\vec{E}_B ; \vec{E}_C=\vec{E}_D
C) \vec{E}_C \neq \vec{E}_D ; \vec{E}_A>\vec{E}_B
D) \vec{E}_A>\vec{E}_B ; \vec{E}_C=\vec{E}_D
318
MediumJEE Mains2013
Two capacitors ${C_1} and {C_2} are charged to 120 V and 200 V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then
Options:
A) 5{C_1} = 3{C_2}
B) 3{C_1} = 5{C_2}
C) 3{C_1} + 5{C_2} = 0
D) 9{C_1} = 4{C_2}
319
MediumJEE Mains2025
Two small spherical balls of mass 10 g each with charges -2 \mu \mathrm{C} and 2 \mu \mathrm{C}, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of 100 \mu \mathrm{C} / \mathrm{m}^2 such that length of rod makes an angle of 30^{\circ} with electric field generated by charge sheet. Net torque acting on the rod is: (Take \varepsilon_{\mathrm{o}}: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2 )
Options:
A) 1.12 Nm
B) 2.24 Nm
C) 11.2 Nm
D) 112 Nm
320
MediumJEE Mains2012
The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau $ of this circuit lies between
Options:
A) 100 sec and 150 sec
B) 0 and 50 sec
C) 50 sec and 100 sec
D) 150 sec and 200 sec
321
EasyJEE Mains2025
The electrostatic potential on the surface of uniformly charged spherical shell of radius \mathrm{R}=10 \mathrm{~cm} is 120 V . The potential at the centre of shell, at a distance \mathrm{r}=5 \mathrm{~cm} from centre, and at a distance \mathrm{r}=15 cm from the centre of the shell respectively, are:
Options:
A) 0 \mathrm{~V}, 120 \mathrm{~V}, 40 \mathrm{~V}
B) 120 \mathrm{~V}, 120 \mathrm{~V}, 80 \mathrm{~V}
C) 40 \mathrm{~V}, 40 \mathrm{~V}, 80 \mathrm{~V}
D) 0 \mathrm{~V}, 0 \mathrm{~V}, 80 \mathrm{~V}
322
MediumJEE Mains2010
Let $C be the capacitance of a capacitor discharging through a resistor R. Suppose {t_1} is the time taken for the energy stored in the capacitor to reduce to half its initial value and {t_2} is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio {t_1}/{t_2}$ will be
Options:
A) 1
B) {1 \over 2}
C) {1 \over 4}
D) 2
323
MediumJEE Mains2025
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) Both (A) and (R) are correct and (R) is the correct explanation of (A) 2.
B) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
C) (A) is not correct but (R) is correct
D) (A) is correct but (R) is not correct
324
MediumJEE Mains2008
A parallel plate capacitor with air between the plates has capacitance of $9 pF. The separation between its plates is 'd'. The space between the plates has dielectric constant {k_1} =3 and thickness {d \over 3} while the other one has dielectric constant {k_2} = 6 and thickness {{2d} \over 3}$. Capacitance of the capacitor is now
Options:
A) 1.8 pF
B) 45 pF
C) 40.5 pF
D) 20.25 pF
325
EasyJEE Mains2025
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and B (shown in the figure) is :
Options:
A) 1 V
B) \frac{1}{4} \mathrm{~V}
C) \frac{3}{4} \mathrm{~V}
D) \frac{2}{5} \mathrm{~V}
326
MediumJEE Mains2007
A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be
Options:
A) 1/2
B) 1
C) 2
D) 1/4
327
MediumJEE Mains2025
Consider a circular loop that is uniformly charged and has a radius \mathrm{a} \sqrt{2}. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in x y plane at the origin :
Options:
A) a
B) a / 2
C) 0
D) a / \sqrt{2}
328
MediumJEE Mains2007
A parallel plate condenser with a dielectric of dielectric constant $K between the plates has a capacity C and is charged to a potential V$ volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
Options:
A) zero
B) {1 \over 2}\,\left( {K - 1} \right)\,C{V^2}
C) {{C{V^2}\left( {K - 1} \right)} \over K}
D) \left( {K - 1} \right)\,C{V^2}
329
MediumJEE Mains2025
Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density +\sigma and -2 \sigma. The force experienced by a point charge +q placed at the mid point between two plates will be:
Options:
A) \frac{3 \sigma q}{4 \epsilon_0}
B) \frac{3 \sigma \mathrm{q}}{2 \epsilon_0}
C) \frac{\sigma \mathrm{q}}{4 \epsilon_0}
D) \frac{\sigma q}{2 \epsilon_0}
330
MediumJEE Mains2005
A parallel plate capacitor is made by stacking $n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is 'C'$ then the resultant capacitance is
Options:
A) \left( {n + 1} \right)C
B) \left( {n - 1} \right)C
C) nC
D) C
331
EasyJEE Mains2025
A point charge +q is placed at the origin. A second point charge +9 q is placed at (\mathrm{d}, 0,0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:
Options:
A) (3 \mathrm{d} / 4,0,0)
B) (\mathrm{d} / 4,0,0)
C) (4 \mathrm{d} / 3,0,0)
D) (\mathrm{d} / 3,0,0)
332
MediumJEE Mains2005
A fully charged capacitor has a capacitance $'C'. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity 's' and mass 'm'. If the temperature of the block is raised by '\Delta T', the potential difference 'v'$ across the capacitance is
Options:
A) {{mCAT} \over s}
B) \sqrt {{{2mCAT} \over s}}
C) \sqrt {{{2msAT} \over C}}
D) {{ms\Delta T} \over C}
333
MediumJEE Mains2025
A small bob of mass 100 mg and charge +10 \mu \mathrm{C} is connected to an insulating string of length 1 m . It is brought near to an infinitely long non-conducting sheet of charge density ' \sigma ' as shown in figure. If string subtends an angle of 45^{\circ} with the sheet at equilibrium the charge density of sheet will be. (Given, \epsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}} and acceleration due to gravity, \mathrm{g}=10 \frac{\mathrm{~m}}{\mathrm{~s}^2} )
Options:
A) 1.77 \mathrm{~nC} / \mathrm{m}^2
B) 0.885 \mathrm{~nC} / \mathrm{m}^2
C) 885 \mathrm{~nC} / \mathrm{m}^2
D) 17.7 \mathrm{~nC} / \mathrm{m}^2
334
MediumJEE Mains2003
The work done in placing a charge of $8 \times {10^{ - 18}} coulomb on a condenser of capacity 100$ micro-farad is
Options:
A) 16 \times {10^{ - 32}}\,\,joule
B) 3.1 \times {10^{ - 26}}\,\,joule
C) 4 \times {10^{ - 10}}\,\,joule
D) 32 \times {10^{ - 32}}\,\,joule
335
EasyJEE Mains2025
A point charge causes an electric flux of -2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1} to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given \epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2} )
Options:
A) 17.7 \times 10^{-8} \mathrm{C}
B) -17.7 \times 10^{-8} \mathrm{C}
C) 15.7 \times 10^{-8} \mathrm{C}
D) -15.7 \times 10^{-8} \mathrm{C}
336
MediumJEE Mains2003
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
Options:
A) decreases
B) remains unchanged
C) becomes infinite
D) increases
337
MediumJEE Mains2025
An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \sigma_{\mathrm{o}}. Choose the correct option from the following.
Options:
A) Torque on dipole is zero and net force is directed away from the sheet.
B) Potential energy of dipole is minimum and torque is zero.
C) Potential energy and torque both are maximum.
D) Torque on dipole is zero and net force acts towards the sheet.
338
MediumJEE Mains2002
Capacitance (in $F) of a spherical conductor with radius 1 m$ is
Options:
A) 1.1 \times {10^{ - 10}}
B) {10^{ - 6}}
C) 9 \times {10^{ - 9}}
D) {10^{ - 3}}
339
MediumJEE Mains2025
An electric dipole of mass m, charge q, and length l is placed in a uniform electric field \vec{E} = E_0\hat{i}. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :
Options:
A) \frac{1}{2\pi} \sqrt{\frac{ml}{2qE_0}}
B) 2\pi \sqrt{\frac{ml}{2qE_0}}
C) 2\pi \sqrt{\frac{ml}{qE_0}}
D) \frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{~m} l}{\mathrm{q} \mathrm{E}_0}}
340
MediumJEE Mains2002
If there are $n capacitors in parallel connected to V$ volt source, then the energy stored is equal to
Options:
A) CV
B) {1 \over 2}nC{V^2}
C) C{V^2}
D) {1 \over {2n}}C{V^2}
341
EasyJEE Mains2025
Match List - I with List - II. List - I List - II (A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (I) σ/ε0 (B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ. (II) σ/2ε0 (C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (III) 0 (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. (IV) \frac{\sigma}{\epsilon_0 r^2} Choose the correct answer from the options given below :
Options:
A) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
B) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
C) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
D) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
342
MediumJEE Mains2026
The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K_1=2, K_2=3 and K_3=5 (as shown in figure). If new capacitance is \frac{n}{3} C then the value of n is \_\_\_\_ .
Options:
343
MediumJEE Mains2025
Three infinitely long wires with linear charge density \lambda are placed along the x-a x i s, y-a x i s and z- axis respectively. Which of the following denotes an equipotential surface?
Options:
A) \left(x^2+y^2\right)\left(y^2+z^2\right)\left(z^2+x^2\right)= constant
B) x y z= constant
C) x y+y z+z x= constant
D) (x+y)(y+z)(z+x)= constant
344
EasyJEE Mains2026
A capacitor P with capacitance 10 \times 10^{-6} \mathrm{~F} is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance 20 \times 10^{-6} \mathrm{~F}. The charge on capacitor Q when equilibrium is established will be \alpha \times 10^{-5} C (assume capacitor Q does not have any charge initially), the value of \alpha is \_\_\_\_ .
Options:
345
MediumJEE Mains2025
A particle of mass ' m ' and charge ' q ' is fastened to one end ' A ' of a massless string having equilibrium length l, whose other end is fixed at point ' O '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is
Options:
A) \sqrt{\frac{\mathrm{qE} l}{2 \mathrm{~m}}}
B) \sqrt{\frac{\mathrm{qE} l}{4 \mathrm{~m}}}
C) \sqrt{\frac{\mathrm{qE} l}{\mathrm{~m}}}
D) \sqrt{\frac{2 \mathrm{qE} l}{\mathrm{~m}}}
346
MediumJEE Mains2025
Space between the plates of a parallel plate capacitor of plate area 4 cm2 and separation of 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is _ pF. (Given \epsilon_0 = 8.85 \times 10^{-12} F/m)
Options:
347
EasyJEE Mains2025
A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 \times 10^{-8} \mathrm{C} charge and then removed to a distance such that the force of repulsion between them is 9 \times 10^{-3} \mathrm{~N}. The distance between them is (Take \frac{1}{4 \pi \epsilon_{\mathrm{o}}} as 9 \times 10^9 in SI units)
Options:
A) 1 cm
B) 2 cm
C) 4 cm
D) 3 cm
348
EasyJEE Mains2025
A parallel plate capacitor has charge 5 \times 10^{-6} \mathrm{C}. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is 4 \times 10^{-6} \mathrm{C} then the dielectric constant of the slab is _______________.
Options:
349
MediumJEE Mains2025
In the first configuration (1) as shown in the figure, four identical charges \left(q_0\right) are kept at the corners A, B, C and D of square of side length ' a '. In the second configuration (2), the same charges are shifted to mid points G, E, H and F, of the square. If K=\frac{1}{4 \pi \epsilon_0}, the difference between the potential energies of configuration (2) and (1) is given by :
Options:
A) \frac{K q_0^2}{a}(4-2 \sqrt{2})
B) \frac{K q_0^2}{a}(4 \sqrt{2}-2)
C) \frac{\mathrm{Kq}_0^2}{\mathrm{a}}(3-\sqrt{2})
D) \frac{\mathrm{Kq}_0^2}{\mathrm{a}}(3 \sqrt{2}-2)
350
MediumJEE Mains2025
Four capacitors each of capacitance 16 \mu F are connected as shown in the figure. The capacitance between points A and B is : _________ (in \mu F).
Options:
351
EasyJEE Mains2025
Consider a parallel plate capacitor of area A (of each plate) and separation ' d ' between the plates. If E is the electric field and \varepsilon_0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is
Options:
A) \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}
B) \frac{3}{4} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}
C) \frac{1}{4} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}
D) \frac{1}{2} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}
352
MediumJEE Mains2025
A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is 7 \times 10^8 \mathrm{~V} / \mathrm{s} then the integer value of the distance between the parallel plates is \left(\right. Take, \left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right) ____________ \mu \mathrm{m}.
Options:
353
MediumJEE Mains2025
Two point charges -4 \mu \mathrm{c} and 4 \mu \mathrm{c}, constituting an electric dipole, are placed at (-9,0,0) \mathrm{cm} and (9,0,0) \mathrm{cm} in a uniform electric field of strength 10^4 \mathrm{NC}^{-1}. The work done on the dipole in rotating it from the equilibrium through 180^{\circ} is :
Options:
A) 18.4 mJ
B) 12.4 mJ
C) 16.4 mJ
D) 14.4 mJ
354
EasyJEE Mains2025
At steady state the charge on the capacitor, as shown in the circuit below, is _________ \muC.
Options:
355
MediumJEE Mains2025
Two charges 7 \mu \mathrm{c} and -4 \mu \mathrm{c} are placed at (-7 \mathrm{~cm}, 0,0) and (7 \mathrm{~cm}, 0,0) respectively. Given, \epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}, the electrostatic potential energy of the charge configuration is :
Options:
A) -2.0 J
B) -1.5 J
C) -1.2 J
D) -1.8 J
356
MediumJEE Mains2024
A capacitor of $10 \mu \mathrm{F} capacitance whose plates are separated by 10 \mathrm{~mm} through air and each plate has area 4 \mathrm{~cm}^2 is now filled equally with two dielectric media of K_1=2, K_2=3 respectively as shown in figure. If new force between the plates is 8 \mathrm{~N}$. The supply voltage is ________ V.
Options:
357
HardJEE Mains2025
A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2 a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?
Options:
A) \frac{a}{r} \sim 0.5
B) \frac{a}{r} \sim 3
C) \frac{a}{r} \sim 10
D) \frac{a}{r} \sim 20
358
MediumJEE Mains2024
The electric field between the two parallel plates of a capacitor of $1.5 \mu \mathrm{F} capacitance drops to one third of its initial value in 6.6 \mu \mathrm{s} when the plates are connected by a thin wire. The resistance of this wire is ________ \Omega. (Given, \log 3=1.1$)
Options:
359
MediumJEE Mains2025
The electric flux is \phi=\alpha \sigma+\beta \lambda where \lambda and \sigma are linear and surface charge density, respectively. \left(\frac{\alpha}{\beta}\right) represents
Options:
A) displacement
B) charge
C) electric field
D) area
360
MediumJEE Mains2024
Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F} and 45 \mu \mathrm{F} are connected in parallel to a supply of 100 \mathrm{~V}. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is \frac{9}{x} \mathrm{E}. The value of x$ is _________.
Options:
361
MediumJEE Mains2025
For a short dipole placed at origin O , the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V_0 and E_0, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by
Options:
A) \frac{V_0}{2} and \frac{E_0}{16}
B) zero and \frac{E_0}{8}
C) \mathrm{V}_0 and \frac{\mathrm{E}_0}{4}
D) zero and \frac{E_0}{16}
362
MediumJEE Mains2024
A parallel plate capacitor of capacitance $12.5 \mathrm{~pF} is charged by a battery connected between its plates to potential difference of 12.0 \mathrm{~V}. The battery is now disconnected and a dielectric slab (\epsilon_{\mathrm{r}}=6) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ \times10^{-12} \mathrm{~J}$.
Options:
363
MediumJEE Mains2025
A line charge of length \frac{\mathrm{a}}{2} is kept at the center of an edge B C of a cube ABCDEFGH having edge length ' a ' as shown in the figure. If the density of line charge is \lambda \mathrm{C} per unit length, then the total electric flux through all the faces of the cube will be ___________ . (Take, \epsilon_0 as the free space permittivity)
Options:
A) \frac{\lambda a}{2 \epsilon_0}
B) \frac{\lambda \mathrm{a}}{8 \epsilon_0}
C) \frac{\lambda \mathrm{a}}{4 \epsilon_0}
D) \frac{\lambda \mathrm{a}}{16 \epsilon_0}
364
MediumJEE Mains2024
In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ \mu C.
Options:
365
EasyJEE Mains2024
Five charges $+q,+5 q,-2 q,+3 q and -4 q are situated as shown in the figure. The electric flux due to this configuration through the surface S$ is :
Options:
A) \frac{q}{\epsilon_0}
B) \frac{3 q}{\epsilon_0}
C) \frac{5 q}{\epsilon_0}
D) \frac{4 q}{\epsilon_0}
366
MediumJEE Mains2024
A parallel plate capacitor with plate separation $5 \mathrm{~mm} is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 \mathrm{~mm}, while keeping the battery connections intact, the capacitor draws 25 \%$ more charge from the battery than before. The dielectric constant of the sheet is _________.
Options:
367
EasyJEE Mains2024
Two charged conducting spheres of radii $a and b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
Options:
A) a b
B) \frac{b}{a}
C) \frac{a}{b}
D) \sqrt{a b}
368
EasyJEE Mains2024
A capacitor of capacitance $\mathrm{C} and potential \mathrm{V} has energy \mathrm{E}. It is connected to another capacitor of capacitance 2 \mathrm{C} and potential 2 \mathrm{~V}. Then the loss of energy is \frac{x}{3} \mathrm{E}, where x$ is _______.
Options:
369
MediumJEE Mains2024
Two identical conducting spheres P and S with charge Q on each, repel each other with a force $16 \mathrm{~N}. A third identical uncharged conducting sphere \mathrm{R} is successively brought in contact with the two spheres. The new force of repulsion between \mathrm{P} and \mathrm{S}$ is :
Options:
A) 1 N
B) 6 N
C) 12 N
D) 4 N
370
MediumJEE Mains2024
In the given figure, the charge stored in $6 \mu F capacitor, when points A and B are joined by a connecting wire is __________ \mu C$.
Options:
371
MediumJEE Mains2024
\sigma$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :
Options:
A) \sigma / \epsilon_o R
B) \sigma / \in_o
C) \sigma / 2 \epsilon_o
D) \sigma / 4 \epsilon_o
372
MediumJEE Mains2024
A $16 \Omega wire is bend to form a square loop. A 9 \mathrm{~V} battery with internal resistance 1 \Omega is connected across one of its sides. If a 4 \mu F capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \frac{x}{2} \mu J, where x=$ _________
Options:
373
EasyJEE Mains2024
The vehicles carrying inflammable fluids usually have metallic chains touching the ground:
Options:
A) To protect tyres from catching dirt from ground
B) It is a custom
C) To alert other vehicles
D) To conduct excess charge due to air friction to ground and prevent sparking
374
MediumJEE Mains2024
The charge accumulated on the capacitor connected in the following circuit is _______ $\mu \mathrm{C} (Given \mathrm{C}=150 \mu \mathrm{F})
Options:
375
EasyJEE Mains2024
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :
Options:
A) 1019
B) 1039
C) 1029
D) 1036
376
EasyJEE Mains2023
In the given figure the total charge stored in the combination of capacitors is 100~ \mu \mathrm{C}. The value of ' x ' is _________.
Options:
377
MediumJEE Mains2024
A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:
Options:
A) \frac{q}{2 \epsilon_0}
B) Zero
C) \frac{q}{4 \epsilon_0}
D) \frac{q}{8 \epsilon_0}
378
MediumJEE Mains2023
In the circuit shown, the energy stored in the capacitor is $n ~\mu \mathrm{J}. The value of n$ is __________
Options:
379
EasyJEE Mains2024
An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{~Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :
Options:
A)
B)
C)
D)
380
MediumJEE Mains2023
In the given circuit, $\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=0.2 \mu \mathrm{F}, \mathrm{C}_{3}=2 \mu \mathrm{F}, \mathrm{C}_{4}=4 \mu \mathrm{F}, \mathrm{C}_{5}=2 \mu \mathrm{F}, \mathrm{C}_{6}=2 \mu \mathrm{F}, The charge stored on capacitor \mathrm{C}_{4} is ____________ \mu \mathrm{C}$.
Options:
381
EasyJEE Mains2024
C_1 and C_2 are two hollow concentric cubes enclosing charges 2 Q and 3 Q respectively as shown in figure. The ratio of electric flux passing through C_1 and C_2 is :
Options:
A) 3: 2
B) 5: 2
C) 2: 5
D) 2: 3
382
EasyJEE Mains2023
A $600 ~\mathrm{pF} capacitor is charged by 200 \mathrm{~V} supply. It is then disconnected from the supply and is connected to another uncharged 600 ~\mathrm{pF} capacitor. Electrostatic energy lost in the process is ____________ \mu \mathrm{J}
Options:
383
EasyJEE Mains2024
Force between two point charges $q_1 and q_2 placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric constant K=5 at 'r / 5' \mathrm{cm}$ apart will be:
Options:
A) 5 F
B) 25 F
C) F / 5
D) F / 25
384
MediumJEE Mains2023
As shown in the figure, two parallel plate capacitors having equal plate area of $200 \mathrm{~cm}^{2} are joined in such a way that a \neq b. The equivalent capacitance of the combination is x \in_{0} \mathrm{~F}. The value of x$ is ____________.
Options:
385
EasyJEE Mains2024
Two charges $q and 3 q are separated by a distance 'r' in air. At a distance x from charge q, the resultant electric field is zero. The value of x$ is :
Options:
A) \frac{r}{3(1+\sqrt{3})}
B) \frac{(1+\sqrt{3})}{r}
C) \frac{r}{(1+\sqrt{3})}
D) r(1+\sqrt{3})
386
MediumJEE Mains2023
A parallel plate capacitor with plate area $\mathrm{A} and plate separation \mathrm{d} is filled with a dielectric material of dielectric constant K=4. The thickness of the dielectric material is x, where x < d. Let \mathrm{C}_{1} and \mathrm{C}_{2} be the capacitance of the system for \chi=\frac{1}{3} d and \mathcal{X}=\frac{2 d}{3}, respectively. If \mathrm{C}_{1}=2 \mu \mathrm{F} the value of \mathrm{C}_{2} is __________ \mu \mathrm{F}
Options:
387
MediumJEE Mains2024
A particle of charge '$-q' and mass 'm' moves in a circle of radius 'r' around an infinitely long line charge of linear charge density '+\lambda'. Then time period will be given as : (Consider k$ as Coulomb's constant)
Options:
A) T^2=\frac{4 \pi^2 m}{2 k \lambda q} r^3
B) T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}
C) T=\frac{1}{2 \pi} \sqrt{\frac{2 k \lambda q}{m}}
D) T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}
388
MediumJEE Mains2023
For the given circuit, in the steady state, \left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|= ________ V.
Options:
389
EasyJEE Mains2024
The electrostatic potential due to an electric dipole at a distance '$r$' varies as :
Options:
A) \frac{1}{r^3}
B) \frac{1}{\mathrm{r}}
C) \frac{1}{r^2}
D) r
390
MediumJEE Mains2023
Two parallel plate capacitors C_{1} and C_{2} each having capacitance of 10 \mu \mathrm{F} are individually charged by a 100 V D.C. source. Capacitor C_{1} is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor \mathrm{C}_{2} is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor C_{1} is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ________ V. (Assuming Dielectric constant =10 )
Options:
391
EasyJEE Mains2024
An electric field is given by $(6 \hat{i}+5 \hat{j}+3 \hat{k}) \mathrm{N} / \mathrm{C}. The electric flux through a surface area 30 \hat{i} \mathrm{~m}^2$ lying in YZ-plane (in SI unit) is :
Options:
A) 60
B) 90
C) 180
D) 150
392
MediumJEE Mains2023
A capacitor of capacitance $900 \mu \mathrm{F} is charged by a 100 \mathrm{~V} battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as x \times 10^{-} { }^{2} \mathrm{~J}. The value of x$ is _____________.
Options:
393
EasyJEE Mains2024
Two charges of $5 Q and -2 Q are situated at the points (3 a, 0) and (-5 a, 0) respectively. The electric flux through a sphere of radius '4 a$' having center at origin is :
Options:
A) \frac{2 Q}{\varepsilon_0}
B) \frac{7 Q}{\varepsilon_0}
C) \frac{3 Q}{\varepsilon_0}
D) \frac{5 Q}{\varepsilon_0}
394
MediumJEE Mains2023
A capacitor has capacitance 5$\muF when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness \frac{d}{2} is inserted between the plates. Capacitance of the capacitor in the presence of slab will be __________ \mu$F.
Options:
395
EasyJEE Mains2024
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) Both (A) and (R) are correct and (R) is the correct explanation of (A)
B) (A) is correct but (R) is not correct
C) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
D) (A) is not correct but (R) is correct
396
EasyJEE Mains2023
A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $\frac{x}{4} pF. The value of x$ is ____________.
Options:
397
EasyJEE Mains2024
An electric charge $10^{-6} \mu \mathrm{C} is placed at origin (0,0) \mathrm{m} of \mathrm{X}-\mathrm{Y} co-ordinate system. Two points \mathrm{P} and \mathrm{Q} are situated at (\sqrt{3}, \sqrt{3}) \mathrm{m} and (\sqrt{6}, 0) \mathrm{m} respectively. The potential difference between the points \mathrm{P} and \mathrm{Q}$ will be :
Options:
A) \sqrt{3} \mathrm{~V}
B) \sqrt{6} \mathrm{~V}
C) 0 \mathrm{~V}
D) 3 \mathrm{~V}
398
EasyJEE Mains2022
As show in the figure, in steady state, the charge stored in the capacitor is ____________ $\times\, 10^{-6}$ C.
Options:
399
MediumJEE Mains2023
The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as :
Options:
A) \frac{1}{r^{2}}
B) \frac{1}{r}
C) r
D) \frac{1}{r^{3}}
400
MediumJEE Mains2022
A parallel plate capacitor with width $4 \mathrm{~cm}, length 8 \mathrm{~cm} and separation between the plates of 4 \mathrm{~mm} is connected to a battery of 20 \mathrm{~V}. A dielectric slab of dielectric constant 5 having length 1 \mathrm{~cm}, width 4 \mathrm{~cm} and thickness 4 \mathrm{~mm} is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ____________ \epsilon_{0} J. (Where \epsilon_{0}$ is the permittivity of free space)
Options:
401
MediumJEE Mains2023
A $10 ~\mu \mathrm{C} charge is divided into two parts and placed at 1 \mathrm{~cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:
Options:
A) 9 ~\mu\mathrm{C}, 1 ~\mu \mathrm{C}
B) 5 ~\mu\mathrm{C}, 5 ~\mu \mathrm{C}
C) 8 ~\mu\mathrm{C}, 2 ~\mu \mathrm{C}
D) 7 ~\mu\mathrm{C}, 3 ~\mu \mathrm{C}
402
MediumJEE Mains2022
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $\left(t_{1}\right. and \left.t_{2}\right) as shown in figure. The two different dielectric materials are separated by a conducting foil \mathrm{F}$. The voltage of the conducting foil is V.
Options:
403
EasyJEE Mains2023
Two charges each of magnitude $0.01 ~\mathrm{C} and separated by a distance of 0.4 \mathrm{~mm} constitute an electric dipole. If the dipole is placed in an uniform electric field '\vec{E}' of 10 dyne/C making 30^{\circ} angle with \vec{E}$, the magnitude of torque acting on dipole is:
Options:
A) 4 \cdot 0 \times 10^{-10} ~\mathrm{Nm}
B) 1.5 \times 10^{-9} ~\mathrm{Nm}
C) 1.0 \times 10^{-8} ~\mathrm{Nm}
D) 2.0 \times 10^{-10} ~\mathrm{Nm}
404
MediumJEE Mains2022
Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ___________ V.
Options:
405
EasyJEE Mains2023
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If an electric dipole of dipole moment $30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below.
Options:
A) A is true but R is false
B) A is false but R is true
C) Both A and R are true but R is NOT the correct explanation of A
D) Both A and R are true and R is the correct explanation of A
406
EasyJEE Mains2022
A capacitor C1 of capacitance 5 $\muF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 \muF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is __________ \mu$C.
Options:
407
EasyJEE Mains2023
In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor
Options:
A) move in the straight line paths in the same direction
B) move with the uniform velocity throughout from lower potential to higher potential
C) drift from higher potential to lower potential.
D) move in the curved paths from lower potential to higher potential
408
MediumJEE Mains2022
A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is ${x \over {15}}{{{ \in _0}A} \over b}$. The value of x is ____________.
Options:
409
EasyJEE Mains2023
Electric potential at a point '$\mathrm{P}' due to a point charge of 5 \times 10^{-9} \mathrm{C} is 50 \mathrm{~V}. The distance of '\mathrm{P}' from the point charge is: (Assume, \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{+9} ~\mathrm{Nm}^{2} \mathrm{C}^{-2}$ )
Options:
A) 0.9 cm
B) 90 cm
C) 3 cm
D) 9 cm
410
EasyJEE Mains2022
A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ___________ nJ.
Options:
411
EasyJEE Mains2023
Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $\mathrm{R}, with distance r$ from the centre O is represented by:
Options:
A)
B)
C)
D)
412
EasyJEE Mains2022
The equivalent capacitance between points A and B in below shown figure will be __________ $\mu$F.
Options:
413
MediumJEE Mains2023
A dipole comprises of two charged particles of identical magnitude $q and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance 'l'. If the dipole is placed in a uniform electric field '\bar{E}'; in such a way that dipole axis makes a very small angle with the electric field, '\bar{E}$'. The angular frequency of the oscillations of the dipole when released is given by:
Options:
A) \sqrt{\frac{3 q E}{2 m l}}
B) \sqrt{\frac{4 q E}{m l}}
C) \sqrt{\frac{8 q E}{3 m l}}
D) \sqrt{\frac{8 q E}{m l}}
414
EasyJEE Mains2021
A parallel plate capacitor of capacitance 200 $\mu$F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be ____________J.
Options:
415
EasyJEE Mains2023
For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -
Options:
A)
B)
C)
D)
416
EasyJEE Mains2021
A capacitor of 50 $\muF is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________\mu$C.
Options:
417
MediumJEE Mains2023
Let $\sigma be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region E_{I}, E_{I I} and E_{I I I}$ are:
Options:
A) \vec{E}_{I}=0, \vec{E}_{I I}=\frac{\sigma}{\epsilon_{0}} \hat{n}, E_{I I I}=0
B) \vec{E}_{I}=\frac{\sigma}{2 \epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{\sigma}{2 \epsilon_{0}} \hat{n}
C) \vec{E}_{I}=-\frac{\sigma}{\epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{\sigma}{\epsilon_{0}} \hat{n}
D) \vec{E}_{I}=\frac{2 \sigma}{\epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{2 \sigma}{\epsilon_{0}} \hat{n}
418
EasyJEE Mains2021
The circuit shown in the figure consists of a charged capacitor of capacity 3 $\muF and a charge of \muC. At time t = 0, when the key is closed, the value of current flowing through the 5 M\Omega resistor is 'x' \mu$-A. The value of 'x to the nearest integer is ___________.
Options:
419
MediumJEE Mains2023
Considering a group of positive charges, which of the following statements is correct ?
Options:
A) Net potential of the system cannot be zero at a point but net electric field can be zero at that point
B) Net potential of the system at a point can be zero but net electric field can't be zero at that point.
C) Both the net potential and the net electric field cannot be zero at a point.
D) Both the net potential and the net field can be zero at a point.
420
MediumJEE Mains2021
A parallel plate capacitor has plate area 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.The value of $\varepsilon 0 = 8.85 \times 10-12 F.m-$1.The value of 'x' to the nearest integer is _____________.
Options:
421
EasyJEE Mains2023
Which of the following correctly represents the variation of electric potential $(\mathrm{V}) of a charged spherical conductor of radius (\mathrm{R}) with radial distance (\mathrm{r})$ from the center?
Options:
A)
B)
C)
D)
422
EasyJEE Mains2021
A 2$\muF capacitor C1 is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C2 of 8 \muF. The charge in C2 on equilibrium condition is ____________ \mu$C. (Round off to the Nearest Integer)
Options:
423
EasyJEE Mains2023
As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius a and outer radius b. The electric field due to charge \mathrm{Q} in three different regions \mathrm{I}, \mathrm{II} and \mathrm{III} is given by: (\mathrm{I}: r < a, \mathrm{II}: a < r < b, III: r>b )
Options:
A) E_I=0, E_{I I}=0, E_{I I I} \neq 0
B) E_I \neq 0, E_{I I}=0, E_{III}=0
C) E_I \neq 0, E_{I I}=0, E_{III} \neq 0
D) E_I=0, E_{I I}=0, E_{I I I}=0
424
MediumJEE Mains2021
A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _____________ pJ. (Assume no friction)
Options:
425
EasyJEE Mains2023
Electric field in a certain region is given by $\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$ are :
Options:
A) \mathrm{Nm}^{2} \mathrm{C} ; \mathrm{Nm}^{3} \mathrm{C}
B) \mathrm{Nm}^{3} \mathrm{C}^{-1} ; \mathrm{Nm}^{2} \mathrm{C}^{-1}
C) \mathrm{Nm}^{3} \mathrm{C} ; \mathrm{Nm}^{2} \mathrm{C}
D) \mathrm{Nm}^{2} \mathrm{C}^{-1} ; \mathrm{Nm}^{3} \mathrm{C}^{-1}
426
MediumJEE Mains2021
Four identical rectangular plates with length, l = 2 cm and breadth, b = ${3 \over 2} cm are arranged as shown in figure. The equivalent capacitance between A and C is {{x{\varepsilon _0}} \over d}$. The value of x is ______________. (Round off to the Nearest Integer)
Options:
427
MediumJEE Mains2023
Two isolated metallic solid spheres of radii $\mathrm{R} and 2 \mathrm{R} are charged such that both have same charge density \sigma. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is \sigma^{\prime}. The ratio \frac{\sigma^{\prime}}{\sigma}$ is :
Options:
A) \frac{5}{3}
B) \frac{5}{6}
C) \frac{9}{4}
D) \frac{4}{3}
428
MediumJEE Mains2021
In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig.) the capacitance of the set-up will be __________$\varepsilon $o. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)
Options:
429
EasyJEE Mains2023
A point charge $2\times10^{-2}~\mathrm{C} is moved from P to S in a uniform electric field of 30~\mathrm{NC^{-1}}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be
Options:
A) 600 mJ
B) -1200$ mJ
C) 1200 mJ
D) -600$ mJ
430
MediumJEE Mains2020
An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2 $\Omega $. The potential difference (in V) across the capacitor when it is fully charged is ______.
Options:
431
MediumJEE Mains2023
In a cuboid of dimension $2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}, a charge q is placed at the center of the surface '\mathrm{S}' having area of 4 \mathrm{~L}^{2}. The flux through the opposite surface to '\mathrm{S}$' is given by
Options:
A) \frac{q}{2 \epsilon_{0}}
B) \frac{q}{3 \epsilon_{0}}
C) \frac{q}{12 \epsilon_{0}}
D) \frac{q}{6 \in_{0}}
432
MediumJEE Mains2020
A 5 $\mu F capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 \mu F capacitor. If the energy change during the charge redistribution is {X \over {100}}J$ then value of X to the nearest integer is _____.
Options:
433
EasyJEE Mains2023
A point charge of 10 $\muC is placed at the origin. At what location on the X-axis should a point charge of 40 \muC be placed so that the net electric field is zero at x=2$cm on the X-axis?
Options:
A) x=6$ cm
B) x=8$ cm
C) x=4$ cm
D) x=-4$ cm
434
MediumJEE Mains2020
A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) _____
Options:
435
MediumJEE Mains2023
The electric potential at the centre of two concentric half rings of radii R$_1 and R_2, having same linear charge density \lambda$ is :
Options:
A) \frac{\lambda}{2\in_0}
B) \frac{\lambda}{\in_0}
C) \frac{2\lambda}{\in_0}
D) \frac{\lambda}{4\in_0}
436
MediumMHT CET2025
The potential difference across the 4 capacitor in the following circuit is
Options:
A) 3.4 V
B) 4.6 V
C) 5.4 V
D) 6.2 V
437
EasyJEE Mains2023
If two charges q$_1 and q_2$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
Options:
A) d\sqrt k
B) 1\,.\,5d\sqrt k
C) k\sqrt d
D) 2d\sqrt k
438
MediumMHT CET2025
A capacitor of unknown capacity is connected across a battery of V volt. The charge stored in it is Q coulomb. When potential across the capacitor is reduced by \mathrm{V}_1 volt, the charge stored in it becomes \mathrm{Q}_1 coulomb. The potential V is
Options:
A) \frac{\mathrm{QV}_1}{\mathrm{Q}-\mathrm{Q}_1}
X
B) \frac{Q_1 V_1}{Q+Q_1}
C) \frac{Q_1}{Q}
D) \frac{Q}{Q_1}
439
MediumJEE Mains2022
Two identical metallic spheres $\mathrm{A} and \mathrm{B} when placed at certain distance in air repel each other with a force of \mathrm{F}. Another identical uncharged sphere \mathrm{C} is first placed in contact with \mathrm{A} and then in contact with \mathrm{B}$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:
Options:
A) 3F/2
B) 3F/4
C) F
D) 2F
440
MediumMHT CET2025
Five capacitors, each of capacitance ' C ' are connected as shown in the figure. The ratio of equivalent capacitance between P and R and the equivalent capacitance between P and Q is
Options:
A) 1: 4
B) 2: 3
C) 3: 1
D) 5: 2
441
MediumJEE Mains2022
A spherically symmetric charge distribution is considered with charge density varying as $\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases} Where, r(r < R)$ is the distance from the centre O (as shown in figure). The electric field at point P will be:
Options:
A) \frac{\rho_{0} \mathrm{r}}{4 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)
B) \frac{\rho_{0} r}{3 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)
C) \frac{\rho_{0} r}{4 \varepsilon_{0}}\left(1-\frac{r}{R}\right)
D)
\frac{\rho_{0} r}{5 \varepsilon_{0}}\left(1-\frac{r}{R}\right)
442
MediumMHT CET2025
The function of a dielectric in a capacitor is
Options:
A) to reduce the effective potential on plates,
B) to increase the effective potential on plates.
C) to decrease the capacity of capacitance.
D) to reduce the plate area of the capacitor.
443
EasyJEE Mains2022
Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options given below.
Options:
A) Both Statement I and Statement II are correct
B) Both Statement I and Statement II are incorrect
C) Statement I is correct but Statement II is incorrect
D) Statement I is incorrect but Statement II is correct
444
MediumMHT CET2025
Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors \mathrm{C}_3 and \mathrm{C}_1 is
Options:
A) 1.5
B) 2.5
C) 3.5
D) 4.5
445
MediumJEE Mains2022
A uniform electric field $\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m} is created between two parallel plates of length 1 \mathrm{~m} as shown in figure, (where \mathrm{m}= mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 \mathrm{~m} / \mathrm{s}. The angle of the deviation (\theta)$ of the path of the electron as it comes out of the field will be _________.
Options:
A)
\tan ^{-1}(4)
B)
\tan ^{-1}(2)
C) \tan ^{-1}\left(\frac{1}{3}\right)
D) \tan ^{-1}(3)
446
MediumMHT CET2025
The capacity of air filled parallel plate capacitor is \mathrm{C}_0. One-half of the space between the plates is filled with a dielectric constant ' K ' as shown in figure. The new capacity becomes \mathrm{C}_{\mathrm{n}}. The ratio \mathrm{C}_{\mathrm{n}} to \mathrm{C}_0 is
Options:
A) \left(\frac{\mathrm{K}+1}{2}\right)
B) \left(\frac{\mathrm{K}+1}{3}\right)
C) \left(\frac{\mathrm{K}+1}{4}\right)
D) 4(\mathrm{~K}+1)
447
EasyJEE Mains2022
A charge of $4 \,\mu \mathrm{C}$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :
Options:
A) 1 \,\mu \mathrm{C} and 3 \,\mu\mathrm{C}
B) 2 \,\mu \mathrm{C} and 2\, \mu \mathrm{C}
C) 0 and $4\, \mu\, \mathrm{C}
D) 1.5 \,\mu \mathrm{C} and 2.5\, \mu \mathrm{C}
448
MediumMHT CET2025
Seven capacitors each of capacitance 2 \mu \mathrm{~F} are to be connected in a configuration to obtain an effective capacitance \left(\frac{10}{11}\right) \mu \mathrm{F}. The combination is
Options:
A)
B)
C)
D)
449
MediumJEE Mains2022
Two identical positive charges $Q each are fixed at a distance of '2a' apart from each other. Another point charge q_{0} with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \mathrm{q}_{0} executes \mathrm{SHM}. The time period of oscillation of charge \mathrm{q}_{0}$ will be :
Options:
A) \sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}
B) \sqrt{\frac{q_{0} Q}{4 \pi^{3} \varepsilon_{0} m a^{3}}}
C) \sqrt{\frac{2 \pi^{2} \varepsilon_{0} m a^{3}}{q_{0} Q}}
D) \sqrt{\frac{8 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}
450
MediumMHT CET2025
Two identical metal plates are given charges q_1 and q_2\left(q_2 < q_1\right) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance ' C ', the potential difference ' V ' between the plates is
Options:
A) \frac{q_1-q_2}{c}
B) \frac{q_1+q_2}{C}
C) \frac{q_1-q_2}{2 C}
D) \frac{q_1+q_2}{2 C}
451
EasyJEE Mains2022
Two uniformly charged spherical conductors $A and B of radii 5 \mathrm{~mm} and 10 \mathrm{~mm} are separated by a distance of 2 \mathrm{~cm}. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B$ will be :
Options:
A) 1 : 2
B) 2 : 1
C) 1 : 1
D) 1 : 4
452
MediumMHT CET2025
Five capacitors, each of capacity ' C ' are connected as shown in the figure. The resultant capacity between A and B is 14 \mu \mathrm{~F}. The capacity of each capacitor is
Options:
A) 2 \mu \mathrm{~F}
B) 3.5 \mu \mathrm{~F}
C) 4 \mu \mathrm{~F}
D) 2.8 \mu \mathrm{~F}
453
MediumJEE Mains2022
Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :
Options:
A) x = d
B) x = {d \over 2}
C) x = {d \over {\sqrt 2 }}
D) x = {d \over {2\sqrt 2 }}
454
MediumMHT CET2025
Two capacitors of 100 \mu \mathrm{~F} and 50 \mu \mathrm{~F} are connected in parallel. If the potential difference across 100 \mu \mathrm{~F} is 20 V and across 50 \mu \mathrm{~F} is 40 V , then the common potential of the parallel combination will be (same polarities of the capacitor connected together)
Options:
A) 20 V
B) 60 V
C) \frac{3}{80}
D) \frac{80}{3} \mathrm{~V}
455
EasyJEE Mains2022
If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be :
Options:
A) 3 Vm$-$1, directed along positive x-axis.
B) 3 Vm$-$1, directed along negative x-axis.
C) 6 Vm$-$1, directed along positive x-axis.
D) 6 Vm$-$1, directed along negative x-axis.
456
MediumMHT CET2025
A 4 \mu \mathrm{~F} capacitor is charged to 10 V . The battery is then disconnected and a pure 10 mH coil is connected across the capacitor so that LC oscillations are set up. The maximum current in the coil is
Options:
A) 0.2 A
B) 0.1 A
C) 0.4 A
D) 0.25 A
457
EasyJEE Mains2022
A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $\times 105 NC-1. If the charge on the particle is 40 \muC and the initial velocity is 200 ms-$1, how much distance it will travel before coming to the rest momentarily :
Options:
A) 1 m
B) 5 m
C) 10 m
D) 0.5 m
458
MediumMHT CET2025
A parallel plate air capacitor has capacity ' C ' and distance of separation between plates is ' d '. If a conducting sheet of thickness \frac{2 d}{3} is inserted in between the plates, the capacitance becomes C_1. The ratio of \frac{C_1}{C} is
Options:
A) 2: 1
B) 4: 1
C) 3: 1
D) 5: 1
459
EasyJEE Mains2022
Two point charges A and B of magnitude +8 $\times 10-6 C and -8 \times 10-6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 \times 104 NC-$1. The distance 'd' between the point charges A and B is :
Options:
A) 2.0 m
B) 3.0 m
C) 1.0 m
D) 4.0 m
460
MediumMHT CET2025
Initially n identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then
Options:
A) potential difference and total energy of the combination remain the same.
B) potential difference remains the same and energy increases n times.
C) potential difference becomes nV and energy remains the same.
D) potential difference is nV and energy increases n times.
461
MediumJEE Mains2022
Given below are two statements : Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true.
B) Both Statement I and Statement II are false.
C) Statement I is true but Statement II is false.
D) Statement I is false but Statement II is true.
462
MediumMHT CET2025
A series combination of 10 capacitors, each of value ' \mathrm{C}_1 ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' \mathrm{C}_2 ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' \mathrm{C}_2 ' is
Options:
A) \frac{\mathrm{C}_1}{5}
B) \frac{8}{5} \mathrm{C}_1
C) \frac{64}{5} C_1
D) \frac{\mathrm{C}_1}{40}
463
EasyJEE Mains2022
The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :
Options:
A) {q \over {4\pi { \in _0}{a^2}}}\left( {{1 \over {\sqrt 2 }} + {1 \over 2}} \right)
B) {q \over {4\pi { \in _0}{a^2}}}\left( {1 + {1 \over {\sqrt 2 }}} \right)
C) {q \over {4\pi { \in _0}{a^2}}}\left( {1 - {1 \over {\sqrt 2 }}} \right)
D) {q \over {4\pi { \in _0}{a^2}}}\left( {{1 \over {\sqrt 2 }} - {1 \over 2}} \right)
464
MediumMHT CET2025
The graph shows the variation of voltage (v) across the plates of two parallel plate capacitos A and B versus increase of charge Q stored in them. Then
Options:
A) capacity of both capacitors is same.
B) capacity of A is higher than B.
C) capacity of B is higher than A.
D) capacity of both is zero.
465
EasyJEE Mains2022
If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :
Options:
A) {q \over {{ \in _0}}}
B) {q \over {{ 2\in _0}}}
C) {q \over {{ 4\in _0}}}
D) {q \over {{ 2\pi\in _0}}}
466
MediumMHT CET2025
Three capacitors each of capacitance ' C ' and breakdown voltage ' V ' are connected in series. The capacitance and breakdown voltage of the series combination will be respectively
Options:
A) 3 \mathrm{C}, 3 \mathrm{~V}
B) \frac{\mathrm{C}}{3}, \frac{\mathrm{~V}}{3}
C) 3 \mathrm{C}, \frac{\mathrm{V}}{3}
D) \frac{\mathrm{C}}{3}, 3 \mathrm{~V}
467
MediumJEE Mains2022
Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m. The ratio of net force on a charged ball to the force between any two charged balls will be :
Options:
A) 1 : 1
B) 1 : 4
C) \sqrt3$ : 2
D) \sqrt3$ : 1
468
MediumMHT CET2025
If the charge on the capacitor is increased by 3C, the energy stored in it increases by 21 \%. The original charge on the capacitor is
Options:
A) 6 C
B) 3 C
C) 30 C
D) 90 C
469
EasyJEE Mains2022
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $\mu$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :
Options:
A) 1 : 4
B) 4 : 1
C) 1 : 8
D) 8 : 1
470
MediumMHT CET2025
A parallel plate capacitor having plate area ' A ' and separation ' d ' is charged to a potential difference ' V '. The charging battery is disconnected and the plates are pulled apart to four times the initial separation. The work required to increase the distance between the plates is ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{\varepsilon_0 A V^2}{3 d}
B) \frac{\varepsilon_0 A V^2}{4 d}
C) \frac{2 \varepsilon_0 A V^2}{d}
D) \frac{3 \varepsilon_0 A V^2}{2 d}
471
EasyJEE Mains2022
Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-polar materials do not have any permanent dipole moment. Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.
Options:
A) Both (A) and (R) are correct and (R) is the correct explanation of (A).
B) Both (A) and (R) are correct and (R) is not the correct explanation of (A).
C) (A) is correct but (R) is not correct.
D) (A) is not correct but (R) is correct.
472
MediumMHT CET2025
A parallel plate capacitor has plate area 50 \mathrm{~cm}^2 and plate separation 3 mm . The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 4 . The capacitance becomes ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{18 \varepsilon_0}{7}
B) \frac{20 \varepsilon_0}{9}
C) \frac{16 \varepsilon_0}{7}
D) \frac{14 \varepsilon_0}{5}
473
EasyJEE Mains2022
In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are :
Options:
A) {E_1} = \sigma /{\varepsilon _0},\,{E_2} = \sigma /2{\varepsilon _0}
B) {E_1} = 2\sigma /{\varepsilon _0},\,{E_2} = \sigma /{\varepsilon _0}
C) {E_1} = {E_2} = \sigma /2{\varepsilon _0}
D) {E_1} = {E_2} = \sigma /{\varepsilon _0}
474
MediumMHT CET2025
The equivalent capacitance between plates ' A ' and ' B ' ( A -area of each plate, d-separation between plates) ( \varepsilon_0 - permittivity of free space) is
Options:
A) \frac{\mathrm{A} \varepsilon_0}{\mathrm{~d}}
B) \frac{2 \mathrm{~A} \varepsilon_0}{\mathrm{~d}}
C) \frac{4 \mathrm{~A} \varepsilon_0}{\mathrm{~d}}
D) \frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}}
475
EasyJEE Mains2022
Two identical charged particles each having a mass 10 g and charge 2.0 $\times 10-7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms-$2]
Options:
A) 12 cm
B) 10 cm
C) 8 cm
D) 5 cm
476
MediumMHT CET2025
The voltage between the plates of a parallel plate capacitor of capacity 1 \mu \mathrm{~F} is changing at the rate of 4 \mathrm{~V} / \mathrm{s}. the displacement current in the capacitor is
Options:
A) 4 \mu \mathrm{~A}
B) 3 \mu \mathrm{~A}
C) 1 \mu \mathrm{~A}
D) 6 \mu \mathrm{~A}
477
MediumJEE Mains2022
A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :
Options:
A) {{\rho q{R^2}} \over {4{\varepsilon _0}}}
B) {{\rho q{R^2}} \over {2{\varepsilon _0}}}
C) {{q\rho } \over {4{\varepsilon _0}{R^2}}}
D) {{4{\varepsilon _0}{R^2}} \over {q\rho }}
478
MediumMHT CET2025
A parallel plate air capacitor has capacitance C_P. It is equally filled with parallel layers of materials of dielectric constants \mathrm{K}_1 and \mathrm{K}_2. Now its capacity becomes C_K. The ratio C_P to C_K is
Options:
A) \mathrm{K}_1+\mathrm{K}_2
B) \frac{K_1+K_2}{K_1 K_2}
C) \frac{K_1+K_2}{2 K_1 K_2}
D) \frac{2 K_1 K_2}{K_1+K_2}
479
EasyJEE Mains2022
A vertical electric field of magnitude 4.9 $\times$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given : g = 9.8 m/s2)
Options:
A) 1.6 $\times 10-$9 C
B) 2.0 $\times 10-$9 C
C) 3.2 $\times 10-$9 C
D) 0.5 $\times 10-$9 C
480
MediumMHT CET2025
A parallel plate capacitor with plate area A and plate separation d is charged by constant current I. A plane surface of area \frac{\mathrm{A}}{2}, parallel to the plates is drawn simultaneously between the plates. The displacement current through this area is
Options:
A) I
B) \frac{\mathrm{I}}{2}
C) \frac{\mathrm{I}}{4}
D) \frac{1}{8}
481
MediumJEE Mains2021
A cube is placed inside an electric field, $\overrightarrow E = 150{y^2}\widehat j$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :
Options:
A) 3.8 $\times 10-$11 C
B) 8.3 $\times 10-$11 C
C) 3.8 $\times 10-$12 C
D) 8.3 $\times 10-$12 C
482
MediumMHT CET2025
Two parallel plate air c apacitors of same capacity ' C ' are connected in parallel to a battery of e.m.f. ' E '. Then one of the capacitors is completely filled with dielectric mnaterial of constant ' K '. The change in the effective capacity of the parallel combination is
Options:
A) \frac{\mathrm{C}}{(\mathrm{K}-1)}
B) \frac{\mathrm{KC}}{\mathrm{K}-1}
C) \mathrm{KC}+1
D) \mathrm{C}(\mathrm{K}-1)
483
EasyJEE Mains2021
Choose the incorrect statement :(1) The electric lines of force entering into a Gaussian surface provide negative flux.(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.(3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.(4) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.Choose the most appropriate answer from the options given below
Options:
A) (3) and (4) only
B) (2) and (4) only
C) (4) only
D) (1) and (3) only
484
MediumMHT CET2025
The plates of a parallel plate capacitor are separated by a distance 'd' with air as the medium between them. A dielectric slab of dielectric constant 3 is introduced between the plates so as to increase the capacity by 50 \%. The thickness of the dielectric slab is
Options:
A) \frac{\mathrm{d}}{2}
B) \frac{\mathrm{d}}{3}
C) \frac{\mathrm{d}}{5}
D) \frac{5 \mathrm{~d}}{6}
485
EasyJEE Mains2021
Two particles A and B having charges 20$\muC and -5\mu$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?
Options:
A) At 5 cm from 20 $\mu$C on the left side of system
B) At 5 cm from $-5 \mu$C on the right side
C) At 1.25 cm from $-5 \mu$C between two charges
D) At midpoint between two charges
486
MediumMHT CET2024
The graph shows the variation of voltage ' V ' across the plates of two capacitors A and B versus increase in charge ' Q ' stored in them. Then
Options:
A) capacitance A has high capacity.
B) capacitance B has high capacity.
C) both have same capacity.
D) capacity of A=2 times capacity of B.
487
MediumJEE Mains2021
Figure shows a rod AB, which is bent in a 120$^\circ circular arc of radius R. A charge (-Q) is uniformly distributed over rod AB. What is the electric field \overrightarrow E $ at the centre of curvature O ?
Options:
A) {{3\sqrt 3 Q} \over {8\pi {\varepsilon _0}{R^2}}}(\widehat i)
B) {{3\sqrt 3 Q} \over {8{\pi ^2}{\varepsilon _0}{R^2}}}(\widehat i)
C) {{3\sqrt 3 Q} \over {16{\pi ^2}{\varepsilon _0}{R^2}}}(\widehat i)
D) {{3\sqrt 3 Q} \over {8{\pi ^2}{\varepsilon _0}{R^2}}}( - \widehat i)
488
MediumMHT CET2024
Air capacitor has capacitance ' \mathrm{C}_1 '. The space between two plates of capacitor is filled with two dielectrics as shown in figure. The new capacitance of the capacitor is ' \mathrm{C}_2 '. The ratio \frac{C_1}{C_2} is (d= distance between two plates of capacitor, \mathrm{K}_1 and \mathrm{K}_2 are dielectric constants of two dielectrics respectively)
Options:
A) \mathrm{K}_1+\mathrm{K}_2
B) \frac{\mathrm{K}_1+\mathrm{K}_2}{\mathrm{~K}_1-\mathrm{K}_2}
C) \frac{2 \mathrm{~K}_1 \mathrm{~K}_2}{\mathrm{~K}_1+\mathrm{K}_2}
D) \frac{\mathrm{K}_1+\mathrm{K}_2}{2 \mathrm{~K}_1 \mathrm{~K}_2}
489
MediumJEE Mains2021
A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-
Options:
A) E = {\sigma \over {2{\varepsilon _0}}}\left( {1 - {Z \over {{{({Z^2} + {R^2})}^{1/2}}}}} \right)
B) E = {\sigma \over {2{\varepsilon _0}}}\left( {1 + {Z \over {{{({Z^2} + {R^2})}^{1/2}}}}} \right)
C) E = {{2{\varepsilon _0}} \over \sigma }\left( {{1 \over {{{({Z^2} + {R^2})}^{1/2}}}} + Z} \right)
D) E = {\sigma \over {2{\varepsilon _0}}}\left( {{1 \over {({Z^2} + {R^2})}} + {1 \over {{Z^2}}}} \right)
490
MediumMHT CET2024
Two identical capacitors A and B are connected in series to a battery of E.M.F., 'E'. Capacitor B contains a slab of dielectric constant \mathrm{K} . \mathrm{Q}_{\mathrm{A}} and \mathrm{Q}_{\mathrm{B}} are the charges stored in A and B . When the dielectric slab is removed, the corresponding charges are \mathrm{Q}_{\mathrm{A}}^{\prime} and \mathrm{Q}_{\mathrm{B}}^{\prime}. Then
Options:
A) \mathrm{\frac{Q_A^{\prime}}{Q_A}=\frac{K}{2}}
B) \frac{\mathrm{Q}_{\mathrm{B}}^{\prime}}{\mathrm{Q}_{\mathrm{B}}}=\frac{\mathrm{K}+1}{2}
C) \frac{\mathrm{Q}_{\mathrm{A}}^{\prime}}{\mathrm{Q}_{\mathrm{A}}}=\frac{\mathrm{K}+1}{\mathrm{~K}}
D) \frac{\mathrm{Q}_{\mathrm{B}}^{\prime}}{\mathrm{Q}_{\mathrm{B}}}=\frac{\mathrm{K}+1}{2 \mathrm{~K}}
491
MediumJEE Mains2021
The two thin coaxial rings, each of radius 'a' and having charges +Q and $-$Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :
Options:
A) {Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]
B) {Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]
C) {Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]
D) {Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]
492
MediumMHT CET2024
A series combination of n_1 capacitors, each of value C_1 is charged by a source of potential difference 6 V . Another parallel combination of \mathrm{n}_2 capacitors, each of value \mathrm{C}_2 is charged by a source of potential difference 2 V . Total energy of both the combinations is same. The value of \mathrm{C}_2 in terms of \mathrm{C}_1 is
Options:
A) \frac{3 C_1}{n_1 n_2}
B) \frac{9 \mathrm{n}_2}{\mathrm{n}_1} \mathrm{C}_1
C) \frac{3 \mathrm{n}_2}{\mathrm{n}_1} \mathrm{C}_1
D) \frac{9 C_1}{n_1 n_2}
493
MediumJEE Mains2021
A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $\overrightarrow E $ as a function of distance r from centre O is given by
Options:
A)
B)
C)
D)
494
MediumMHT CET2024
In the circuit shown in the following figure, the potential difference cross 3 \mu \mathrm{~F} capacitor is
Options:
A) 4 V
B) 6 V
C) 10 V
D) 16 V
495
MediumJEE Mains2021
What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?
Options:
A) {1 \over {4\pi {\varepsilon _0}}}{q \over {{l^2}}}
B) {1 \over {4\pi {\varepsilon _0}}}{q \over {(2{l^2})}}\left( {2\sqrt 2 - 1} \right)
C) {q \over {4\pi {\varepsilon _0}{{(2l)}^2}}}
D) {1 \over {4\pi {\varepsilon _0}}}{{2q} \over {2{l^2}}}\left( {\sqrt 2 } \right)
496
MediumMHT CET2024
Three condensers of capacities ' \mathrm{C}_1 ', ' \mathrm{C}_2 ', ' \mathrm{C}_3 ' are connected in series with a source of e.m.f. ' V '. The potentials across the three condensers are in the ratio
Options:
A) 1: 1: 1
B) \mathrm{C}_1: \mathrm{C}_2: \mathrm{C}_3
C) \mathrm{C}_1^2: \mathrm{C}_2^2: \mathrm{C}_3^2
D) \frac{1}{\mathrm{C}_1}: \frac{1}{\mathrm{C}_2}: \frac{1}{\mathrm{C}_3}
497
MediumJEE Mains2021
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical?
Options:
A) x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 2}}}
B) x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 3}}}
C) x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}g}}} \right)^{{1 \over 3}}}
D) x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}{g^2}}}} \right)^{{1 \over 3}}}
498
MediumMHT CET2024
When three capacitors of equal capacities are connected in parallel and one of the same capacity, capacitor is connected in series with the combination. The resultant capacity is 4.5 \mu \mathrm{~F}. The capacity of each capacitor is
Options:
A) 5 \mu \mathrm{~F}
B) 7 \mu \mathrm{~F}
C) 6 \mu \mathrm{~F}
D) 8 \mu \mathrm{~F}
499
MediumJEE Mains2021
Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$^\circ with the axis. The ratio of the dipole moment of A and B, {{{p_1}} \over {{p_2}}} is : (take \sin 37^\circ = {3 \over 5}$)
Options:
A) {3 \over 8}
B) {3 \over 2}
C) {2 \over 3}
D) {4 \over 3}
500
MediumMHT CET2024
Two parallel plate air capacitors of same capacity ' C ' are connected in series to a battery of emf ' E '. Then one of the capacitors is completely filled with dielectric material of constant ' K '. The change in the effective capacity of the series combination is
Options:
A) \frac{\mathrm{C}}{2}\left[\frac{\mathrm{~K}+1}{\mathrm{~K}-1}\right]
B) \frac{2}{\mathrm{C}}\left[\frac{\mathrm{K}-1}{\mathrm{~K}+1}\right]
C) \frac{\mathrm{C}}{2}\left[\frac{\mathrm{~K}-1}{\mathrm{~K}+1}\right]
D) \frac{\mathrm{C}}{2}\left[\frac{\mathrm{~K}-1}{\mathrm{~K}+1}\right]^2
501
MediumJEE Mains2021
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $\times 10-$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
Options:
A) 0.485 mC
B) 815.1 nC
C) 8.8 $\mu$C
D) 4.44 $\mu$C
502
MediumMHT CET2024
Seven capacitors each of capacitance 2 \mu \mathrm{~F} are connected in a configuration to obtain an effective capacitance \frac{6}{13} \mu \mathrm{~F}. The combination which will achieve this will have
Options:
A) 5 capacitors in parallel and then 2 capacitors series.
B) 4 capacitors in parallel and then 3 capacitors series.
C) 3 capacitors in parallel and then 4 capacitors in series.
D) 2 capacitors in parallel and then 5 capacitors in series.
503
MediumJEE Mains2021
A certain charge Q is divided into two parts q and (Q $- q). How should the charges Q and q be divided so that q and (Q -$ q) placed at a certain distance apart experience maximum electrostatic repulsion?
Options:
A) Q = 2q
B) Q = 4q
C) Q = 3q
D) Q = ${q \over 2}
504
MediumMHT CET2024
Two identical capacitors have the same capacitance ' C '. One of them is charged to potential \mathrm{V}_1 and other to \mathrm{V}_2. The negative ends of capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is
Options:
A) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1^2+\mathrm{V}_2^2\right)
B) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1^2-\mathrm{V}_2^2\right)
C) \frac{1}{4} C\left(V_1+V_2\right)^2
D) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1-\mathrm{V}_2\right)^2
505
MediumJEE Mains2021
An oil drop of radius 2 mm with a density 3g cm$-3 is held stationary under a constant electric field 3.55 \times 105 V m-$1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s2)
Options:
A) 48.8 $\times$ 1011
B) 1.73 $\times$ 1010
C) 17.3 $\times$ 1010
D) 1.73 $\times$ 1012
506
MediumMHT CET2024
The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is
Options:
A) 1: 2
B) 1: 4
C) 4: 1
D) 2: 1
507
MediumJEE Mains2021
Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
Options:
A) 0.424 nC m$-$2
B) 4.0 nC m$-$2
C) 47.88 C/m
D) 0.07 nC m$-$2
508
MediumMHT CET2024
Air capacitor has capacitance of 1 \mu \mathrm{~F}. Now the space between two plates of capacitor is filled with two dielectrics as shown in figure. The capacitance of the capacitor is [ \mathrm{d}= distance between two plates of capacitor, \mathrm{K}_1 and \mathrm{K}_2 are dielectric constants of first dielectric and second dielectric respectively]
Options:
A) 3 \mu \mathrm{~F}
B) 6 \mu \mathrm{~F}
C) 8 \mu \mathrm{~F}
D) 12 \mu \mathrm{~F}
509
MediumJEE Mains2021
Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both Statement I and Statement II are true
B) Statement I is false but Statement II is true
C) Statement I is true but Statement II is false
D) Both Statement I and Statement II are false
510
MediumMHT CET2024
The function of dielectric in a capacitor is
Options:
A) to reduce the effective potential on plates.
B) to increase the effective potential on plates.
C) to decrease the capacitance.
D) to reduce the plate area of capacitor.
511
MediumJEE Mains2021
An inclined plane making an angle of 30$^\circ with the horizontal is placed in a uniform horizontal electric field 200{N \over C} as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.[g = 9.8 m/s2; \sin 30^\circ = {1 \over 2}; \cos 30^\circ = {{\sqrt 3 } \over 2}$]
Options:
A) 0.46 s
B) 0.92 s
C) 1.3 s
D) 2.3 s
512
MediumMHT CET2024
In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respectively are
Options:
A) 2 A and 3 \mu \mathrm{C}
B) \frac{6}{11} \mathrm{~A} and \frac{12}{7} \mu \mathrm{C}
C) 11 A and 3 \mu \mathrm{C}
D) zero ampere and 3 \mu \mathrm{C}
513
MediumJEE Mains2021
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = ${{\sqrt 3 } \over 2}L$.
Options:
A) {Q \over {4\pi {\varepsilon _0}{L^2}}}
B) {Q \over {3\pi {\varepsilon _0}{L^2}}}
C) {Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}
D) {{\sqrt 3 Q} \over {4\pi {\varepsilon _0}{L^2}}}
514
MediumMHT CET2024
A parallel plate capacitor of capacitance ' C ' is connected to a battery and charged to a potential difference ' V '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V . The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
Options:
A) \frac{3}{2} \mathrm{~CV}^2
B) 8 \mathrm{~CV}^2
C) \frac{13}{2} \mathrm{~CV}^2
D) 18 \mathrm{~CV}^2
515
MediumJEE Mains2021
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow E $ through the shaded area is :
Options:
A) {q \over {24{\varepsilon _0}}}
B) {q \over {48{\varepsilon _0}}}
C) {q \over {4{\varepsilon _0}}}
D) {q \over {8{\varepsilon _0}}}
516
MediumMHT CET2024
A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF . The space between the plates is now filled with two dielectrics, the first having \mathrm{K}_1=3 and thickness \mathrm{d}_1=\mathrm{d} / 3, while the 2^{\text {nd }} has \mathrm{K}_2=6 and thickness d_2=2 \mathrm{~d} / 3. The capacitance of the new capacitor is :
Options:
A) 3.8 pF
B) 20.25 pF
C) 40.5 pF
D) 45 pF
517
MediumJEE Mains2021
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)
Options:
A) {\left( {{{2{q^2}} \over {\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}
B) {\left( {{{{q^2}} \over {2\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}
C) {\left( {{{2\pi {\varepsilon _0}m{d^3}} \over {{q^2}}}} \right)^{{1 \over 2}}}
D) {\left( {{{\pi {\varepsilon _0}m{d^3}} \over {2{q^2}}}} \right)^{{1 \over 2}}}
518
MediumMHT CET2024
A parallel plate capacitor has plate area 40 \mathrm{~cm}^2 and plate separation 2 mm . The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5 . The capacitance of the system is ( \varepsilon_0= permittivity of vacuum)
Options:
A) 24 \varepsilon_0 \mathrm{~F}
B) \frac{3}{10} \varepsilon_0 \mathrm{~F}
C) \frac{10}{3} \varepsilon_0 \mathrm{~F}
D) 10 \varepsilon_0 \mathrm{~F}
519
MediumJEE Mains2021
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $-$Q. The electric field at the centre of cube is :
Options:
A) {{2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)
B) {{ - Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)
C) {Q \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)
D) {{ - 2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)
520
MediumMHT CET2024
A parallel plate capacitor is charged and then isolated. If the separation between the plates is increased, which one of the following statement is NOT correct?
Options:
A) Charge remains constant after it is isolated.
B) Potential difference across the plates decreases.
C) Potential difference across the plates increases.
D) Capacitance of capacitor decreases.
521
MediumJEE Mains2020
Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?
Options:
A) {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}} > F > 0$ for r < R
B) F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$ for r > R
C) F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$ for all r
D) F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}}$ for r < R
522
MediumMHT CET2024
Two circular metal plates each of radius ' r ' are kept parallel to each other distance ' d ' apart. The capacitance of the capacitor formed is ' \mathrm{C}_1 '. If the radius of each of the plates is increased to \sqrt{2} times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' \mathrm{C}_2 '. The ratio of the capacitances \mathrm{C}_1: \mathrm{C}_2 is
Options:
A) 1: 1
B) 1: 2
C) 1: 4
D) 4: 1
523
MediumJEE Mains2020
Two identical electric point dipoles have dipole moments ${\overrightarrow p _1} = p\widehat i and {\overrightarrow p _2} = - p\widehat i and are held on the x axis at distance 'a$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :
Options:
A) {p \over a}\sqrt {{3 \over {2\pi { \in _0}ma}}}
B) {p \over a}\sqrt {{1 \over {\pi { \in _0}ma}}}
C) {p \over a}\sqrt {{1 \over {2\pi { \in _0}ma}}}
D) {p \over a}\sqrt {{2 \over {\pi { \in _0}ma}}}
524
MediumMHT CET2024
The amount of work done in increasing the voltage across the plates of a capacitor form 5 V to 10 V is ' W '. The work done in increasing it from 10 V to 15 V will be (nearly)
Options:
A) 0.6 W
B) W
C) 1.25 W
D) 1.67 W
525
MediumJEE Mains2020
Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then ${{{Q_1}} \over {{Q_2}}}$ is proportional to :
Options:
A) {{x_1^3} \over {x_2^3}}
B) {{x_2^2} \over {x_1^2}}
C) {{{x_1}} \over {{x_2}}}
D) {{{x_2}} \over {{x_1}}}
526
MediumMHT CET2024
Charge on a parallel plate capacitor of capacity C is Q , the electric field intensity between its two plates separated by a distance of t is
Options:
A) \frac{\mathrm{Qt}}{\mathrm{C}}
B) \frac{\mathrm{Q}}{\mathrm{Ct}}
C) \frac{\mathrm{C}}{\mathrm{Qt}}
D) \frac{\mathrm{Ct}}{\mathrm{Q}}
527
MediumJEE Mains2020
Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively. (Take V = 0 at infinity)
Options:
A) V = 0; E = 0
B) V = {{10q} \over {4\pi {\varepsilon _0}R}}; E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}
C) V = {{10q} \over {4\pi {\varepsilon _0}R}}$; E = 0
D) V = 0; $E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}
528
MediumMHT CET2024
A circuit having a self inductance of 1 henry carries a current of 1 A . To prevent the sparking when the circuit is broken, a capacitor which can withstand 500 V is connected across the switch. What is the minimum value of the capacitance of the capacitor?
Options:
A) 2 \mu \mathrm{~F}
B) 4 \mu \mathrm{~F}
C) 6 \mu \mathrm{~F}
D) 8 \mu \mathrm{~F}
529
MediumJEE Mains2020
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then : (assume the remaining portion to be spherical).
Options:
A) v2 = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]
B) v2 = $2y\left[ {{{qQR} \over {4\pi {\varepsilon _0}{{\left( {R + y} \right)}^3}m}} + g} \right]
C) v2 = $2y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]
D) v2 = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}{R^2}ym}} + g} \right]
530
MediumMHT CET2023
A parallel plate capacitor with air medium between the plates has a capacitance of $10 \mu \mathrm{F}. The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant K_1=2 and \mathrm{K}_2=4$. The capacitance of the system will be
Options:
A) 10 $\mu$F
B) 20 $\mu$F
C) 30 $\mu$F
D) 40 $\mu$F
531
MediumJEE Mains2020
A particle of charge q and mass m is subjected to an electric field E = E0 (1 – $ax2) in the x-direction, where a$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
Options:
A) a
B) \sqrt {{2 \over a}}
C) \sqrt {{3 \over a}}
D) \sqrt {{1 \over a}}
532
MediumMHT CET2023
Two condensers one of capacity $\frac{\mathrm{C}}{2} and other capacity \mathrm{C} are connected to a battery of voltage \mathrm{V}$ as shown. The work done in charging fully both the condensers is
Options:
A) \frac{1}{2} CV^2
B) \frac{3}{4} CV^2
C) \frac{3}{2} CV^2
D) {2} CV^2
533
MediumJEE Mains2020
A two point charges 4q and -q are fixed on the x-axis at x = $ - {d \over 2} and x = {d \over 2}$ respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :
Options:
A) increase by ${{3{q^2}} \over {4\pi {\varepsilon _0}d}}
B) increase by ${{2{q^2}} \over {3\pi {\varepsilon _0}d}}
C) decrease by ${{{q^2}} \over {4\pi {\varepsilon _0}d}}
D) decrease by ${{4{q^2}} \over {3\pi {\varepsilon _0}d}}
534
MediumMHT CET2023
Which of the following combination of 7 identical capacitors each of $2 \mu \mathrm{F} gives a capacitance of \frac{10}{11} \mu \mathrm{F}$ ?
Options:
A) 5 in parallel and 2 in series
B) 4 in parallel and 3 in series
C) 3 in parallel and 4 in series
D) 2 in parallel and 5 in series
535
MediumJEE Mains2020
Two charged thin infinite plane sheets of uniform surface charge density ${\sigma _ + } and {\sigma _ - }, where |{\sigma _ + }| > |{\sigma _ - }$|, intersect at right angle. Which of the following best represents the electric field lines for this system :
Options:
A)
B)
C)
D)
536
MediumMHT CET2023
In a parallel plate capacitor with air between the plates, the distance $d$ between the plates is changed and the space is filled with dielectric constant 8. The capacity of the capacitor is increased 16 times, the distance between the plates is
Options:
A) 2d
B) 4d
C) d/2
D) d/4
537
MediumJEE Mains2020
Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :
Options:
A) {{3{Q_2}} \over {4\pi {\varepsilon _0}R}}
B) {{3{Q_1}} \over {4\pi {\varepsilon _0}R}}
C) {{3{Q_1}} \over {16\pi {\varepsilon _0}R}}
D) {{{Q_2}} \over {4\pi {\varepsilon _0}R}}
538
MediumMHT CET2023
In the given figure, the equivalent capacitance between points A and B is
Options:
A) 1.5 C
B) 2 C
C) 3 C
D) 6 C
539
MediumJEE Mains2020
Two isolated conducting spheres S1 and S2 of radius ${2 \over 3}R and {1 \over 3}R have 12 \mu C and –3 \mu $C charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively :
Options:
A) 4.5 $\mu $C on both
B) +4.5 $\mu C and –4.5 \mu $C
C) 6 $\mu C and 3 \mu $C
D) 3 $\mu C and 6 \mu $C
540
MediumMHT CET2023
If the charge on the capacitor is increased by 3 coulombs, the energy stored in it increases by $44 \%$. The original charge on the capacitor is
Options:
A) 10 C
B) 15 C
C) 20 C
D) 25 C
541
MediumJEE Mains2020
A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :
Options:
A) {1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}$Q
B) {1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {2\left( {{R^2} + {r^2}} \right)}}Q
C) {1 \over {4\pi {\varepsilon _0}}}{{\left( {R + 2r} \right)Q} \over {2\left( {{R^2} + {r^2}} \right)}}
D) {1 \over {4\pi {\varepsilon _0}}}{{\left( {2R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}Q
542
MediumMHT CET2023
In the given capacitive network the resultant capacitance between point $\mathrm{A} and \mathrm{B}$ is
Options:
A) 8 $\mu$F
B) 4 $\mu$F
C) 2 $\mu$F
D) 16 $\mu$F
543
MediumJEE Mains2020
A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).
Options:
A)
B)
C)
D)
544
MediumMHT CET2023
The equivalent capacity between terminal $\mathrm{A} and \mathrm{B}$ is
Options:
A) \frac{\mathrm{C}}{4}
B) \frac{3 \mathrm{C}}{4}
C) \frac{\mathrm{C}}{3}
D) \frac{4 \mathrm{C}}{3}
545
MediumJEE Mains2020
A charged particle (mass m and charge q) moves along X-axis with velocity V0. When it passes through the origin it enters a region having uniform electric field $\overrightarrow E = - E\widehat j$ which extends upto x = d. Equation of path of electron in the region x > d is
Options:
A) y = ${{qEd} \over {mV_0^2}}\left( {x - d} \right)
B) y = ${{qEd} \over {mV_0^2}}\left( {{d \over 2} - x} \right)
C) y = ${{qEd} \over {mV_0^2}}x
D) y = ${{qE{d^2}} \over {mV_0^2}}x
546
MediumMHT CET2023
The potential on the plates of capacitor are $+20 \mathrm{~V} and -20 \mathrm{~V}. The charge on the plate is 40 \mathrm{C}$. The capacitance of the capacitor is
Options:
A) 2 F
B) 1 F
C) 4 F
D) 0.5 F
547
MediumJEE Mains2020
Consider a sphere of radius R which carries a uniform charge density $\rho . If a sphere of radius {{R \over 2}} is carved out of it, as shown, the ratio {{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}} of magnitude of electric field {\overrightarrow {{E_A}} } and {\overrightarrow {{E_B}} }$, respectively, at points A and B due to the remaining portion is :
Options:
A) {{17} \over {54}}
B) {{18} \over {54}}
C) {{18} \over {34}}
D) {{21} \over {34}}
548
MediumMHT CET2023
Two spherical conductors of capacities $3 \mu \mathrm{F} and 2 \mu \mathrm{F} are charged to same potential having radii 3 \mathrm{~cm} and 2 \mathrm{~cm} respectively. If '\sigma_1' and '\sigma_2' represent surface density of charge on respective conductors then \frac{\sigma_1}{\sigma_2}$ is
Options:
A) \frac{1}{3}
B) \frac{1}{2}
C) \frac{2}{3}
D) \frac{3}{4}
549
MediumJEE Mains2020
An electric dipole of moment $\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} C.m is at the origin (0, 0, 0). The electric field due to this dipole at \overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k (note that \overrightarrow r .\overrightarrow p = 0$ ) is parallel to :
Options:
A) \left( { + \widehat i + 3\widehat j - 2\widehat k} \right)
B) \left( { + \widehat i - 3\widehat j - 2\widehat k} \right)
C) \left( { - \widehat i + 3\widehat j - 2\widehat k} \right)
D) \left( { - \widehat i - 3\widehat j + 2\widehat k} \right)
550
MediumMHT CET2023
Three identical capacitors of capacitance '$\mathrm{C}$' each are connected in series and this connection is connected in parallel with one more such identical capacitor. Then the capacitance of whole combination is
Options:
A) 3 \mathrm{C}
B) 2 \mathrm{C}
C) \frac{4}{3} \mathrm{C}
D) \frac{3}{4} \mathrm{C}
551
MediumJEE Mains2020
Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is :
Options:
A) (R1/R2)2
B) (R2/R1)
C) (R1/R2)3
D) R1/R2
552
MediumMHT CET2023
A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$\mathrm{K}$' is inserted between the plates and then taken out. Then electric field between the plates
Options:
A) remains the same
B) increases
C) decreases
D) becomes zero
553
MediumJEE Mains2020
A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)
Options:
A)
B)
C)
D)
554
MediumMHT CET2023
Two identical capacitors have the same capacitance '$C'. One of them is charged to a potential V_1 and the other to V_2$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
Options:
A) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1^2-\mathrm{V}_2^2\right)
B) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1^2+\mathrm{V}_2^2\right)
C) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1-\mathrm{V}_2\right)^2
D) \frac{1}{4} \mathrm{C}\left(\mathrm{V}_1+\mathrm{V}_2\right)^2
555
MediumJEE Mains2020
Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is :
Options:
A) {3{\sqrt 3 q} \over 4{\pi {\varepsilon _0}{d^2}}}
B) {{\sqrt 3 q} \over 4{\pi {\varepsilon _0}{d^2}}}
C) {{\sqrt 3 q} \over {\pi {\varepsilon _0}{d^2}}}
D) {{2\sqrt 3 q} \over {\pi {\varepsilon _0}{d^2}}}
556
MediumMHT CET2023
If a capacitor of capacity $900 ~\mu \mathrm{F} is charged to 100 \mathrm{~V} and its total energy is transferred to a capacitor of capacity 100 ~\mu \mathrm{F}$, then its potential will be
Options:
A) 30 \mathrm{~V}
B) 200 \mathrm{~V}
C) 300 \mathrm{~V}
D) 400 \mathrm{~V}
557
MediumJEE Mains2020
In finding the electric field using Gauss Law the formula $\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}} is applicable. In the formula {{\varepsilon _0}}$ is permittivity of free space, A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?
Options:
A) Only when $\left| {\overrightarrow E } \right|$ = constant on the surface.
B) For any choice of Gaussian surface.
C) Only when the Gaussian surface is an
equipotential surface.
D) Only when the Gaussian surface is an
equipotential surface and $\left| {\overrightarrow E } \right|$ is constant on
the surface.
558
MediumMHT CET2023
Two dielectric slabs having dielectric constant '$\mathrm{K}_1' and '\mathrm{K}_2' of thickness \frac{\mathrm{d}}{4} and \frac{3 \mathrm{~d}}{4} are inserted between the plates as shown in figure. The net capacitance between A and B is \left[\varepsilon_0\right.$ is permittivity of free space]
Options:
A) \frac{2 \mathrm{~A} \varepsilon_0}{\mathrm{~d}}\left[\frac{\mathrm{K}_1 \mathrm{~K}_2}{3 \mathrm{~K}_1+\mathrm{K}_2}\right]
B) \frac{3 \mathrm{~A} \varepsilon_0}{\mathrm{~d}}\left[\frac{\mathrm{K}_1+\mathrm{K}_2}{\mathrm{~K}_1 \mathrm{~K}_2}\right]
C) \frac{3 \mathrm{~A}_0}{2 \mathrm{~d}}\left[\frac{\mathrm{K}_1+\mathrm{K}_2}{\mathrm{~K}_1 \mathrm{~K}_2}\right]
D) \frac{4 A \varepsilon_0}{d}\left[\frac{K_1 K_2}{3 K_1+K_2}\right]
559
MediumJEE Mains2020
Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the region shown between them is given by :
Options:
A) {\sigma \over {{ \in _0}}}\left[ {\left( {1 + {{\sqrt 3 } \over 2}} \right)\widehat y + {{\widehat x} \over 2}} \right]
B) {\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y + {{\widehat x} \over 2}} \right]
C) {\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y - {{\widehat x} \over 2}} \right]
D) {\sigma \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} \right)\widehat y - {{\widehat x} \over 2}} \right]
560
MediumMHT CET2023
A parallel plate capacitor has plate area '$\mathrm{A}' and separation between plates is 'd'. It is charged to a potential difference of \mathrm{V}_0 volt. The charging battery is then disconnected and plates are pulled apart three times the initial distance. The work done to increase the distance between the plates is \left(\varepsilon_0=\right.$ permittivity of free space)
Options:
A) \frac{3 \varepsilon_0 \mathrm{AV}_0{ }^2}{\mathrm{~d}}
B) \frac{\varepsilon_0 \mathrm{AV}_0^2}{2 \mathrm{~d}}
C) \frac{\varepsilon_0 \mathrm{AV}_0{ }^2}{3 \mathrm{~d}}
D) \frac{\varepsilon_0 \mathrm{AV}_0{ }^2}{\mathrm{~d}}
561
MediumJEE Mains2019
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $\rho (r) = kr, where r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite points, at equal distance, a$ from the centre. If A and B do not experience any force, then :
Options:
A) a = {8^{ - 1/4}}R
B) a = {2^{ - 1/4}}R
C) a = {{3R} \over {{2^{1/4}}}}
D) a = {R \over {\sqrt 3 }}
562
MediumMHT CET2023
Two capacitors $\mathrm{C}_1=3 \mu \mathrm{F} and \mathrm{C}_2=2 \mu \mathrm{F} are connected in series across d.c. source of 100 \mathrm{~V}. The ratio of the potential across C_2 to C_1$ is
Options:
A) 2: 3
B) 3: 2
C) 6: 5
D) 5: 6
563
MediumJEE Mains2019
A point dipole $\overrightarrow p = - {p_0}\widehat x$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)
Options:
A) {{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}
B) 0,{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}
C) {{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}
D) 0,{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}
564
MediumMHT CET2023
The mean electrical energy density between plates of a charged air capacitor is (where $\mathrm{q}= charge on capacitor, \mathrm{A}=$ Area of capacitor plate)
Options:
A) \frac{q^2}{2 \varepsilon_0 A^2}
B) \frac{\mathrm{q}}{2 \varepsilon_0 \mathrm{~A}^2}
C) \frac{\mathrm{q}^2}{2 \varepsilon_0 \mathrm{~A}}
D) \frac{\varepsilon_0 \mathrm{~A}}{\mathrm{q}^2}
565
MediumJEE Mains2019
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\overrightarrow P $ as shown. In this case :
Options:
A) surface charge density on the inner surface is uniform and equal to ${{\left( {Q/2} \right)} \over {4\pi {a^2}}}
B) surface charge density on the inner surface of the shell is zero everywhere
C) surface charge density on the outer surface depends on $\left| {\overrightarrow P } \right|
D) electric field outside the shell is the same as that of a point charge at the centre of the shell
566
MediumMHT CET2023
A parallel combination of two capacitors of capacities '$2 ~\mathrm{C}' and '\mathrm{C}' is connected across 5 \mathrm{~V} battery. When they are fully charged, the charges and energies stored in them be '\mathrm{Q}_1', 'Q_2' and 'E_1', 'E_2' respectively. Then \frac{E_1-E_2}{Q_1-Q_2} in \mathrm{J} / \mathrm{C}$ is (capacity is in Farad, charge in Coulomb and energy in J)
Options:
A) \frac{5}{4}
B) \frac{4}{5}
C) \frac{5}{2}
D) \frac{2}{5}
567
MediumJEE Mains2019
In free space, a particle A of charge 1$\mu C is held fixed at a point P. Another particle B of the same charge and mass 4\mu g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : \left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]
Options:
A) 1.0 m/s
B) 6.32 $ \times $ 104 m/s
C) 2.0 $ \times $ 103 m/s
D) 1.5 $ \times $ 102 m/s
568
MediumMHT CET2023
The capacitance of a parallel plate capacitor is $2.5 ~\mu \mathrm{F}. When it is half filled with a dielectric as shown in figure, its capacitance becomes 5 ~\mu \mathrm{F}$. The dielectric constant of the dielectric is
Options:
A) 7.5
B) 3
C) 4
D) 5
569
MediumJEE Mains2019
A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :
Options:
A) \sqrt {{2 \over m}} {\left( {{2 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}
B) \sqrt {{2 \over m}} {\left( {{1 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}
C) \sqrt {{2 \over m}} {\left( {{1 \over {5}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}
D) \sqrt {{2 \over m}} {\left( {{4 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}
570
MediumMHT CET2023
The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1 and C_2 with their capacitance in the ratio 1: 2$ so that energy stored in these two cases becomes same is
Options:
A) 3: \sqrt{2}
B) \sqrt{2}: 3
C) 2: 9
D) 9: 2
571
MediumJEE Mains2019
Four point charges –q, +q, +q and –q are placed on y-axis at y = –2d, y = –d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as :-
Options:
A) E \propto {1 \over D^3}
B) E \propto {1 \over D}
C) E \propto {1 \over D^4}
D) E \propto {1 \over D^2}
572
MediumMHT CET2023
The potential energy of charged parallel plate capacitor is $v_0. If a slab of dielectric constant \mathrm{K}$ is inserted between the plates, then the new potential energy will be
Options:
A) \frac{v_0}{\mathrm{~K}}
B) v_0 \mathrm{~K}^2
C) \frac{v_0}{\mathrm{~K}^2}
D) \mathrm{v}_0^2
573
MediumJEE Mains2019
A system of three charges are placed as shown in the figure : If D >> d, the potential energy of the system is best given by :
Options:
A) {1 \over {4\pi {\varepsilon _0}}}\left[ { {{{q^2}} \over d} + {{qQd} \over {{D^2}}}} \right]
B) {1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {2{D^2}}}} \right]
C) {1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {{D^2}}}} \right]
D) {1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} + {2{qQd} \over {{D^2}}}} \right]
574
MediumMHT CET2022
A parallel plate air capacitor has a uniform electric field 'E' in the space between the plates. Area of each plate is A and the distance between the plates is '$\mathrm{d}'. The energy stored in the capacitor is \left[\varepsilon_0=\right.$ permittivity of free space)
Options:
A) 2 \varepsilon_0 \mathrm{EAd}
B) \frac{1}{2} \varepsilon_0 \mathrm{E}^2 \mathrm{Ad}
C) \frac{\varepsilon_0 \mathrm{E}^2}{2 \mathrm{Ad}}
D) \frac{\mathrm{E}^2 \mathrm{Ad}}{2 \varepsilon_0}
575
MediumJEE Mains2019
The electric field in a region is given by $\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge $ , where E is in NC–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = –5 is V2, then V1 – V2 is :-
Options:
A) –520 V
B) 180 V
C) –48 V
D) 320 V
576
MediumMHT CET2022
A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved further apart by pulling them by means of insulating handles, then
Options:
A) the capacitance of the capacitor increases
B) the charge on the capacitor decreases
C) the voltage across the capacitor increases
D) the energy stored in the capacitor decreases
577
MediumJEE Mains2019
A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-
Options:
A) v \propto \left( {{r \over {{r_0}}}} \right)
B) v \propto \ln \left( {{r \over {{r_0}}}} \right)
C) v \propto {e^{ + r/{r_0}}}
D) v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)}
578
MediumMHT CET2022
The force between the plates of a parallel plate capacitor of capacitance '$\mathrm{C}' and distance of separation of the plates '\mathrm{d}' with a potential difference '\mathrm{V}$' between the plates is
Options:
A) \frac{\mathrm{V}^2 \mathrm{~d}}{\mathrm{C}}
B) \frac{\mathrm{C}^2 \mathrm{~V}^2}{\mathrm{~d}^2}
C) \frac{\mathrm{CV}^2}{2 \mathrm{~d}}
D) \frac{\mathrm{C}^2 \mathrm{~V}^2}{2 \mathrm{~d}^2}
579
MediumJEE Mains2019
The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g = 10 m/s2)
Options:
A) tan–1(5.0)
B) tan–1(2.0)
C) tan–1(0.5)
D) tan–1(0.2)
580
MediumMHT CET2021
A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the e.m.f. of the battery. The ratio of the energy stored int he capacitor to the work done by the battery will be
Options:
A) 2
B) \frac{1}{2}
C) 1
D) \frac{1}{4}
581
MediumJEE Mains2019
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –4 Q, the new potential difference between the same two surfaces is :
Options:
A) V
B) 2V
C) –2V
D) 4V
582
MediumMHT CET2021
Capacitors of capacities $\mathrm{C}_1, \mathrm{C}_2 and \mathrm{C}_3 are connected in series. If the combination is connected to a supply of '\mathrm{V}' volt, then potential difference across capacitor '\mathrm{C}_1$' is
Options:
A) \frac{\mathrm{C}_2 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_2}{\mathrm{C}_1 \mathrm{C}_2 V}
B) \frac{\mathrm{C}_2 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_2}{\mathrm{C}_1 \mathrm{C}_2 \mathrm{C}_3 \mathrm{V}}
C) \frac{\mathrm{C}_2 \mathrm{C}_3 \mathrm{V}}{\mathrm{C}_2 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_2}
D) \frac{\mathrm{C}_1 \mathrm{C}_2 \mathrm{C}_3 \mathrm{V}}{\mathrm{C}_2 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_3+\mathrm{C}_1 \mathrm{C}_2}
583
MediumJEE Mains2019
Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :
Options:
A) 2q\ell \widehat j
B) \left( {q\ell } \right){{\widehat i + \widehat j} \over {\sqrt 2 }}
C) \sqrt 3 \,q\ell {{\widehat j - \widehat i} \over {\sqrt 2 }}
D) - \sqrt 3 \,q\ell \widehat j
584
MediumMHT CET2021
The plates of a parallel plate capacitor of capacity '$\mathrm{C}_1' are moved closer together until they ant half their original separation. The new capacitance '\mathrm{C}_2$' is
Options:
A) \mathrm{C}_2=\frac{C_1}{2}
B) \mathrm{C}_2=\mathrm{C}_1
C) \mathrm{C}_2=2 \mathrm{C}_1
D) \mathrm{C}_2=3 \mathrm{C}_1
585
MediumJEE Mains2019
There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R (t) is :
Options:
A)
B)
C)
D)
586
MediumMHT CET2021
Two identical capacitors have the same capacitance '$\mathrm{C}'. One of them is charged to potential '\mathrm{V_1}' and the other to \mathrm{V_2}$. The negative ends of the capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is
Options:
A) \frac{1}{4} C\left(V_1-V_2\right)^2
B) \frac{1}{2} C\left(v_1^2+v_2^2\right)
C) \frac{1}{2} C\left(V_1^2-V_2^2\right)
D) \frac{1}{2} C\left(V_1+V_2\right)^2
587
MediumJEE Mains2019
An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?
Options:
A) - 7 $ \times $ 10–27 J
B) - 9 \times $ 10–20 J
C) - 10 \times $ 10–29 J
D) - 20 \times $ 10–18 J
588
MediumMHT CET2021
If the potential difference across a capacitor is increased from $5 \mathrm{~V} to 15 \mathrm{~V}$, then the ratio of final energy to initial energy stored in the capacitor is
Options:
A) 1: 3
B) 27: 1
C) 3: 1
D) 9: 1
589
MediumJEE Mains2019
The given graph shows variation (with distance r form centre) of :
Options:
A) Electric field of a uniformly charged sphere
B) Electric field of a uniformly charged spherical shell
C) Potential of a uniformly charged sphere
D) Potential of a uniformly charged spherical shell
590
MediumMHT CET2021
The charge on each capacitor when a voltage source os 15 V is connected in the circuit as shown, is
Options:
A) 75 $\mu$C
B) 150 $\mu$C
C) 30 $\mu$C
D) 60 $\mu$C
591
MediumJEE Mains2019
Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :
Options:
A) {{ - q} \over {1 + \sqrt 2 }}
B) + q
C) -$ 2q
D) {{ - \sqrt 2 q} \over {\sqrt 2 + 1}}
592
MediumMHT CET2021
Two parallel plates with dielectric placed between the plates are as shown in figure. The resultant capacity of capacitor will be [A = area of plate. $t_1, t_2 and t_3 are thickness of dielectric slabs, \mathrm{k}_1, \mathrm{k}_2 and \mathrm{k}_3$ are dielectric constants.
Options:
A) \frac{A \varepsilon_0}{\left[\frac{t_1+t_2+t_3}{k_1+k_2+k_3}\right]}
B)
\frac{A \varepsilon_0\left(k_1 k_2 k_3\right)}{t_1 t_2 t_3}
C)
A \varepsilon_0\left[\frac{k_1}{t_1}+\frac{k_2}{t_2}+\frac{k_3}{t_3}\right]
D)
\frac{A \varepsilon_0}{\left[\frac{t_1}{k_1}+\frac{t_2}{k_2}+\frac{t_3}{k_3}\right]}
593
MediumJEE Mains2019
Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -
Options:
A) {{{Q_2}} \over {4\pi {\varepsilon _0}}}
B) {{{Q^2}} \over {2\sqrt 2 \pi {\varepsilon _0}}}
C) {{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 3 }}} \right)
D) {{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 5 }}} \right)
594
MediumMHT CET2021
In parallel plate capacitor, electric field between the plates is '$E'. If the charge on the plates is 'Q$' then the force on each plate is
Options:
A) QE
B) \frac{\mathrm{QE}^2}{2}
C) \mathrm{QE}^2
D) \frac{\mathrm{QE}}{2}
595
MediumJEE Mains2019
Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = $\left( {{y \over 3}} \right), the force on Q will be close to - \left( {{y \over 3} > > 2a} \right)
Options:
A) 9F
B) 3F
C) F/3
D) 27F
596
MediumMHT CET2021
If the charge on the capacitor is increased by 2 C the energy stored in it increased by 21%. Total original charge on the capacitor is
Options:
A) 10 C
B) 5 C
C) 20 C
D) 15 C
597
MediumJEE Mains2019
A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -
Options:
A) {{Q\left( {{a^2} + {b^2} + {c^2}} \right)} \over {4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}
B) {Q \over {4\pi {\varepsilon _0}\left( {a + b + c} \right)}}
C) {Q \over {12\pi {\varepsilon _0}}}{{ab + bc + ca} \over {abc}}
D) {{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}
598
MediumMHT CET2021
When the battery across the plates of a charged condenser is disconnected and a dielectric slab is introduced between its plates then the energy stored
Options:
A) becomes infinity
B) does not change
C) increases
D) decreases
599
MediumJEE Mains2019
Two electric dipoles, A, B with respective dipole moments ${\overrightarrow d _A} = - 4qai and {\overrightarrow d _B} = - 2qai$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -
Options:
A) {{\sqrt 2 R} \over {\sqrt 2 + 1}}
B) {R \over {\sqrt 2 + 1}}
C) {{\sqrt 2 R} \over {\sqrt 2 - 1}}
D) {R \over {\sqrt 2 - 1}}
600
MediumMHT CET2021
In the given figure potential at point 'A' is 900 volt and point 'B' is earthed. What will be the potential at point 'P' ?
Options:
A) 900 V
B) 100 V
C) 300 V
D) 600 V
601
MediumJEE Mains2019
Two point charges q1$\left( {\sqrt {10} \mu C} \right) and q2(- 25 \mu C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, [take {1 \over {4\pi { \in _0}}} = 9 \times 109 Nm2C-$2]
Options:
A) \left( {63\widehat i - 27\widehat j} \right) \times {10^2}
B) \left( { - 63\widehat i + 27\widehat j} \right) \times {10^2}
C) \left( {81\widehat i - 81\widehat j} \right) \times {10^2}
D) \left( { - 81\widehat i + 81\widehat j} \right) \times {10^2}
602
MediumMHT CET2021
Two identical parallel plate air capacitors are connected in series to a battery of emf '$\mathrm{V}'. If one of the capacitor is inserted in liquid of dielectric constant '\mathrm{K}$' then, potential difference of the other capacitor will become
Options:
A) \frac{\mathrm{K}-1}{\mathrm{KV}}
B) \frac{\mathrm{K}+1}{\mathrm{KV}}
C) \left(\frac{\mathrm{KV}}{\mathrm{K}+1}\right)
D) \frac{\mathrm{KV}}{\mathrm{K}-1}
603
MediumJEE Mains2019
Charge is distributed within a sphere of radius R with a volume charge density $\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :
Options:
A) a log $\left( {1 - {Q \over {2\pi aA}}} \right)
B) {a \over 2} log \left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)
C) a log $\left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)
D) {a \over 2} log \left( {1 - {Q \over {2\pi aA}}} \right)
604
MediumMHT CET2021
A condenser of capacity '$\mathrm{C}_1' is charged to potential '\mathrm{V}_1' and then disconnected. Uncharged capacitor of capacity '\mathrm{C}_2' is connected in parallel with '\mathrm{C}_1'. The resultant potential '\mathrm{V}_2$' is
Options:
A) \frac{V_1 C_2}{C_1}
B) \frac{\mathrm{C}_2}{\mathrm{C}_1+\mathrm{C}_2}
C) \frac{C_1 V_1}{C_2}
D) \frac{C_1 V_1}{C_1+C_2}
605
MediumJEE Mains2019
Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :
Options:
A) - {Q \over 4}
B) + ${Q \over 2}
C) + ${Q \over 4}
D) - {Q \over 2}
606
MediumMHT CET2021
The resultant capacity between points A and B in the given circuit is
Options:
A) C
B) \mathrm{\frac{C}{3}}
C) 3C
D) 2C
607
MediumJEE Mains2019
For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :
Options:
A) {R \over {\sqrt 5 }}
B) {R \over {\sqrt 2 }}
C) R
D) R$\sqrt 2
608
MediumMHT CET2021
An air filled parallel plate capacitor has a capacity $2 \mathrm{~pF}. The sepeartion of the plates is doubled and the interspace between the plates is filled with dielectric material, then the capacity is increased to 6 ~\mathrm{pF}$. The dielectric constant of the material is
Options:
A) 3
B) 6
C) 2
D) 4
609
MediumJEE Mains2018
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :
Options:
A) F
B) {{3F} \over 4}
C) {{3F} \over 8}
D) {{F} \over 2}
610
MediumMHT CET2021
In the arrangement of the capacitors as shown in figure, each capacitor is of 6 $\mu$F, then equivalent capacity between points A and B is
Options:
A) 12 $\mu$F
B) 6 $\mu$F
C) 4 $\mu$F
D) 10 $\mu$F
611
MediumJEE Mains2018
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $ + \sigma , - \sigma and + \sigma $ respectively. The potential of shell B is :
Options:
A) {\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over c} + a} \right]
B) {\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over a} + c} \right]
C) {\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over b} + c} \right]
D) {\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over b} + a} \right]
612
MediumMHT CET2021
A parallel plate air capacitor is charged upto 100 V. A plate 2 mm thick is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by 1.6 mm. The dielectric constant of the thick plate is
Options:
A) 4
B) 5
C) 2
D) 3
613
MediumJEE Mains2018
A solid ball of radius R has a charge density $\rho given by \rho = \rho o (1 - {\raise0.5ex\hbox{\scriptstyle r} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle R}}) for 0 \le r \le $ R. The electric field outside the ball is :
Options:
A) {{{\rho _o}{R^3}} \over {{ \in _o}{r^2}}}
B) {{{\rho _o}{R^3}} \over {12{ \in _o}{r^2}}}
C) {{4{\rho _o}{R^3}} \over {3{ \in _o}{r^2}}}
D) {{3{\rho _o}{R^3}} \over {4{ \in _o}{r^2}}}
614
MediumMHT CET2021
A parallel plate capacitor filled with oil of a dielectric constant 3 between the plates has capacitance 'C'. If the oil is removed, then the capacitance of the capacitor will be
Options:
A) \mathrm{\frac{C}{\sqrt3}}
B) 3C
C) \sqrt3$C
D) \mathrm{\frac{C}{3}}
615
MediumJEE Mains2018
A charge $Q is placed at a distance a/2$ above the center of the square surface of edge a as shown in the figure. The electric flux through the square surface is
Options:
A) {Q \over {{ \in _0}}}
B) {Q \over {2{ \in _0}}}
C) {Q \over {3{ \in _0}}}
D) {Q \over {6{ \in _0}}}
616
MediumMHT CET2020
Two capacitors of capacities 2 \mu \mathrm{~F} and 4 \mu \mathrm{~F} are connected in parallel. A third capacitor of 6 \mu \mathrm{~F} capacity is connected in series with this combination. A battery of 12 V is connected across this combination. The charge on 2 \mu \mathrm{~F} capacitor is
Options:
A) 12\mu \mathrm{C}
B) 11 \mu \mathrm{C}
C) 14 \mu \mathrm{C}
D) 16 \mu \mathrm{C}
617
MediumJEE Mains2018
A body of mass $M and charge q is connected to spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x=0, with an amplitude A. An electric field E is applied along the x$-direction. Which of the following statements is correct ?
Options:
A) The new equilibrium position is at a distance ${{qE} \over {2k}} from x=0.
B) The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} + {1 \over 2}{{{q^2}{E^2}} \over k}.
C) The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} - {1 \over 2}{{{q^2}{E^2}} \over k}.
D) The new equilibrium position is at a distance ${{2qE} \over k} from x=0.
618
MediumMHT CET2020
Five capacitors each of capacity $C are connected as shown in figure. If their resultant capacity is 2 \mu \mathrm{F}$, then the capacity of each condenser is
Options:
A) 5 $\mu$F
B) 2 $\mu$F
C) 2.5 $\mu$F
D) 10 $\mu$F
619
MediumJEE Mains2017
Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be ${\Phi _1}, {\Phi _2}, {\Phi _3} and {\Phi _4}$. Then :
Options:
A) {\Phi _1} < {\Phi _2} = {\Phi _3} > {\Phi _4}
B) {\Phi _1} > {\Phi _2} > {\Phi _3} > {\Phi _4}
C) {\Phi _1} = {\Phi _2} = {\Phi _3} = {\Phi _4}
D) {\Phi _1} > {\Phi _3} ; {\Phi _2} < {\Phi _4}
620
MediumMHT CET2020
The capacitance of a parallel plate capacitor with air as medium is $3 \mu \mathrm{F}. With the introduction of a dielectric medium between the plates, the capacitance becomes 15 \mu \mathrm{F}. The permittivity of the medium in \mathrm{SI} unit is [\varepsilon_0=8.85 \times 10^{-12} \mathrm{SI}$ unit]
Options:
A) 8.845 \times 10^{-11}
B) 0.4425 \times 10^{-10}
C) 15
D) 5
621
MediumJEE Mains2017
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P,$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field ?
Options:
A) 589.5 V
B) 589.2 V
C) 589.4 V
D) 589.6 V
622
MediumMHT CET2019
In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2 . If the initial capacity of the capacitor is 4 \mu \mathrm{~F}. then its new capacity is
Options:
A) 32 \mu \mathrm{~F}
B) 18 \mu \mathrm{~F}
C) 8 \mu \mathrm{~F}
D) 44 \mu \mathrm{~F}
623
MediumJEE Mains2017
An electric dipole has a fixed dipole moment $\overrightarrow p , which makes angle \theta with respect to x-axis. When subjected to an electric field \mathop {{E_1}}\limits^ \to = E\widehat i , it experiences a torque \overrightarrow {{T_1}} = \tau \widehat k . When subjected to another electric field \mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j it experiences a torque \mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to . The angle \theta$ is:
Options:
A) 90o
B) 45o
C) 30o
D) 60o
624
MediumMHT CET2019
Which of the following combinations of 7 identical capacitors each of 2 \mu \mathrm{~F} gives a resultant capacitance of 10 / 11 \mu \mathrm{~F} ?
Options:
A) 3 in parallel and 4 in series
B) 2 in parallel and 5 in series
C) 4 in parallel and 3 in series
D) 5 in parallel and 2 in series
625
MediumJEE Mains2016
Within a spherical charge distribution of charge density $\rho (r), N equipotential surfaces of potential V0, V0 + \Delta V, V0 + 2\Delta V, .......... V0 + N\Delta V (\Delta V > 0), are drawn and have increasing radii r0, r1, r2,..........rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and \Delta $V then :
Options:
A) \rho (r) \alpha $ r
B) \rho $ (r) = constant
C) \rho (r) \alpha {1 \over r}
D) \rho (r) \alpha {1 \over {{r^2}}}
626
MediumNEET2025
The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K_1 and K_2 with thickness \frac{3}{8} d and \frac{d}{2}, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K_1=1.25 K_2, the value of K_1 is:
Options:
A) 1.60
B) 1.33
C) 2.66
D) 2.33
627
MediumJEE Mains2016
The potential (in volts) of a charge distribution is given by. V(z) = 30 $- 5x2 for \left| z \right| \le 1 m. V(z) = 35 - 10 \left| z \right| for \left| z \right| \ge 1 m. V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume {\rho _0} (in units of {\varepsilon _0}$) which is spread over a certain region, then choose the correct statement.
Options:
A) {\rho _0} = 10 {\varepsilon _0} for \left| z \right| \le 1 m and {\rho _0} = 0$ elsewhere
B) {\rho _0} = 20 {\varepsilon _0}$ in the entire region
C) {\rho _0} = 40 {\varepsilon _0}$ in the entire region
D) {\rho _0} = 20 {\varepsilon _0} for \left| z \right| \le 1 m and {\rho _0} = 0$ elsewhere
628
MediumNEET2024
A $12 \mathrm{~pF} capacitor is connected to a 50 \mathrm{~V} battery, the electrostatic energy stored in the capacitor in \mathrm{nJ}$ is
Options:
A) 15
B) 7.5
C) 0.3
D) 150
629
MediumJEE Mains2016
The region between two concentric spheres of radii $'a' and 'b', respectively (see figure), have volume charge density \rho = {A \over r}, where A is a constant and r$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :
Options:
A) {{2Q} \over {\pi \left( {{a^2} - {b^2}} \right)}}
B) {{2Q} \over {\pi \,{a^2}}}
C) {Q \over {2\pi \,{a^2}}}
D) {Q \over {2\pi \,\left( {{b^2} - {a^2}} \right)}}
630
MediumNEET2024
The capacitance of a capacitor with charge $q and a potential difference V$ depends on
Options:
A) both $q and V
B) the geometry of the capacitor
C) q$ only
D) V$ only
631
MediumJEE Mains2015
A long cylindrical shell carries positives surfaces change $\sigma in the upper half and negative surface charge - \sigma $ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)
Options:
A)
B)
C)
D)
632
MediumNEET2024
The steady state current in the circuit shown below is :
Options:
A) 0.67 A
B) 1.5 A
C) 2 A
D) 1 A
633
MediumJEE Mains2014
Assume that an electric field $\overrightarrow E = 30{x^2}\widehat i exists in space. Then the potential difference {V_A} - {V_O}, where {V_O} is the potential at the origin and {V_A} the potential at x=2 m$ is :
Options:
A) 120 J/C
B) -120 J/C
C) -80 J/C
D) 80 J/C
634
MediumNEET2024
In the following circuit, the equivalent capacitance between terminal A and terminal B is :
Options:
A) 2 $\mu$F
B) 1 $\mu$F
C) 0.5 $\mu$F
D) 4 $\mu$F
635
MediumJEE Mains2013
Two charges, each equals to $q, are kept at x=-a and x=a on the x-axis. A particle of mass m and charge {q_0} = {q \over 2} is placed at the origin. If charge {q_0} is given a small displacement \left( {y < < a} \right) along the y$-axis, the net force acting on the particle is proportional to
Options:
A) y
B) -y
C) {1 \over y}
D) -{1 \over y}
636
MediumNEET2024
If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then A. the charge stored in it, increases. B. the energy stored in it, decreases. C. its capacitance increases. D. the ratio of charge to its potential remains the same. E. the product of charge and voltage increases. Choose the most appropriate answer from the options given below:
Options:
A) A, B and E only
B) A, C and E only
C) B, D and E only
D) A, B and C only
637
MediumJEE Mains2013
A charge $Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A$ is
Options:
A) {Q \over {8\pi {\varepsilon _0}L}}
B) {{3Q} \over {4\pi {\varepsilon _0}L}}
C) {Q \over {4\pi {\varepsilon _0}L\,\ln \,2}}
D) {{Q\ln \,2} \over {4\pi {\varepsilon _0}L\,{}^s}}
638
MediumNEET2023
The equivalent capacitance of the arrangement shown in figure is:
Options:
A) 30 $\mu$F
B) 15 $\mu$F
C) 25 $\mu$F
D) 20 $\mu$F
639
MediumJEE Mains2012
This question has statement- $1 and statement- 2. Of the four choices given after the statements, choose the one that best describe the two statements. An insulating solid sphere of radius R has a uniformly positive charge density \rho . As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero. Statement- 1: When a charge q is take from the centre of the surface of the sphere its potential energy changes by {{q\rho } \over {3{\varepsilon _0}}} Statement- 2: The electric field at a distance r\left( {r < R} \right) from the center of the sphere is {{\rho r} \over {3{\varepsilon _0}}}.
Options:
A) Statement- $1 is true, Statement- 2 is true; Statement- 2 is not the correct explanation of Statement- 1$.
B) Statement $1 is true, Statement 2$ is false.
C) Statement $1 is false, Statement 2$ is true.
D) Statement- $1 is true, Statement- 2 is true; Statement- 2 is the correct explanation of Statement- 1$.
640
MediumNEET2023
To produce an instantaneous displacement current of $2 \mathrm{~mA} in the space between the parallel plates of a capacitor of capacitance 4 ~\mu \mathrm{F}, the rate of change of applied variable potential difference \left(\frac{\mathrm{dV}}{\mathrm{dt}}\right)$ must be :-
Options:
A) 800 \mathrm{~V} / \mathrm{s}
B) 500 \mathrm{~V} / \mathrm{s}
C) 200 \mathrm{~V} / \mathrm{s}
D) 400 \mathrm{~V} / \mathrm{s}
641
MediumJEE Mains2012
In a uniformly charged sphere of total charge $Q and radius R, the electric field E$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
Options:
A)
B)
C)
D)
642
MediumNEET2023
The equivalent capacitance of the system shown in the following circuit is:
Options:
A) 3$\mu$F
B) 6$\mu$F
C) 9$\mu$F
D) 2$\mu$F
643
MediumJEE Mains2011
Two identical charged spheres suspended from a common point by two massless strings of length $l are initially a distance d\left( {d < < 1} \right) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity v. Then as a function of distance x$ between them,
Options:
A) v\, \propto \,{x^{ - 1}}
B) y\, \propto \,{x^{{\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}
C) v\, \propto \,x
D) v\, \propto \,{x^{ - {\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}
644
MediumNEET2022
The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to
Options:
A) {C \over 4}
B) 2C
C) {C \over 2}
D) 4C
645
MediumJEE Mains2011
The electrostatic potential inside a charged spherical ball is given by $\phi = a{r^2} + b where r is the distance from the center and a,b$ are constants. Then the charge density inside the ball is:
Options:
A) - 6a{\varepsilon _0}r
B) - 24\pi a{\varepsilon _0}
C) - 6a{\varepsilon _0}
D) - 24\pi {\varepsilon _0}r
646
MediumNEET2022
The effective capacitances of two capacitors are 3 $\muF and 16 \mu$F, when they are connected in series and parallel respectively. The capacitance of two capacitors are :
Options:
A) 1.2 $\muF, 1.8 \mu$F
B) 10 $\muF, 6 \mu$F
C) 8 $\muF, 8 \mu$F
D) 12 $\muF, 4 \mu$F
647
MediumJEE Mains2010
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30^ \circ } with each other. When suspended in a liquid of density 0.8g c{m^{ - 3}}, the angle remains the same. If density of the material of the sphere is 1.6 g c{m^{ - 3}},$ the dielectric constant of the liquid is
Options:
A) 4
B) 3
C) 2
D) 1
648
MediumNEET2022
A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostatic energy stored by the system (b) is
Options:
A) 4.5 $\times 10-$6 J
B) 3.25 $\times 10-$6 J
C) 2.25 $\times 10-$6 J
D) 1.5 $\times 10-$6 J
649
MediumJEE Mains2010
A thin semi-circular ring of radius $r has a positive charges q distributed uniformly over it. The net field \overrightarrow E at the center O$ is
Options:
A) {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j
B) - {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j
C) - {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j
D) {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j
650
MediumNEET2021
A parallel plate capacitor has a uniform electric field $\overrightarrow E in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : (\varepsilon $0 = permittivity of free space)
Options:
A) {{{E^2}Ad} \over {{\varepsilon _0}}}
B) {1 \over 2}{\varepsilon _0}{E^2}
C) {\varepsilon _0}EAd
D) {1 \over 2}{\varepsilon _0}{E^2}Ad
651
MediumJEE Mains2010
Let there be a spherically symmetric charge distribution with charge density varying as $\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right) upto r=R, and \rho \left( r \right) = 0 for r>R, where r is the distance from the erigin. The electric field at a distance r\left( {r < R} \right)$ from the origin is given by
Options:
A) {{{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)
B) {{4\pi {\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)
C) {{4{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)
D) {{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)
652
MediumNEET2021
The equivalent capacitance of the combination shown in the figure is :
Options:
A) 3C/2
B) 3C
C) 2C
D) C/2
653
MediumJEE Mains2009
Two points $P and Q are maintained at the potentials of 10 V and -4 V, respectively. The work done in moving 100 electrons from P to Q$ is :
Options:
A) 9.60 \times {10^{ - 17}}J
B) - 2.24 \times {10^{ - 16}}J
C) 2.24 \times {10^{ - 16}}J
D) - 9.60 \times {10^{ - 17}}J
654
MediumNEET2020
The capacitance of a parallel plate capacitor with air as medium is 6$\mu F. With the introduction of a dielectric medium, the capacitance become 30 \mu F The permittivity of the medium is :\left( {{\varepsilon _0} = 8.85 \times {{10}^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}} \right)
Options:
A) 1.77 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}
B) 0.44 \times {10^{ - 10}}{C^2}{N^{ - 1}}{m^{ - 2}}
C) 5.00{C^2}{N^{ - 1}}{m^{ - 2}}
D) 0.44 \times {10^{ - 13}}{C^2}{N^{ - 1}}{m^{ - 2}}
655
MediumJEE Mains2009
(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.) Statement-1 : For a charged particle moving from point $P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q.$ Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.
Options:
A) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C) Statement- 1 is false, Statement- 2 is true.
D) Statement- 1 true, Statement- 2 is false
656
MediumNEET2019
A parallel plate capacitor of capacitance 20 $\mu $F is being charged by a voltage source whose potential is changing at the rate of 3V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :
Options:
A) zero, zero
B) zero, 60 $\mu $A
C) 60 $\mu A, 60 \mu $A
D) 60 $\mu $A, zero
657
MediumJEE Mains2009
A charge $Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/q$ equals:
Options:
A) -1
B) 1
C) - {1 \over {\sqrt 2 }}
D) - 2\sqrt 2
658
MediumNEET2018
The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is
Options:
A) Independent of the distance between the
plates
B) Linearly proportional to the distance
between the plates
C) Proportional to the square root of the
distance between the plates
D) Inversely proportional to the distance
between the plates
659
MediumJEE Mains2009
Let $P\left( r \right) = {Q \over {\pi {R^4}}}r be the change density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance {r_1}$ from the center of the sphere, the magnitude of electric field is :
Options:
A) {Q \over {4\pi \,{ \in _0}\,r_1^2}}
B) {{Qr_1^2} \over {4\pi \,{ \in _0}\,{R^4}}}
C) {{Qr_1^2} \over {3\pi \,{ \in _0}\,{R^4}}}
D) 0
660
MediumNEET2017
A capacitor is charged by a battery. The battery is removed and another identical unchanged capacitor is connected in parallel. The total electrostatic energy of resulting system
Options:
A) decreases by a factor of 2
B) remains the same
C) increases by a factor of 2
D) increases by a factor of 4
661
MediumJEE Mains2008
A thin spherical shell of radius $R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 \le r < \infty , where r$ is the distance from the center of the shell?
Options:
A)
B) c
C)
D)
662
MediumNEET2016
A parallel-plate capacitor of area a, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k1, k2, k3 and k4 as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by
Options:
A) k = k1 + k2 + k3 + 3k4
B) k = ${2 \over 3}$ (k1 + k2 + k3) + 2k4
C) {2 \over k} = {3 \over {{k_1} + {k_2} + {k_3}}} + {1 \over {{k_4}}}
D) {1 \over k} = {1 \over {{k_1}}} + {1 \over {{k_2}}} + {1 \over {{k_3}}} + {3 \over {2{k_4}}}
663
MediumJEE Mains2007
Charges are placed on the vertices of a square as shown. Let $\overrightarrow E be the electric field and V the potential at the center. If the charges on A and B are interchanged with those on D and C$ respectively, then
Options:
A) \overrightarrow E changes, V$ remains unchanged
B) \overrightarrow E remains unchanged, V$ changes
C) both $\overrightarrow E and V$ change
D) \overrightarrow E and V$ remain unchanged
664
MediumNEET2016
A capacitor of 2 $\mu $F is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is
Options:
A) 75%
B) 80%
C) 0%
D) 20%
665
MediumJEE Mains2007
The potential at a point $x (measured in \mu \,m) due to some charges situated on the x-axis is given by V\left( x \right) = 20/\left( {{x^2} - 4} \right) volt The electric field E at x = 4\,\mu \,m$ is given by
Options:
A) (10/9) volt / \mu m and in the + ve x$ direction
B) \left( {5/3} \right) volt/ \mu m and in the -ve x$ direction
C) \left( {5/3} \right) volt/\mu m and in the +ve x$ direction
D) \left( {10/9} \right) volt/ \mu \,m and in the -ve x$ direction
666
MediumNEET2015
A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is
Options:
A) {{C{V^2}} \over d}
B) {{{C^2}{V^2}} \over {2{d^2}}}
C) {{{C^2}{V^2}} \over {2d}}
D) {{C{V^2}} \over {2d}}
667
MediumJEE Mains2007
An electric charge ${10^{ - 3}}\,\,\mu \,C is placed at the origin (0,0) of X-Y co-ordinate system. Two points A and B are situated at \left( {\sqrt 2 ,\sqrt 2 } \right) and \left( {2,0} \right) respectively. The potential difference between the points A and B$ will be
Options:
A) 4.5$ volts
B) 9$ volts
C) zero
D) 2$ volts
668
MediumNEET2015
A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dieletric constant K, which can just fill the air gap of the capacitor, is now inserted in it . Which of the following is incorrect ?
Options:
A) The change in energy stored is ${1 \over 2}C{V^2}\left( {{1 \over K} - 1} \right)
B) The charge on the capacitor is not conserved.
C) The potential difference between the plates decreases K times.
D) The energy stored in the capaciotor decreases K times.
669
MediumJEE Mains2006
An electric dipole is placed at an angle of ${30^ \circ }$ to a non-uniform electric field. The dipole will experience
Options:
A) a translation force only in the direction of the field
B) a translation force only in a direction normal to the direction of the field
C) a torque as well as a translational force
D) a torque only
670
MediumNEET2014
Two thin dielectric slabs of dielectric constants K1 and K2(K1 < K2) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by
Options:
A)
B)
C)
D)
671
MediumJEE Mains2006
Two spherical conductors $A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B$ is
Options:
A) 4:1
B) 1:2
C) 2:1
D) 1:4
672
MediumNEET2012
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
Options:
A) {1 \over 2}{\varepsilon _0}{E^2}
B) {{{E^2}Ad} \over {{\varepsilon _0}}}
C) {1 \over 2}{\varepsilon _0}{E^2}Ad
D) {\varepsilon _0}EAd
673
MediumJEE Mains2006
Two insulating plates are both uniformly charged in such a way that the potential difference between them is ${V_2} - {V_1} = 20\,V. (i.e., plate 2 is at a higher potential). The plates are separated by d=0.1 m and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? \left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)
Options:
A) 2.65 \times {10^6}\,m/s
B) 7.02 \times {10^{12}}\,m/s
C) 1.87 \times {10^6}\,m/s
D) 32 \times {10^{ - 19}}\,m/s
674
MediumNEET2011
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
Options:
A) {1 \over 2}{\varepsilon _0}{E^2}
B) {{{E^2}Ad} \over {{\varepsilon _0}}}
C) {1 \over 2}{\varepsilon _0}{E^2}Ad
D) {\varepsilon _0}EAd
675
MediumJEE Mains2005
Two point charges $+8q and -2q are located at x=0 and x=L respectively. The location of a point on the x$ axis at which the net electric field due to these two point charges is zero is
Options:
A) {L \over 4}
B) 2 L
C) 4 L
D) 8 L
676
MediumNEET2010
Two parallel metal plates having charges +Q and $-$Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
Options:
A) become zero
B) increase
C) decrease
D) remain same
677
MediumJEE Mains2005
Two thin wire rings each having a radius $R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and -q.$ The potential difference between the centres of the two rings is
Options:
A) {q \over {2\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]
B) {{qR} \over {4\pi \,{ \in _0}\,{d^2}}}
C) {q \over {4\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]
D) zero
678
MediumNEET2010
A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it. as the first combination has. The value of C2. in terms of C1, is then
Options:
A) {{2{C_1}} \over {{n_1}{n_2}}}
B) 16{{{n_2}} \over {{n_1}}}{C_1}
C) 2{{{n_2}} \over {{n_1}}}{C_1}
D) {{16{C_1}} \over {{n_1}{n_2}}}
679
MediumJEE Mains2005
A charged ball $B hangs from a silk thread S, which makes angle \theta with a large charged conducting sheet P, as shown in the figure. The surface charge density \sigma $ of the sheet is proportional to f
Options:
A) \cot \,\theta
B) \cos \,\theta
C) \tan \,\theta
D) \sin \,\theta
680
MediumNEET2009
Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltages of the combination will be
Options:
A) 3C,{V \over 3}
B) {C \over 3},3V
C) 3C,3V
D) {C \over 3},{V \over 3}
681
MediumJEE Mains2004
Four charges equal to -$Q are placed at the four corners of a square and a charge q is at its center. If the system is in equilibrium the value of q$ is
Options:
A) - {Q \over 2}\left( {1 + 2\sqrt 2 } \right)
B) {Q \over 4}\left( {1 + 2\sqrt 2 } \right)
C) - {Q \over 4}\left( {1 + 2\sqrt 2 } \right)
D) {Q \over 2}\left( {1 + 2\sqrt 2 } \right)
682
MediumNEET2008
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
Options:
A) {1 \over 2}{\varepsilon _0}{E^2}
B) {{{E^2}Ad} \over {{\varepsilon _0}}}
C) {1 \over 2}{\varepsilon _0}{E^2}Ad
D) {\varepsilon _0}EAd
683
MediumJEE Mains2004
A charged oil drop is suspended in a uniform field of $3 \times {10^4} v/m so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge = 9.9 \times {10^{ - 15}}\,\,kg and g = 10\,m/{s^2}$)
Options:
A) 1.6 \times {10^{ - 18}}\,C
B) 3.2 \times {10^{ - 18}}\,C
C) 3.3 \times {10^{ - 18}}\,C
D) 4.8 \times {10^{ - 18}}\,C
684
MediumNEET2007
Two condensers, one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is
Options:
A) {1 \over 4}C{V^2}
B) {3 \over 4}C{V^2}
C) {1 \over 2}C{V^2}
D) 2CV2
685
MediumJEE Mains2004
A charge particle $'q' is shot towards another charged particle 'Q' which is fixed, with a speed 'v'. It approaches 'Q' upto a closest distance r and then returns. If q were given a speed of '2v'$ the closest distances of approaches would be
Options:
A) r/2
B) 2r
C) r
D) r/4
686
MediumNEET2006
A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulting handle. As a result the potential difference between the plates
Options:
A) increases
B) decreases
C) does not charge
D) becomes zero
687
MediumJEE Mains2004
Two spherical conductors $B and C having equal radii and carrying equal charges on them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that B but uncharged is brought in contact with B, then brought in correct with C and finally removed away from both. The new force of repulsion between B and C$ is
Options:
A) F/8
B) 3 F/4
C) F/4
D) 3 F/8
688
MediumNEET2005
A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is
Options:
A) 4/7
B) 3/22
C) 7/4
D) 22/3
689
MediumJEE Mains2003
Three charges $ - {q_1}, + {q_2} and - {q_3} are placed as shown in the figure. The x-component of the force on - {q_1}$ is proportional to
Options:
A) {{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}\cos \theta
B) {{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\sin \theta
C) {{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\cos \theta
D) {{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}sin\theta
690
MediumNEET2003
Three capacitors each of capacity 4 $\mu F are to be connected in such a way that the effective capacitance is 6\mu F.$ This can be done by
Options:
A) connecting all of them in series
B) connecting them in parallel
C) connecting two in series and one in parallel
D) connecting two in parallel and one in series
691
MediumJEE Mains2003
If the electric flux entering and leaving an enclosed surface respectively is ${\phi _1} and {\phi _2},$ the electric charge inside the surface will be
Options:
A) \left( {{\phi _2} - {\phi _1}} \right){\varepsilon _0}
B) \left( {{\phi _2} + {\phi _1}} \right)/{\varepsilon _0}
C) \left( {{\phi _1} - {\phi _2}} \right)/{\varepsilon _0}
D) \left( {{\phi _1} + {\phi _2}} \right){\varepsilon _0}
692
MediumNEET2002
A capacitor of capacity C1 charged upto V volt and then connected to an uncharged capacitor of capacity C2. The final potential difference across each will be
Options:
A) {{{C_1}V} \over {{C_1} + {C_2}}}
B) {{{C_2}V} \over {{C_1} + {C_2}}}
C) \left( {1 - {{{C_2}} \over {{C_1}}}} \right)V
D) \left( {1 + {{{C_2}} \over {{C_1}}}} \right)
693
MediumJEE Mains2003
A thin spherical conducting shell of radius $R has a charge q. Another charge Q is placed at the center of the shell. The electrostatic potential at a point P a distance {R \over 2}$ from the center of the shell is
Options:
A) {{2Q} \over {4\pi {\varepsilon _0}R}}
B) {{2Q} \over {4\pi {\varepsilon _0}R}} - {{2q} \over {4\pi {\varepsilon _0}R}}
C) {{2Q} \over {4\pi {\varepsilon _0}R}} + {q \over {4\pi {\varepsilon _0}R}}
D) {{\left( {q + Q} \right)2} \over {4\pi {\varepsilon _0}R}}
694
MediumNEET2001
Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by
Options:
A) {1 \over 2}{\varepsilon _0}{{{V^2}} \over {{d^2}}}
B) {1 \over {2{\varepsilon _0}}}{{{V^2}} \over {{d^2}}}
C) {1 \over 2}C{V^2}
D) {{{Q^2}} \over {2C}}.
695
MediumJEE Mains2002
On moving a charge of $20 coulomb by 2 cm, 2 J$ of work is done, then the potential differences between the points is
Options:
A) 0.1 V
B) 8 V
C) 2V
D) 0.5 V.
696
MediumNEET2000
A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is
Options:
A) U/2
B) U/4
C) 4U
D) 2U
697
MediumJEE Mains2002
A charged particle $q is placed at the centre O of cube of length L(ABCDEFGH). Another same charge q is placed at a distance L from O. Then the electric flux through ABCD$ is
Options:
A) q/4\,\pi \,{ \in _0}L
B) zero
C) q/2\,\pi \,{ \in _0}L
D) q/3\,\pi \,{ \in _0}L
698
MediumVITEEE2023
A parallel plate capacitor with air between the plates has a capacitance of $15 \mathrm{~pF}. the separation between the plates is d. The space between the plates is now filled with two dielectrics constant k_1=3 and thickness d / 3 while the other one has dielectric constant k_2=6 and thickness 2 d / 3$. Capacitance of the capacitor is now
Options:
A) 18 pF
B) 90 pF
C) 67.5 pF
D) 81 pF
699
MediumJEE Mains2002
If a charge $q is placed at the center of the line joining two equal charges Q such that the system is in equilibrium then the value of q$ is
Options:
A) Q/2
B) - Q/2
C) Q/4
D) - Q/4
700
MediumVITEEE2022
A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a) and then in Fig.(b). Then ratio of the capacitor in the two arrangements is
Options:
A) 25 : 24
B) 24 : 25
C) 12 : 13
D) 13 : 12
701
MediumJEE Mains2026
A point charge q=1 \mu \mathrm{C} is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q=24 \mu \mathrm{C}, distributed uniformly along its length, as shown in figure. Force between q and wire is \_\_\_\_ N. (Use : \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}^2 )
Options:
702
MediumVITEEE2022
A parallel plate capacitor with plate area $A and separation between the plates d is charged by a constant current i. Consider a plane surface of area A / 2$ parallel to the plates and drawn simultaneously between the plates. The displacement current through this area is
Options:
A) i
B) i/2
C) i/4
D) i/8
703
EasyJEE Mains2025
The electric field in a region is given by \overrightarrow{\mathrm{E}}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \mathrm{~N} / \mathrm{C}. The flux of the field through a rectangular surface parallel to x-z plane is 6.0 \,\mathrm{Nm}^2 \mathrm{C}^{-1}. The area of the surface is _____________ \mathrm{cm}^2.
Options:
704
MediumVITEEE2021
A parallel plate capacitor of capacitance $5 \mu \mathrm{F} is charged to 120 \mathrm{~V} and then connected to another uncharged capacitor. If the potential falls to 40 \mathrm{~V}$, and capacitance of the second capacitor is
Options:
A) 5 $\mu$F
B) 10 $\mu$F
C) 15 $\mu$F
D) 20 $\mu$F
705
EasyJEE Mains2025
An electric dipole of dipole moment 6 \times 10^{-6} \mathrm{Cm} is placed in uniform electric field of magnitude 10^{6} \mathrm{V} / \mathrm{m}. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _______ J.
Options:
706
MediumVITEEE2021
Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is
Options:
A) 1: 1
B) 1: 2
C) 1: 3
D) 1: 4
707
MediumJEE Mains2025
A square loop of sides a=1 \mathrm{~m} is held normally in front of a point charge \mathrm{q}=1 \mathrm{C} at a distance \frac{\mathrm{a}}{2}. The flux of the electric field through the shaded region is \frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}, where the value of p is ________ .
Options:
708
EasyJEE Mains2025
A positive ion A and a negative ion B has charges 6.67 \times 10^{-19} \mathrm{C} and 9.6 \times 10^{-10} \mathrm{C}, and masses 19.2 \times 10^{-27} \mathrm{~kg} and 9 \times 10^{-27} \mathrm{~kg} respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is \mathrm{P} \times 10^{-13}, where the value of P is _________. (Take \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1} and universal gravitational constant as 6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2} )
Options:
709
EasyJEE Mains2024
An electric field $\vec{E}=(2 x \hat{i}) N C^{-1} exists in space. A cube of side 2 \mathrm{~m} is placed in the space as per figure given below. The electric flux through the cube is ______ \mathrm{Nm}^2 / \mathrm{C}$.
Options:
710
EasyJEE Mains2024
At the centre of a half ring of radius $\mathrm{R}=10 \mathrm{~cm} and linear charge density 4 \mathrm{~nC} \mathrm{~m}^{-1}, the potential is x \pi \mathrm{V}. The value of x$ is _________.
Options:
711
MediumJEE Mains2024
If the net electric field at point $\mathrm{P} along \mathrm{Y} axis is zero, then the ratio of \left|\frac{q_2}{q_3}\right| is \frac{8}{5 \sqrt{x}}, where x=$ ________.
Options:
712
EasyJEE Mains2024
An electric field, $\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}} passes through the surface of 4 \mathrm{~m}^2 area having unit vector \hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right). The electric flux for that surface is _________ \mathrm{Vm}$.
Options:
713
MediumJEE Mains2024
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P is \frac{x \sigma}{\epsilon_0}. The value of x$ is _________ (all quantities are measured in SI units).
Options:
714
EasyJEE Mains2024
The electric field at point $\mathrm{p} due to an electric dipole is \mathrm{E}. The electric field at point \mathrm{R} on equitorial line will be \frac{\mathrm{E}}{x}. The value of x$ :
Options:
715
MediumJEE Mains2024
An infinite plane sheet of charge having uniform surface charge density $+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2 is placed on x-y plane. Another infinitely long line charge having uniform linear charge density +\lambda_e \mathrm{C} / \mathrm{m} is placed at z=4 \mathrm{~m} plane and parallel to y-axis. If the magnitude values \left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right| then at point (0,0,2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \pi \sqrt{n}: 1. The value of n$ is _________.
Options:
716
MediumJEE Mains2024
Suppose a uniformly charged wall provides a uniform electric field of 2 \times 10^4 \mathrm{~N} / \mathrm{C} normally. A charged particle of mass 2 \mathrm{~g} being suspended through a silk thread of length 20 \mathrm{~cm} and remain stayed at a distance of 10 \mathrm{~cm} from the wall. Then the charge on the particle will be \frac{1}{\sqrt{x}} \mu \mathrm{C} where x= ___________ . [use \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ]
Options:
717
MediumJEE Mains2024
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle \theta with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 \mathrm{~g} / \mathrm{cc}, the dielectric constant of water will be __________. (Take density of water =1 \mathrm{~g} / \mathrm{cc} )
Options:
718
MediumJEE Mains2024
The distance between charges $+q and -q is 2 l and between +2 q and -2 q is 4 l. The electrostatic potential at point P at a distance r from center O is -\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}, where the value of \alpha is __________. (Use \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~Nm}^2 \mathrm{C}^{-2}$)
Options:
719
MediumJEE Mains2024
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^{\circ} with each other. When suspended in a liquid of density 0.7 \mathrm{~g} / \mathrm{cm}^3, the angle remains same. If density of material of the sphere is 1.4 \mathrm{~g} / \mathrm{cm}^3, the dielectric constant of the liquid is _______ \left(\tan 37^{\circ}=\frac{3}{4}\right)
Options:
720
MediumJEE Mains2024
An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $\mathrm{S} having surface charge density +\sigma. The electron at t=0 is at a distance of 1 \mathrm{~m} from S and has a speed of 1 \mathrm{~m} / \mathrm{s}. The maximum value of \sigma if the electron strikes S at t=1 \mathrm{~s} is \alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}, the value of \alpha$ is ___________.
Options:
721
MediumJEE Mains2024
Two charges of $-4 \mu \mathrm{C} and +4 \mu \mathrm{C} are placed at the points \mathrm{A}(1,0,4) \mathrm{m} and \mathrm{B}(2,-1,5) \mathrm{m} located in an electric field \overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}. The magnitude of the torque acting on the dipole is 8 \sqrt{\alpha} \times 10^{-5} \mathrm{Nm}, where \alpha=$ _________.
Options:
722
EasyJEE Mains2024
The electric potential at the surface of an atomic nucleus $(z=50) of radius 9 \times 10^{-13} \mathrm{~cm} is __________ \times 10^6 \mathrm{~V}$.
Options:
723
MediumJEE Mains2024
A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2 is used to make a ring of radius 30 \mathrm{~cm}. A positive charge of 2 \pi \mathrm{~C} is uniformly distributed over the ring, while another positive charge of 30 \mathrm{pC} is kept at the centre of the ring. The tension in the ring is ______ \mathrm{N}; provided that the ring does not get deformed (neglect the influence of gravity). (given, \frac{1}{4 \pi \epsilon_0}=9 \times 10^9$ SI units)
Options:
724
MediumJEE Mains2023
Three point charges $\mathrm{q},-2 \mathrm{q} and 2 \mathrm{q} are placed on x-axis at a distance x=0, x=\frac{3}{4} R and x=R respectively from origin as shown. If \mathrm{q}=2 \times 10^{-6} \mathrm{C} and \mathrm{R}=2 \mathrm{~cm}, the magnitude of net force experienced by the charge -2 q$ is ___________ N.
Options:
725
MediumJEE Mains2023
A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma and +\lambda are placed parallel at 5 \mathrm{~m} distance from each other. Points 'P' and 'Q' are at \frac{3}{\pi} m and \frac{4}{\pi} m perpendicular distances from line charge towards sheet charge, respectively. '\mathrm{E}_{\mathrm{P}}' and '\mathrm{E}_{\mathrm{Q}}' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If \frac{E_{p}}{E_{0}}=\frac{4}{a} for 2|\sigma|=|\lambda|, then the value of a$ is ___________.
Options:
726
MediumJEE Mains2023
64 identical drops each charged upto potential of $10 ~\mathrm{mV} are combined to form a bigger drop. The potential of the bigger drop will be __________ \mathrm{mV}$.
Options:
727
MediumJEE Mains2023
As shown in the figure, a configuration of two equal point charges $\left(q_{0}=+2 \mu \mathrm{C}\right) is placed on an inclined plane. Mass of each point charge is 20 \mathrm{~g}. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \mathrm{h}=x \times 10^{-3} \mathrm{~m}. The value of x is ____________. (Take \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
Options:
728
MediumJEE Mains2023
An electron revolves around an infinite cylindrical wire having uniform linear charge density $2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1} in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}. Given mass of electron =9 \times 10^{-31} \mathrm{~kg}
Options:
729
MediumJEE Mains2023
Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities $\sigma,-\sigma and \sigma$ respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is _________ cm.
Options:
730
EasyJEE Mains2023
An electric dipole of dipole moment is $6.0 \times 10^{-6} ~\mathrm{C m} placed in a uniform electric field of 1.5 \times 10^{3} ~\mathrm{NC}^{-1} in such a way that dipole moment is along electric field. The work done in rotating dipole by 180^{\circ} in this field will be ___________ \mathrm{m J}$.
Options:
731
MediumJEE Mains2023
A cubical volume is bounded by the surfaces $\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}. The electric field in the region is given by \overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}. Where \mathrm{E}_{0}=4 \times 10^{4} ~\mathrm{NC}^{-1} \mathrm{~m}^{-1}. If \mathrm{a}=2 \mathrm{~cm}, the charge contained in the cubical volume is \mathrm{Q} \times 10^{-14} \mathrm{C}. The value of \mathrm{Q} is ________________. (Take \epsilon_{0}=9 \times 10^{-12} ~\mathrm{C}^{2} / \mathrm{Nm}^{2}$)
Options:
732
MediumJEE Mains2023
Two equal positive point charges are separated by a distance $2 a. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \mathrm{q}_{0} becomes maximum is \frac{a}{\sqrt{x}}. The value of x$ is __________.
Options:
733
MediumJEE Mains2023
Expression for an electric field is given by $\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}. The electric flux through the cube of side 20 \mathrm{~cm} when placed in electric field (as shown in the figure) is __________ \mathrm{V} \mathrm{~cm}$.
Options:
734
MediumJEE Mains2023
As shown in figure, a cuboid lies in a region with electric field E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} / \mathrm{C}. The magnitude of charge within the cuboid is n \in_{0} C. The value of n is _________ (if dimension of cuboid is 1 \times 2 \times 3 \mathrm{~m}^{3} )
Options:
735
MediumJEE Mains2023
For a charged spherical ball, electrostatic potential inside the ball varies with $r as \mathrm{V}=2ar^2+b. Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is -\lambda a\varepsilon. The value of \lambda is ____________. \varepsilon$ = permittivity of the medium
Options:
736
EasyJEE Mains2023
A point charge $q_1=4q_0 is placed at origin. Another point charge q_2=-q_0 is placed at x=12 cm. Charge of proton is q_0. The proton is placed on x$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.
Options:
737
MediumJEE Mains2023
A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($\theta$) of deviation of the path of electron as it comes out of the field is ___________ (in degree).
Options:
738
EasyJEE Mains2023
A stream of a positively charged particles having ${q \over m} = 2 \times {10^{11}}{C \over {kg}} and velocity {\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s is deflected by an electric field 1.8\widehat j kV/m. The electric field exists in a region of 10 cm along x direction. Due to the electric field, the deflection of the charge particles in the y$ direction is _________ mm.
Options:
739
EasyJEE Mains2022
Two electric dipoles of dipole moments $1.2 \times 10^{-30} \,\mathrm{Cm} and 2.4 \times 10^{-30} \,\mathrm{Cm} are placed in two different uniform electric fields of strengths 5 \times 10^{4} \,\mathrm{NC}^{-1} and 15 \times 10^{4} \,\mathrm{NC}^{-1} respectively. The ratio of maximum torque experienced by the electric dipoles will be \frac{1}{x}. The value of x$ is __________.
Options:
740
EasyJEE Mains2022
A long cylindrical volume contains a uniformly distributed charge of density $\rho \,\mathrm{Cm}^{-3}. The electric field inside the cylindrical volume at a distance x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m} from its axis is ________ \mathrm{Vm}^{-1}$.
Options:
741
MediumJEE Mains2022
Three point charges of magnitude $5 \mu \mathrm{C}, 0.16 \mu \mathrm{C} and 0.3 \mu \mathrm{C} are located at the vertices A, B, C of a right angled triangle whose sides are A B=3 \mathrm{~cm}, B C=3 \sqrt{2} \mathrm{~cm} and C A=3 \mathrm{~cm} and point A is the right angle corner. Charge at point \mathrm{A} experiences ____________ \mathrm{N}$ of electrostatic force due to the other two charges.
Options:
742
EasyJEE Mains2022
The volume charge density of a sphere of radius $6 \mathrm{~m} is 2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ \times 10^{10} \,\mathrm{NC}^{-1}. [Given : Permittivity of vacuum \epsilon_{0}=8.85 \times 10^{-12} \,\mathrm{C}^{2}\, \mathrm{~N}^{-1}-\mathrm{m}^{-2}$ )
Options:
743
MediumJEE Mains2022
Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.
Options:
744
MediumJEE Mains2022
27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.
Options:
745
MediumJEE Mains2021
A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x < < 1 m). The particle executes SHM. Its angular frequency of oscillation will be ____________ $\times$ 105 rad/s if q2 = 10 C2.
Options:
746
MediumJEE Mains2021
The total charge enclosed in an incremental volume of 2 $\times 10-9 m3 located at the origin is ___________ nC, if electric flux density of its field is found asD = e-x sin y \widehat i - e-x cos y \widehat j + 2z \widehat k$ C/m2
Options:
747
MediumJEE Mains2021
A body having specific charge 8 $\mu$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be _______________ s.
Options:
748
MediumJEE Mains2021
An infinite number of point charges, each carrying 1 $\muC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............The total force on a 1C point charge, placed at the origin, is x \times 103 N.The value of x, to the nearest integer, is __________. [Take {1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$ Nm2/C2]
Options:
749
EasyJEE Mains2021
The electric field in a region is given by $\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j with {E_0} = 4.0 \times {10^3}{N \over C}. The flux of this field through a rectangular surface area 0.4 m2 parallel to the Y-Z plane is __________ Nm2C-$1.
Options:
750
EasyJEE Mains2021
27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is __________ times that of a smaller drop.
Options:
751
EasyJEE Mains2021
Two identical conducting spheres with negligible volume have 2.1 nC and $-0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is __________ \times 10-9 N.[Given : 4\pi {\varepsilon _0} = {1 \over {9 \times {{10}^9}}}$ SI unit]
Options:
752
MediumJEE Mains2021
Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is ${a \over {21}} \times {10^{ - 8}}C. The value of 'a' will be ___________. [Given g = 10 ms-$2]
Options:
753
EasyJEE Mains2021
The electric field in a region is given by $\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y - z plane) to that of the surface of area 0.3 m2 (parallel to x - z plane) is a : b, where a = __________ [Here {\widehat i}, {\widehat j} and {\widehat k}$ are unit vectors along x, y and z-axes respectively.]
Options:
754
MediumJEE Mains2021
512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.
Options:
755
MediumJEE Mains2021
A point charge of +12$\muC is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ \times$ 103 Nm2/C.
Options:
756
MediumJEE Mains2020
An electric field $\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j N/C passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as {\phi _I} and {\phi _{II}} respectively. The difference between \left( {{\phi _I} - {\phi _{II}}} \right)$ is (in Nm2/C) _______.
Options:
757
MediumJEE Mains2015
A uniformly charged solid sphere of radius $R has potential {V_0} (measured with respect to \infty ) on its surface. For this sphere the equipotential surfaces with potentials {{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}} \over 4} and {{{V_0}} \over 4} have radius {R_1},\,\,{R_2},\,\,{R_3} and {R_4}$ respectively. Then
Options:
A) {R_1} = 0 and {R_2} < \left( {{R_4} - {R_3}} \right)
B) 2R < {R_4}
C) {R_1} = 0 and {R_2} > \left( {{R_4} - {R_3}} \right)
D) {R_1} \ne 0 and \left( {{R_2} - {R_1}} \right) > \left( {{R_4} - {R_3}} \right)
758
MediumMHT CET2025
\text { The electric flux through the surface }
Options:
A) in figure (c) is the largest
B) in figure (b) is same as figure (c) but is smaller than figure (d)
C) is the same for all the figures
D) in figure (d) is the least
759
MediumMHT CET2025
An electric dipole of length 2 cm is placed with its axis making an angle of 60^{\circ} to a uniform electric field of 10^{+5} \mathrm{~N} / \mathrm{C}. If it experiences a torque of 9 \sqrt{3} \mathrm{Nm}, the magnitude of the charge on the dipole is \left(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)
Options:
A) 7 \times 10^{-3} \mathrm{C}
B) 8 \times 10^{-3} \mathrm{C}
C) 9 \times 10^{-3} \mathrm{C}
D) \frac{9}{2} \times 10^{-3} \mathrm{C}
760
MediumMHT CET2025
A charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up, the total electric flux coming out of the surface
Options:
A) decreases.
B) increases.
C) remains unchanged.
D) becomes zero.
761
MediumMHT CET2025
The point charges +\mathrm{q},-\mathrm{q},-\mathrm{q},+\mathrm{q},+\mathrm{Q} and -q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon ' O ' due to the five charges at \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} and F is twice the electric field at centre ' O ' due to charge +Q at E alone. The value of Q is
Options:
A) \frac{\mathrm{q}}{2}
B) q
C) 2 q
D) 4 q
762
MediumMHT CET2025
Out of the following statements which is NOT the characteristics of electric lines of force?
Options:
A) Electric lines of force originate from a positively charged object and end on negatively charged object.
B) The electric lines of force do not intersect each other.
C) The electric lines of force pass through the conductor.
D) The electric lines of force are crowded in a region where electric intensity is large.
763
MediumMHT CET2025
Charges of 2 \mu \mathrm{C} and -3 \mu \mathrm{C} are placed at two points A and B separated by distance of 1 m . The distance of the point from A where net potential is zero is
Options:
A) 0.667 m
B) 0.5 m
C) 0.4 m
D) 0.6 m
764
MediumMHT CET2025
Assuming the drops to be spherical, 27 identical drops of mercury are charged simultaneously to the same potential of 20 volt. If all the charged drops are made to combine to form one big drop, then potential of big drop will be
Options:
A) 90 V
B) 180 V
C) 270 V
D) 360 V
765
MediumMHT CET2025
Two equally charged small balls placed at a fixed distance experience a force ' F '. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. the force experienced by this ball is
Options:
A) \frac{\mathrm{F}}{2}
B) F
C) 2 F
D) 4 F
766
MediumMHT CET2025
Three charges Q(-2 q) and (-2 q) are placed at the vertices of an isosceles right angled triangle as shown in figure. The net electrostatic potential energy is zero if Q is equal to
Options:
A) \sqrt{2} q
B) \frac{\mathrm{q}}{2}
C) \frac{\mathrm{q}}{\sqrt{2}}
D) \frac{q}{2 \sqrt{2}}
767
MediumMHT CET2025
Two point charges \mathrm{q}_1 and \mathrm{q}_2 are ' l ' distance apart. If one of the charges is doubled and distance between them is halved. The magnitude of force becomes n times, where n is
Options:
A) 1
B) 2
C) 8
D) 16
768
MediumMHT CET2025
' n ' identical small spherical drops of water, each of radius ' r ' and charged to the same potential ' v ' are combined to form a big drop. The potential of a big drop is
Options:
A) nv
B) n \sqrt{v}
C) n^{1 / 3} v
D) \mathrm{n}^{2 / 3} \mathrm{v}
769
MediumMHT CET2025
Three charges ' +3 q ', ' Q ' and ' +q ' are placed in a straight line of length ' l ' at points at distances 0, \frac{l}{2} and l respectively. The value of Q in order to have the net force on +q to be zero, \mathrm{Q}=\mathrm{xq}. The value of x is
Options:
A) \frac{1}{4}
B) \frac{-3}{4}
C) -3
D) 4
770
MediumMHT CET2025
Two point charges +10 \mu \mathrm{C} and 4 \mu \mathrm{C} are placed 10 cm apart in air. The work required to be done to bring them 2 cm closer is $ \left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI units }\right)
Options:
A) 0.65 J
B) 0.9 J
C) 1.2 J
D) 2.3 J
771
MediumMHT CET2025
Out of the following molecules the one which represents the polar molecule is
Options:
A) (d)
B) (a)
C) (c)
D) (b)
772
MediumMHT CET2025
The electric field intensity near a conducting surface having uniform surface charge density ' \sigma ' is given by ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{\sigma}{\varepsilon_0} and is parallel to the surface
B) \frac{2 \sigma}{\varepsilon_0} and is parallel to the surface
C) \frac{\sigma}{\varepsilon_0} and is normal to the surface
D) \frac{2 \sigma}{\varepsilon_0} and is normal to the surface
773
MediumMHT CET2025
A regular hexagon of side 6 cm has a charge of 2 \mu \mathrm{C} at each of its vertices, what is the potential at the centre of the hexagon? $ \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit }\right]
Options:
A) 1.5 \times 10^5 \mathrm{~V}
B) 1.8 \times 10^6 \mathrm{~V}
C) 2.4 \times 10^5 \mathrm{~V}
D) 3.2 \times 10^6 \mathrm{~V}
774
MediumMHT CET2025
Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' \mathrm{q}_1 ' and ' \mathrm{q}_2 ' is ' \mathrm{F}_{12} ' and that between ' \mathrm{q}_1 ' and ' \mathrm{q}_3 ' is \mathrm{F}_{13}, then the ratio of F_{13} to F_{12} is
Options:
A) \frac{1}{\sqrt{2}}
B) \sqrt{2}
C) \frac{1}{2}
D) 2
775
MediumMHT CET2025
Three charges each of magnitude 3 \mu \mathrm{C}, are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be nearly \left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\right. SI unit ]
Options:
A) 1.4 J
B) 2.7 J
C) 4.1 J
D) 8.2 J
776
MediumMHT CET2025
Earth is assumed to be a charged conducting sphere having volume V and surface area A . The capacitance of the earth in free space is ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{2 \pi \varepsilon_0 V}{A}
B) \frac{8 \pi \varepsilon_0 \mathrm{~V}}{\mathrm{~A}}
C) \frac{12 \pi \varepsilon_0 \mathrm{~V}}{\mathrm{~A}}
D) \frac{4 \pi \varepsilon_0 V}{A}
777
MediumMHT CET2025
A charge \mathrm{Q} \mu \mathrm{C} is placed at the centre of a cube. The flux through two opposite faces of the cube is ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{\mathrm{Q}}{6 \varepsilon_0}
B) \frac{\mathrm{Q}}{3 \varepsilon_0}
C) \frac{\mathrm{Q}}{\varepsilon_0}
D) \frac{\mathrm{Q}}{2 \varepsilon_0}
778
MediumMHT CET2025
Four charges 2 \mu \mathrm{C},-3 \mu \mathrm{C}, 4 \mu \mathrm{C},-4 \mu \mathrm{C} and -1 \mu \mathrm{C} are enclosed by the Gaussian surface of radius 2 m . Net outward flux through the Gaussian surface is (in \mu \mathrm{V}-\mathrm{m} ) [ \varepsilon_0= permittivity of free space]
Options:
A) \frac{2}{\varepsilon_0}
B) zero
C) \frac{3}{\varepsilon_0}
D) \frac{5}{\varepsilon_0}
779
MediumMHT CET2025
The electric field intensity on the surface of a solid charged sphere of radius \mathbf{r} and volume charge density \sigma is ( \varepsilon_0= permittivity of free space)
Options:
A) zero
B) \frac{5 \sigma r}{6 \varepsilon_0}
C) \frac{1}{4 \pi \varepsilon_0} \frac{\sigma}{\mathrm{r}}
D) \frac{\sigma \mathrm{r}}{3 \varepsilon_0}
780
MediumMHT CET2025
The electric charges ' +2 q ', ' +2 q ', ' -2 q ' and ' -2 q ' are placed at the corners of square of side ' 2 L ' as shown in figure. The electric potential at point 'A', midway between the two charges ' +2 q ' and ' +2 q ' is ( \varepsilon_0= permittivity of free space)
Options:
A) \quad \frac{1}{4 \pi \varepsilon_0}\left(\frac{2 q}{L}\right)\left[1+\frac{1}{\sqrt{5}}\right]
B) \frac{\mathrm{q}}{\pi \varepsilon_0 \mathrm{~L}}\left[1-\frac{1}{\sqrt{5}}\right]
C) \frac{\mathrm{q}}{\pi \varepsilon_0 \mathrm{~L}}\left[1+\frac{1}{\sqrt{5}}\right]
D) \frac{1}{4 \pi \varepsilon_0}\left(\frac{2 q}{L}\right)\left[1-\frac{1}{\sqrt{5}}\right]
781
MediumMHT CET2025
An electric dipole having each charge of magnitude 2 \mu \mathrm{C} is placed in an electric field of intensity 8 \times 10^{+4} \mathrm{~N} / \mathrm{C}. If the maximum torque acting on the dipole is 4 \times 10^{-3} \mathrm{~N}-\mathrm{m}, the length of the dipole is
Options:
A) 10 mm
B) 25 mm
C) 15 mm
D) 20 mm
782
MediumMHT CET2025
A hollow cylinder has a charge ' q ' coulomb within it. If ' \phi ' is the electric flux in unit of V-m associated with the curved surface C , the flux linked with the plane surface ' A ' in unit of V-m will be [ \varepsilon_0= permittivity of free space]0
Options:
A) \frac{\phi}{3}
B) \left(\frac{\mathrm{q}}{\varepsilon_0}-\phi\right)
C) \quad \frac{1}{2}\left(\frac{\mathrm{q}}{\mathrm{\varepsilon}_0}-\phi\right)
D) \frac{\mathrm{q}}{2 \varepsilon_0}
783
MediumMHT CET2025
Three concentric charged metallic spherical sheets A, B and C have radii a, b, c potentials V_A, \mathrm{V}_{\mathrm{B}}, \mathrm{V}_{\mathrm{C}} and charge densities +\sigma,-\sigma and +\sigma respectively. The value of potential \mathrm{V}_{\mathrm{A}} is ( \varepsilon_0= permittivity of free space)
Options:
A) \quad \frac{\sigma}{\varepsilon_0}(\mathrm{a}+\mathrm{b}+\mathrm{c})
B) \frac{\sigma}{\varepsilon_0}(-\mathrm{a}+\mathrm{b}-\mathrm{c})
C) \frac{\sigma}{\varepsilon_0}(\mathrm{a}-\mathrm{b}+\mathrm{c})
D) \quad \frac{\sigma}{3 \varepsilon_0}(\mathrm{a}+\mathrm{b}+\mathrm{c})
784
MediumMHT CET2025
Three point charges +Q,+2 Q and q are placed at the vertices of an equilateral triangle. The value of charge q in terms of Q, so that electrical potential energy of the system is zero, is given by
Options:
A) \mathrm{q}=\frac{1}{3} \mathrm{Q}
B) \mathrm{q}=\frac{2}{3} \mathrm{Q}
C) \mathrm{q}=-\frac{2}{3} \mathrm{Q}
D) \mathrm{q}=-\frac{3}{2} \mathrm{Q}
785
MediumMHT CET2025
A hollow cylinder has a charge of ' q ' C within it. If \phi is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be
Options:
A) \frac{\phi}{3}
B) \frac{\mathrm{q}}{\varepsilon_0}-\phi
C) \frac{\mathrm{q}}{3 \varepsilon_0}
D) \quad \frac{1}{2}\left(\frac{\mathrm{q}}{\varepsilon_0}-\phi\right)
786
MediumMHT CET2025
A conducting sphere of radius ' R ' is given a charge ' Q ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ \varepsilon_0= permittivity of free space]
Options:
A) zero and \frac{Q}{4 \pi \varepsilon_0 R}
B) \frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2} and zero
C) \frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}} and \frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}
D) zero and zero
787
MediumMHT CET2025
' n ' small spherical drops of same size which are charged to ' V ' volt each coalesce to form a single big drop. The potential of the big drop is
Options:
A) \frac{V}{n}
B) n \cdot V
C) n^{1 / 3} \cdot V
D) \mathrm{n}^{2 / 3} \cdot \mathrm{~V}
788
MediumMHT CET2025
The electric potential ' V ' is given as a function of distance ' x ' (metre) by V=\left(4 x^2+8 x-3\right) V. The value of electric field at x=0.5 \mathrm{~m}, in \mathrm{V} / \mathrm{m} is
Options:
A) -16
B) -12
C) 0
D) +12
789
MediumMHT CET2025
A uniformly charged conducting sphere of diameter 3.5 cm has a surface charge density of 20 \mu \mathrm{Cm}^{-2}. The total electric flux leaving the surface of the sphere is nearly [permittivity of free space, \varepsilon_0=8.85 \times 10^{-12} \mathrm{SI} unit]
Options:
A) 57 \times 10^2 \mathrm{~Wb}
B) 70 \times 10^2 \mathrm{~Wb}
C) 87 \times 10^2 \mathrm{~Wb}
D) 35 \times 10^3 \mathrm{~Wb}
790
MediumMHT CET2025
A charged particle of mass ' m ' and charge ' q ' is at rest. It is acce:lerated in a uniform electric field of intensity ' E ' : for time ' t '. The kinetic energy of the particles after time t is
Options:
A) \frac{E q m}{2 t}
B) \frac{E^2 q^2 t^2}{2 m}
C) \frac{2 \mathrm{E}^2 \mathrm{t}^2}{\mathrm{mq}^2}
D) \frac{\mathrm{Eqt}}{\mathrm{m}}
791
MediumMHT CET2025
Let ' W ' joule be the work done to move an electric charge ' q ' coulomb from a place A, where potential is -5 volt to another place B where potential is ' V ' volt. The value of ' V ' is
Options:
A) W q-5
B) \frac{\mathrm{q}}{\mathrm{w}}+5
C) W-\frac{5}{q}
D) \frac{w}{q}-5
792
MediumMHT CET2025
Two charges \mathrm{q}_1=+6_{\mathrm{q}} and \mathrm{q}_2=-3 \mathrm{q} placed as shown in figure. A proton is placed on x -axis away from \mathrm{q}_2. To remain proton in equilibrium, the distance between \mathrm{q}_1 and proton is
Options:
A) \left(\frac{\sqrt{2}}{\sqrt{2}-1}\right) \mathrm{L}
B) \mathrm{2 L}
C) \frac{\mathrm{L}}{2}
D) \left(\frac{\sqrt{2}}{\sqrt{2}+1}\right) \mathrm{L}
793
MediumMHT CET2025
An electric dipole of dipole moment ' p ' is aligned parallel to a uniform electric field ' E '. The energy required to rotate the dipole by 90^{\circ} is \left[\begin{array}{ll}\sin 0^{\circ}=0, & \sin 90^{\circ}=1 \\ \cos 0^{\circ}=1, & \cos 90^{\circ}=0\end{array}\right]
Options:
A) pE
B) \mathrm{pE}^2
C) p^2 E
D) infinity
794
MediumMHT CET2024
A hollow cylinder has charge ' q ' C within it. If ' \phi ' is the electric flux associated with the curved
Options:
A) \frac{1}{2}\left(\frac{\mathrm{q}}{\varepsilon_0}-\phi\right)
B) \frac{q}{2 \varepsilon_0}
C) \frac{\phi}{3}
D) \frac{q}{\varepsilon_0}-\phi
795
MediumMHT CET2024
' n ' small drops of same size are charged to ' V ' volt each. If they coalesce to form a single large drop, then its potential will be
Options:
A) \mathrm{Vn}^{\frac{1}{3}}
B) \mathrm{Vn}^{\frac{2}{3}}
C) \mathrm{V n}
D) \mathrm{Vn}^{-1}
796
MediumMHT CET2024
Two point charges +8 q and -2 q are located at x=0 and x=\mathrm{L} respectively. The location of a point on the x-axis from the origin, at which the net electric field due to these two point charges is zero is
Options:
A) \frac{\mathrm{L}}{4}
B) \mathrm{4 L}
C) \mathrm{8 L}
D) \mathrm{2 L}
797
MediumMHT CET2024
When the dielectric is placed in an external electric field, the electric field inside the dielectric is
Options:
A) less than the external electric field.
B) larger than the external electric field.
C) equal to the external electric field.
D) equal to or greater than external electric field.
798
MediumMHT CET2024
Charges of 2 \mu \mathrm{C} and -3 \mu \mathrm{C} are placed at two points A and B separated by 1 m . The distance of the point from A , where net potential is zero, is
Options:
A) 0.7 m
B) 0.5 m
C) 0.4 m
D) 0.6 m
799
MediumMHT CET2024
Two point charges +q_1 and q_2 repel each other with a force of 100 \mathrm{~N} . q_1 is increased by 10 \% and q_2 is decreased by 10 \%. If they are kept at their original positions the change in the force of repulsion between them is
Options:
A) decreased by 10 N
B) increased by 10 N
C) increased by 1 N
D) decreased by 1 N
800
MediumMHT CET2024
In an electric field due to charge Q, a charge q moves from point A to B as shown in the figure. The work done is ( \varepsilon_0= permittivity of free space)
Options:
A) \frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{Qq}}{\mathrm{r}^2}
B) \frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{Qq}}{\mathrm{r}^2} \frac{\pi}{6}
C) \frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{Qq}}{\mathrm{r}}
D) zero
801
MediumMHT CET2024
If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the system
Options:
A) increases.
B) decreases.
C) does not change.
D) is zero.
802
MediumMHT CET2024
Two point charges +8 q and -2 q are located at \mathrm{X}=0 (origin) and \mathrm{X}=\mathrm{L} respectively. The net electric field due to these two charges is zero at point P on X-axis. The location of point P from the origin is
Options:
A) \frac{L}{4}
B) 2L
C) 4L
D) 8L
803
MediumMHT CET2024
Consider a long uniformly charged cylinder having constant volume charge density ' \lambda ' and radius ' R '. A Gaussian surface is in the form of a cylinder of radius ' r ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder (r< R), electric field is directly proportional to
Options:
A) \mathrm{r}^{-1}
B) \mathrm{r}
C) \mathrm{r}^2
D) \mathrm{r}^{-2}
804
MediumMHT CET2024
An electric dipole will have minimum potential energy when it subtends an angle $\left[\begin{array}{l} \cos 0^{\circ}=1 \\ \sin 0^{\circ}=0 \end{array}\right]\left[\begin{array}{l} \cos 90^{\circ}=0 \\ \cos \pi=-1 \end{array}\right]
Options:
A) \pi with direction of field.
B) \frac{\pi}{2} with direction of field.
C) \frac{3 \pi}{2} with direction of field.
D) zero with direction of field.
805
MediumMHT CET2024
A particle ' A ' has charge ' +q ' and a particle ' B ' has charge ' +4 q '. Each has same mass ' m '. When they are allowed to fall from rest through the same potential, the ratio of their speeds will become (particle A to particle B)
Options:
A) 2: 1
B) 1: 2
C) 1: 4
D) 4: 1
806
MediumMHT CET2024
A sphere ' A ' of radius ' R ' has a charge ' Q ' on it. The field at point B outside the sphere is ' E '. Now another sphere of radius ' 2 R ' having a charge ' -2 Q ' is placed at B. The total field at the point midway between A and B due to both the spheres is
Options:
A) E
B) 3E
C) 12E
D) 15E
807
MediumMHT CET2024
The point charges +\mathrm{q},-\mathrm{q},-\mathrm{q},+\mathrm{q},+\mathrm{Q} and -q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon ' O ' due to the five charges at A, B, C, D and F is thrice the electric field at centre ' O ' due to charge +Q at E alone. The value of Q is
Options:
A) \frac{+q}{3}
B) \frac{+q}{5}
C) \frac{+q}{6}
D) +6 q
808
MediumMHT CET2024
A small particle carrying a negative charge of 1.6 \times 10^{-19} \mathrm{C} is suspended in equilibrium between two horizontal metal plates 8 cm apart having a potential difference of 980 V across them. The mass of the particle is \left[\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right]
Options:
A) 2 \times 10^{-16} \mathrm{~kg}
B) 2.2 \times 10^{-16} \mathrm{~kg}
C) 20 \times 10^{-16} \mathrm{~kg}
D) 4 \times 10^{-16} \mathrm{~kg}
809
MediumMHT CET2024
Charges 3 \mathrm{Q}, \mathrm{q} and Q are placed along x -axis at positions \mathrm{x}=0, \mathrm{x}=\frac{1}{3} and \mathrm{x}=1 respectively. When the force on charge Q is zero, the value of q is
Options:
A) \frac{\mathrm{Q}}{3}
B) -\frac{\mathrm{Q}}{3}
C) \frac{4}{3} \mathrm{Q}
D) -\frac{4}{3} \mathrm{Q}
810
MediumMHT CET2024
If a unit charge is taken from one point to another point over an equipotential surface, then
Options:
A) work is done on the charge.
B) work is done by the charge.
C) work done on the charge is constantly increasing.
D) work done to move a charge is zero.
811
MediumMHT CET2024
Two point charges \mathrm{q}_1=6 \mu \mathrm{C} and \mathrm{q}_2=4 \mu \mathrm{C} are kept at points A and B in air where A B=10 \mathrm{~cm}. What is the increase in potential energy of the system when \mathrm{q}_2 is moved towards \mathrm{q}_1 by 2 cm ? $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI units }\right)
Options:
A) 0.27 J
B) 0.54 J
C) 0.81 J
D) 54 J
812
MediumMHT CET2024
Two point charges (A and B)+4 q and -4 q are placed along a line separated by a distance I '. Force acting between them is F. If 25 \% of charge from point A is transferred to that at point B , the force between the charges now becomes
Options:
A) \frac{3}{4} \mathrm{~F}
B) \frac{4}{3} \mathrm{~F}
C) \frac{9}{16} \mathrm{~F}
D) \frac{16}{9} \mathrm{~F}
813
MediumMHT CET2024
The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of the electric dipole and the point]
Options:
A) \frac{1}{\mathrm{r}}
B) \frac{1}{r^2}
C) r
D) \frac{1}{\mathrm{r}^3}
814
MediumMHT CET2024
Four electric charges +\mathrm{q},+\mathrm{q},-\mathrm{q} and -q are placed in order at the corners of a square of side 2 L. The electric potential at point midway between the two positive charges is
Options:
A) \frac{1}{4 \pi \mathrm{E}_0} \frac{2 \mathrm{q}}{\mathrm{L}}\left(1+\frac{1}{\sqrt{5}}\right)
B) \frac{1}{4 \pi \mathrm{E}_0} \frac{2 \mathrm{q}}{L}\left(1-\frac{1}{\sqrt{5}}\right)
C) \frac{1}{4 \pi \mathrm{E}_0} \frac{2 \mathrm{q}}{\mathrm{L}}(1-\sqrt{5})
D) \frac{1}{4 \pi \mathrm{E}_0} \frac{2 \mathrm{q}}{\mathrm{L}}(1+\sqrt{5})
815
MediumMHT CET2024
Two point charges +10 q and -4 q are located at \mathrm{x}=0 and \mathrm{x}=\mathrm{L} respectively. What is the location of a point on the x-axis from the origin, which the net electric field due to these two point charges is zero?( r= required distance)
Options:
A) \mathrm{r}=\frac{\sqrt{2}}{\sqrt{5}-\sqrt{2}} right to pt. B
B) \mathrm{r}=\frac{\sqrt{2}}{\sqrt{5}-\sqrt{2}} left to pt.A
C) \mathrm{r}=\frac{\sqrt{2}}{\sqrt{5}+\sqrt{2}} right to pt.B
D) \mathrm{r}=\frac{\sqrt{2}}{\sqrt{5}+\sqrt{2}} left to pt.A
816
MediumMHT CET2024
The van de Graaff Generator is not based on
Options:
A) the phenomenon of Corona Discharge in X-ray tube.
B) the application of electric field and magnetic field which are perpendicular to each other.
C) the property that charge given to a hollow conductor is transferred to its outer surface and distributed uniformly over it.
D) the fact that a charge is continuously supplied to an isolated metallic conductor, the potential of the conductor goes on increasing.
817
MediumMHT CET2024
The electric flux over a sphere of radius ' r ' is ' \phi '. If the radius of the sphere is doubled without changing the charge, the flux will be
Options:
A) 4 \phi
B) 2 \phi
C) \phi
D) \frac{\phi}{2}
818
MediumMHT CET2024
If the electric flux entering and leaving an enclosed surface is \phi_1 and \phi_2 then charge enclosed in the surface is (\varepsilon_0= permittivity of free space)
Options:
A) \frac{\phi_2-\phi_1}{\varepsilon_0}
B) \frac{\phi_2+\phi_1}{\varepsilon_0}
C) \frac{\phi_1-\phi_2}{\varepsilon_0}
D) \varepsilon_0\left(\phi_2-\phi_1\right)
819
MediumMHT CET2024
Two surfaces A and B are enclosing the charges as shown below. The total normal electric induction (T.N.E.I) through the surfaces A and B are respectively.
Options:
A) +2 q and +2 q
B) +q and +3 q
C) +q and +2 q
D) +2 q and +3 q
820
MediumMHT CET2024
A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and increases in size, the total electric flux coming out the surface
Options:
A) becomes zero
B) decreases
C) increases
D) remains unchanged
821
MediumMHT CET2024
If a 10 \mu \mathrm{C} charge exists at the centre of a square, the work done in moving a 2 \mu \mathrm{C} point charge from corner A to corner B of a square ABCD is
Options:
A) Zero
B) 5
C) 2
D) 20
822
MediumMHT CET2024
If the electric flux entering and leaving an enclosed surface are \phi_1 and \phi_2 respectively, the electric charge inside the surface will be
Options:
A) \frac{\phi_2-\phi_1}{\varepsilon_0}
B) \frac{\phi_1+\phi_2}{\varepsilon_0}
C) \varepsilon_0\left(\phi_1-\phi_2\right)
D) \varepsilon_0\left(\phi_2-\phi_1\right)
823
MediumMHT CET2024
An electron of mass ' m ' and charge ' q ' is accelerated from rest in a uniform electric field of intensity ' E '. The velocity acquired by it as it travels a distance ' l ' is ' v '. The ratio \frac{\mathrm{q}}{\mathrm{m}} in terms of E, l and v is
Options:
A) \frac{\mathrm{v}_2}{2 \mathrm{E} l}
B) \frac{\mathrm{v}_2 l}{2 \mathrm{E}}
C) \frac{2 \mathrm{E}}{\mathrm{v}^2 l}
D) \frac{\mathrm{v}_2 l}{\mathrm{E}}
824
MediumMHT CET2024
The electric potential at the centre of two concentric half rings of radii R_1 and R_2, having same linear charge density ' \lambda ' is (\varepsilon_0= permittivity of free space)
Options:
A) \frac{2 \lambda}{\varepsilon_0}
B) \frac{\lambda}{2 \varepsilon_0}
C) \frac{\lambda}{4 \varepsilon_0}
D) \frac{\lambda}{\varepsilon_0}
825
MediumMHT CET2024
A metallic sphere ' A ' isolated from ground is charged to +50 \mu \mathrm{C}. This sphere is brought in contact with other isolated metallic sphere ' B ' of half the radius of sphere ' A '. Then the charge on the two isolated spheres A \& B are in the ratio
Options:
A) 1: 2
B) 2: 1
C) 4: 1
D) 1: 1
826
MediumMHT CET2024
A regular hexagon of side 10 cm has a charge 1 \mu \mathrm{C} at each of its vertices. The potential at the centre of hexagon is \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right. SI unit ]
Options:
A) 1.8 \times 10^5 volt
B) 3.6 \times 10^5 volt
C) 5.4 \times 10^5 volt
D) 7.2 \times 10^5 volt
827
MediumMHT CET2024
Two charged particles each having charge ' q ' and mass ' m ' are held at rest while their separation is ' r '. The speed of the particles when their separation is ' \frac{\mathrm{r}}{2} ' will be ( \varepsilon_0= permittivity of the medium)
Options:
A) \frac{q}{4 \pi \varepsilon_0 \mathrm{mr}}
B) \frac{\mathrm{q}}{2 \pi \varepsilon_0 \mathrm{mr}}
C) \frac{\mathrm{q}}{\sqrt{4 \pi \varepsilon_0 \mathrm{mr}}}
D) \frac{\mathrm{q}^2}{4 \pi \varepsilon_0 \mathrm{mr}}
828
MediumMHT CET2024
A charge +Q is placed at each of the diagonally opposite corners of a square. A charge -q is placed at each of the other diagonally opposite corners as shown. If the net electrical force on +Q is zero, then \frac{+Q}{-q} is equal to
Options:
A) +1
B) +2 \sqrt{2}
C) \frac{+1}{\sqrt{2}}
D) -2 \sqrt{2}
829
MediumMHT CET2024
Two equal point charges ' q ' each exert a force ' F ' on each other, when they are placed distance ' x ' apart in air. When the same charges are placed distance ' y ' apart in a medium of dielectric constant ' k ', they exert the same force. The ratio of distance ' y ' to ' x ' is equal to
Options:
A) \frac{1}{\sqrt{\mathrm{k}}}
B) \sqrt{\mathrm{k}}
C) \frac{\sqrt{\mathrm{k}}}{2}
D) \frac{2}{\sqrt{\mathrm{k}}}
830
MediumMHT CET2024
Three charges 2 q,-q and -q are located at the vertices of an equilateral triangle. At the centre of the triangle
Options:
A) the field is zero but potential is non-zero.
B) the field is non-zero but potential is zero.
C) both field and potential are zero.
D) both field and potential are non-zero.
831
MediumMHT CET2024
An electric dipole of moment \overrightarrow{\mathrm{p}} is lying along a uniform electric field \overrightarrow{\mathrm{E}}. The work done in rotating the dipole through \frac{\pi^{\mathrm{c}}}{3} is \left[\sin 30^{\circ}=\cos 60^{\circ}=0 \cdot 5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right]
Options:
A) 3 pE
B) \sqrt{2} \mathrm{pE}
C) pE
D) \frac{\mathrm{pE}}{2}
832
MediumMHT CET2024
Which of the following statement is correct?
Options:
A) Electric lines of force originate from a -vely charged object and terminate on a +vely charged object.
B) The electric line of force do not pass through an insulator but can pass through a conductor.
C) The electric line of force do not intersect each other.
D) Electric intensity is small in a region where the lines of force are crowded.
833
MediumMHT CET2024
Four point charges each +q is placed on the circumference of a circle of diameter 2 d in such a way that they form a square. The potential at the centre is proportional to
Options:
A) \frac{\mathrm{q}^2}{\mathrm{~d}^2}
B) \frac{\mathrm{q}}{\mathrm{d}}
C) \mathrm{\frac{d}{q}}
D) \frac{\mathrm{d}^2}{\mathrm{q}^2}
834
MediumMHT CET2024
90 J of work is done to move an electric charge of magnitude 3 C from a place A , where potential is -10 V to another place B , where potential is ' \mathrm{V}_1 ' volt. The value of \mathrm{V}_1 is
Options:
A) 10 V
B) 20 V
C) 30 V
D) -40 V
835
MediumMHT CET2024
Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' Q ', the electrostatic potential energy of the system is zero?
Options:
A) -q
B) \frac{\mathrm{q}}{2}
C) -2 q
D) -\frac{\mathrm{q}}{2}
836
MediumMHT CET2024
A uniformly charged conducting sphere of diameter 14 cm has surface charge density of 40 \mu \mathrm{Cm}^{-2}. The total electric flux leaving the surface of the sphere is nearly (Permittivity of free space =8.85 \times 10^{-12} SI unit)
Options:
A) 40 kWb
B) 140 kWb
C) 240 kWb
D) 280 kWb
837
MediumMHT CET2024
The electrostatic potential inside a charged spherical ball is given by \mathrm{V}=\mathrm{ar}^2+\mathrm{b} where ' r ' is the distance from its centre and ' a ' and ' b ' are constants. The volume charge density of the ball is [ \varepsilon_0= permittivity of free space ]
Options:
A) -24 \pi \mathrm{a} \varepsilon_0 \mathrm{r}
B) -6 \mathrm{a} \varepsilon_0 \mathrm{r}
C) -24 \pi \mathrm{a} \varepsilon_0
D) -6 \mathrm{a} \varepsilon_0
838
MediumMHT CET2023
A charge $17.7 \times 10^{-4} \mathrm{C} is distributed uniformly over a large sheet of area 200 \mathrm{~m}^2. The electric field intensity at a distance 20 \mathrm{~cm} from it in air will be \left[\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\right]
Options:
A) 5 \times 10^5 \mathrm{~N} / \mathrm{C}
B) 6 \times 10^5 \mathrm{~N} / \mathrm{C}
C) 7 \times 10^5 \mathrm{~N} / \mathrm{C}
D) 8 \times 10^5 \mathrm{~N} / \mathrm{C}
839
MediumMHT CET2023
If $\mathrm{E}_{\mathrm{a}} and \mathrm{E}_{\mathrm{q}} represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance 'r$' from the centre of the dipole, then
Options:
A) \mathrm{E}_{\mathrm{a}}=\mathrm{E}_{\mathrm{q}}
B) \mathrm{E}_{\mathrm{a}}=\frac{1}{2} \mathrm{E}_{\mathrm{q}}
C) \mathrm{E}_{\mathrm{a}}=\frac{1}{\sqrt{2}} \mathrm{E}_{\mathrm{q}}
D) \mathrm{E}_{\mathrm{a}}=2 \mathrm{E}_{\mathrm{q}}
840
MediumMHT CET2023
The electric field intensity on the surface of a solid charged sphere of radius '$r' and volume charge density '\rho' is (\varepsilon_0=$ permittivity of free space)
Options:
A) \frac{\rho r}{3 \varepsilon_0}
B) \frac{\rho}{4 \pi \varepsilon_0 \mathrm{r}}
C) zero
D) \frac{5 \rho \mathrm{r}}{6 \varepsilon_0}
841
MediumMHT CET2023
A uniformly charged semicircular arc of radius '$r' has linear charge density '\lambda'. The electric field at its centre is ( \varepsilon_0=$ permittivity of free space)
Options:
A) \frac{\lambda}{4 \varepsilon_0}
B) \frac{2 \varepsilon_0}{\lambda}
C) \frac{\lambda}{4 \varepsilon_0 \mathrm{r}}
D) \frac{2 \pi \varepsilon_0}{\lambda}
842
MediumMHT CET2023
A conducting sphere of radius $0.1 \mathrm{~m} has uniform charge density 1.8 \mu \mathrm{C} / \mathrm{m}^2 on its surface. The electric field in free space at radial distance 0.2 \mathrm{~m} from a point on the surface is ( \varepsilon_0=$ permittivity of free space)
Options:
A) \frac{6 \times 10^{-6}}{\varepsilon_0} \mathrm{Vm}^{-1}
B) \frac{6 \times 10^{-8}}{\varepsilon_0} \mathrm{Vm}^{-1}
C) \frac{2 \times 10^{-7}}{\varepsilon_0} \mathrm{Vm}^{-1}
D) \frac{1 \times 10^{-7}}{\varepsilon_0} \mathrm{Vm}^{-1}
843
MediumMHT CET2023
The work done in rotating a dipole placed parallel to the electric field through $180^{\circ} is W. So, the work done in rotating it through 60^{\circ} is \left(\cos 0^{\circ}=1, \cos 60^{\circ}=\frac{1}{2}, \cos 180^{\circ}=-1\right)
Options:
A) 4 W
B) 3 \mathrm{~W}
C) W / 2
D) W / 4
844
MediumMHT CET2023
In the electric field due to a charge $Q, a charge q moves from point A to B. The work done is ( \varepsilon_0=$ permittivity of vacuum)
Options:
A) \frac{1}{4 \pi \varepsilon_0} \frac{Q q}{r^2}
B) \frac{1}{4 \pi \varepsilon_0} \frac{Q q}{r} \times \frac{\pi}{6}
C) \frac{1}{4 \pi \varepsilon_0} \frac{Q q}{r}
D) Zero
845
MediumMHT CET2023
Which of the following statements is 'WRONG' for the conductors?
Options:
A) In static situation, the interior of conductor can have no charge.
B) The net electrostatic field is zero in the interior of a conductor.
C) The electrostatic field just outside the surface of charged conductor must be tangential to the surface at any point.
D) The electrostatic potential is constant within and on the surface of a conductor.
846
MediumMHT CET2023
A charged spherical conductor of radius '$R' is connected momentarily to another uncharged spherical conductor of radius 'r$' by means of a thin conducting wire, then the ratio of the surface charge density of the first to the second conductor is
Options:
A) \mathrm{R}: \mathrm{r}^2
B) \mathrm{R}: \mathrm{r}
C) \mathrm{r: R}
D) \mathrm{1: 1}
847
MediumMHT CET2023
If the magnitude of intensity of electric field at a distance '$r_1' on an axial line and at a distance 'r_2' on an equatorial line due to a given short dipole are equal, then r_1: r_2$, is
Options:
A) \sqrt[3]{2}: 1
B) \sqrt{2}: 1
C) 1: 2
D) 1: \sqrt[3]{2}
848
MediumMHT CET2023
Three charges each of value $+q are placed at the corners of an isosceles triangle \mathrm{ABC} of sides \mathrm{AB} and \mathrm{AC} each equal to 2 \mathrm{a}. The mid points of A B and A C are D and E respectively. The work done in taking a charge Q from D to E is ( \varepsilon_0=$ permittivity of free space)
Options:
A) Zero
B) \frac{3 q \mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{a}}
C) \frac{\mathrm{qQ}}{8 \pi \varepsilon_0 \mathrm{a}}
D) \frac{3 \mathrm{qQ}}{8 \pi \varepsilon_0 \mathrm{a}}
849
MediumMHT CET2023
Select the correct statement from the following.
Options:
A) Gravitational force is stronger than electrostatic force
B) Gravitational as well as electrostatic force always attractive.
C) Gravitational as well as electrostatic force always act along the line joining the two objects.
D) Inverse square law $\left(\mathrm{F} \propto \frac{1}{\mathrm{r}^2}\right)$ is not obeyed by electrostatic force.
850
MediumMHT CET2023
Two point charges '$q 1' and 'q 2' are separated by a distance 'd'. What is the increase in potential energy of the system when 'q 2' is moved towards 'q 1' by a distance '\mathrm{x}' ? (x < d)(\frac{1}{4 \pi \varepsilon_0}=K$, constant)
Options:
A) -\frac{K q_1 q_2 x}{d(d-x)}
B) -\frac{K q_1 q_2}{d(d-x)}
C) \frac{\mathrm{Kq}_1 \mathrm{q}_{2 x}}{\left(\mathrm{~d}^2-\mathrm{x}^2\right)}
D) \frac{\mathrm{Kq}_1 \mathrm{q}_2 \mathrm{x}}{\left(\mathrm{d}^2-\mathrm{x}^2\right)}
851
MediumMHT CET2023
Three point charges $\mathrm{+Q,+2q} and +\mathrm{q} are placed at the vertices of a right angled isosceles triangle. The net electrostatic potential energy of the configuration is zero, if Q$ is equal to
Options:
A) -\frac{\sqrt{2}}{3} q
B) +\frac{\sqrt{2}}{3} q
C) -\frac{3}{\sqrt{2}} q
D) +\frac{3}{\sqrt{2}} \mathrm{q}
852
MediumMHT CET2023
Two electric dipoles of moment $\mathrm{P} and 27 \mathrm{P} are placed on a line with their centres 24 \mathrm{~cm}$ apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between the dipoles from the centre of dipole of moment P?
Options:
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
853
MediumMHT CET2023
An electron of mass '$\mathrm{m}' and charge '\mathrm{q}' is accelerated from rest in a uniform electric field of strength 'E'. The velocity acquired by the electron, when it travels a distance '\mathrm{L}$', is
Options:
A) \sqrt{\frac{2 q \mathrm{~m}}{\mathrm{~mL}}}
B) \sqrt{\frac{2 \mathrm{qEL}}{\mathrm{m}}}
C) \sqrt{\frac{2 \mathrm{Em}}{\mathrm{qL}}}
D) \sqrt{\frac{\mathrm{qE}}{\mathrm{mL}}}
854
MediumMHT CET2023
Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All other parameters are unchanged.)
Options:
A) 5 \mathrm{~F}
B) \frac{F}{3}
C) \frac{F}{4}
D) \frac{F}{5}
855
MediumMHT CET2023
Two charges of equal magnitude '$q' are placed in air at a distance '2 r' apart and third charge '-2 \mathrm{q}' is placed at mid point. The potential energy of the system is \left(\varepsilon_0=\right.$ permittivity of free space)
Options:
A) -\frac{q^2}{8 \pi \varepsilon_0 r}
B) -\frac{3 \mathrm{q}^2}{8 \pi \varepsilon_0 \mathrm{r}}
C) -\frac{5 q^2}{8 \pi \varepsilon_0 r}
D) -\frac{7 q^2}{8 \pi \varepsilon_0 r}
856
MediumMHT CET2023
An electron moving with velocity $1.6 \times 10^7 \mathrm{~m} / \mathrm{s} has wavelength of 0.4 \mathop A\limits^o. The required accelerating voltage for the electron motion is [charge on electron =1.6 \times 10^{-19} \mathrm{C}, mass of electron =9 \times 10^{-31} \mathrm{~kg}$ ]
Options:
A) 7.2 \times 10^3 \mathrm{~V}
B) 7.2 \times 10^2 \mathrm{~V}
C) 7.2 \mathrm{~V}
D) 7.2 \times 10^{-2} \mathrm{~V}
857
MediumMHT CET2023
Three point charges $+\mathrm{q},+2 \mathrm{q} and +\mathrm{Q} are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q$ is
Options:
A) \mathrm{Q}=-\frac{2 \mathrm{q}}{3}
B) Q=-\frac{1}{3} q
C) \mathrm{Q}=\frac{3 \mathrm{q}}{2}
D) Q=\frac{q}{2}
858
MediumMHT CET2023
The bob of a simple pendulum of length '$L' has a mass '\mathrm{m}' and charge '\mathrm{q}'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity \mathrm{g}>\mathrm{qE} / \mathrm{m}$ )
Options:
A) 2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}
B) 2 \pi\left[\frac{\mathrm{L}}{\frac{\mathrm{qE}}{\mathrm{m}}-\mathrm{g}}\right]^{\frac{1}{2}}
C) 2 \pi\left[\frac{\mathrm{L}}{\mathrm{g}-\frac{\mathrm{qE}}{\mathrm{m}}}\right]^{\frac{1}{2}}
D) 2 \pi\left[\frac{\mathrm{L}}{\mathrm{g}+\frac{\mathrm{qE}}{\mathrm{m}}}\right]^{\frac{1}{2}}
859
MediumMHT CET2023
Assume that an electric field $\mathrm{E}=30 \mathrm{x}^2 \hat{\mathrm{i}} exists in space. If '\mathrm{V}_0' is the potential at the origin and 'V_A' is the potential at x=2 \mathrm{~m}, then the potential difference \left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_0\right)$ is
Options:
A) -80 \mathrm{~J}
B) -120 \mathrm{~J}
C) 80 \mathrm{~J}
D) 120 \mathrm{~J}
860
MediumMHT CET2023
An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \mathrm{C} separated by a distance of 3 \mathrm{~cm} placed in an electric field of 2 \times 10^5 \mathrm{~N} / \mathrm{C}$ then the maximum torque acting on dipole is
Options:
A) 12 \times 10^{-1} \mathrm{~N}-\mathrm{m}
B) 24 \times 10^{-3} \mathrm{~N}-\mathrm{m}
C) 12 \times 10^{-3} \mathrm{~N}-\mathrm{m}
D) 24 \times 10^{-1} \mathrm{~N}-\mathrm{m}
861
MediumMHT CET2023
When a charge of $3 ~\mathrm{C} is placed in uniform electric field, it experiences a force of 3000 \mathrm{~N}. Within this field, potential difference between two points separated by a distance of 1 \mathrm{~cm}$ is
Options:
A) 10 \mathrm{~V}
B) 90 \mathrm{~V}
C) 1000 \mathrm{~V}
D) 3000 \mathrm{~V}
862
MediumMHT CET2023
The charges $2 \mathrm{q},-\mathrm{q},-\mathrm{q}$ are located at the vertices of an equilateral triangle. At the circumcentre of the triangle
Options:
A) the field is zero but potential is not zero.
B) the field is non-zero but the potential is zero.
C) both, field and potential are zero.
D) both. field and potential are non-zero.
863
MediumMHT CET2023
A solid metallic sphere has a charge $+3 Q. Concentric with this sphere is a conducting spherical shell having charge -\mathrm{Q}. The radius of the sphere is 'A' and that of the spherical shell is 'B'. (B > A). The electric field at a distance '\mathrm{R}' (\mathrm{A} < \mathrm{R} < \mathrm{B}) from the centre is ( \varepsilon_0=$ permittivity of vacuum)
Options:
A) \frac{\mathrm{Q}}{2 \pi \varepsilon_0 \mathrm{R}}
B) \frac{3 Q}{2 \pi \varepsilon_0 R}
C) \frac{3 \mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}
D) \frac{4 Q}{2 \pi \varepsilon_0 R^2}
864
MediumMHT CET2022
If the radius of the spherical gaussian surface is increased then the electric flux due to a point charge enclosed by the surface
Options:
A) increases
B) remains unchanged
C) decreases
D) zero
865
MediumMHT CET2022
Three equal charges '$\mathrm{q}_1', '^{\prime} \mathrm{q}_2' and '\mathrm{q}_3' are placed on the three corners of a square of side 'a'. If the force between \mathrm{q}_1 and \mathrm{q}_2 is '\mathrm{F}_{12}' and that between \mathrm{q}_1 and \mathrm{q}_3 is '\mathrm{F}_{13}', then the ratio of magnitudes \left(\frac{F_{12}}{F_{13}}\right)$ is
Options:
A) \frac{1}{2}
B) \sqrt{2}
C) \frac{1}{\sqrt{2}}
D) 2
866
MediumMHT CET2021
Three charges each of $+1 \mu \mathrm{C} are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is \mathrm{F}, then the net force on either charge will be [\cos 60^{\circ}=0.5$]
Options:
A) 2 \mathrm{F}
B) 3 \mathrm{F}
C) \sqrt{2} \mathrm{~F}
D) \sqrt{3} \mathrm{~F}
867
MediumMHT CET2021
Four electric charges $+\mathrm{q},+\mathrm{q},-\mathrm{q} and -\mathrm{q} are placed in order at the corners of a square of side 2 \mathrm{~L}$. The electric potential at point midway between the two positive charges is
Options:
A) \frac{1}{4 \pi \epsilon_0} \frac{2 \mathrm{q}}{\mathrm{L}}(1-\sqrt{5})
B) zero
C) \frac{1}{4 \pi \epsilon_0} \frac{2 q}{L}\left(1+\frac{1}{\sqrt{5}}\right)
D) \frac{1}{4 \pi \epsilon_0} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right)
868
MediumMHT CET2021
The electric field intensity on the surface of a charged solid sphere of radius '$r' and volume charge dentiy '\rho' is given by (\epsilon_0=$ permittivity of free space)
Options:
A) zero
B) \frac{\sigma \pi}{3 \epsilon_0}
C) \frac{1}{4 \pi \epsilon_0} \frac{\sigma}{r}
D) \frac{5 \pi}{6 \epsilon_0}
869
MediumMHT CET2021
Let A, B and C be the three points in a uniform electric field $\text { ( } \overrightarrow{\mathrm{E}})$ as shown. The electric potential is
Options:
A) maximum at point $\mathrm{C}
B) maximum at point $\mathrm{A}
C) maximum at point $\mathrm{B}
D) same at all points $\mathrm{A}, \mathrm{B} and \mathrm{C}
870
MediumMHT CET2021
Two positive ions, each carrying a charge 'q' are separated by a distance 'd'. If 'F' is the force of repulsion between the ions, the number of electrons from each ion will be ($\varepsilon = charge on \varepsilon_k$ = permittivity of free space)
Options:
A)
\sqrt{\frac{4 \pi \varepsilon_0 \mathrm{~d}^2}{\mathrm{e}^2}}
B)
\sqrt{\frac{4 \pi \varepsilon_0 \mathrm{Fd}}{\mathrm{e}^2}}
C)
\sqrt{\frac{4 \pi \varepsilon_0 F d^2}{\mathrm{e}}}
D)
\sqrt{\frac{4 \pi \varepsilon_0 \mathrm{Fd}^2}{\mathrm{e}^2}}
871
MediumMHT CET2021
Three charges $-\mathrm{q}, \mathrm{Q} and -\mathrm{q} are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero then the ratio \frac{Q}{q}$ is
Options:
A) 1: 2
B) 1: 1
C) 1: 4
D) 1: 3
872
MediumMHT CET2021
Two point charges $+3 \mu \mathrm{C} and +8 \mu \mathrm{C} repel each other with a force of 40 \mathrm{~N}. If a charge of -5 \mu \mathrm{C}$ is added to each of them, then force between them will become
Options:
A) -$10 N
B) 10 N
C) 20 N
D) -$20 N
873
MediumMHT CET2021
In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. the intensity of electric field due to the proton at distance 'r' is $5 \times 10^{11} \mathrm{NC}^{-1}, the magnitude of force between the electron and proton is [charge on electron =1.6 \times 10^{-19} \mathrm{C}$]
Options:
A) 4 \times 10^8 \mathrm{~N}
B) 8 \times 10^8 \mathrm{~N}
C) 4 \times 10^{-8} \mathrm{~N}
D) 8 \times 10^{-8} \mathrm{~N}
874
MediumMHT CET2021
Two charged metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that of the smaller sphere, the electric field near the larger sphere is
Options:
A) twice that near the smaller sphere
B) quarter of that near the smaller sphere
C) same as that near the smaller sphere
D) half of that near smaller sphere
875
MediumMHT CET2021
A charged spherical conductor has radius '$r'. The potential difference between its surface and 3 point at a distance '3 r' from the centre is 'v' The electric intensity at a distance '3 r$' from the centre of the conductor is
Options:
A) \frac{v}{8 r}
B) \frac{v}{2 r}
C) \frac{v}{4 r}
D) \frac{v}{6 r}
876
MediumMHT CET2021
Two spherical conductors of radii $4 \mathrm{~cm} and 5 \mathrm{~cm} are charged to the same potential. If '\sigma_1' and '\sigma_2' be the respective values of the surface density of charge on the two conductors then the ratio \sigma_1: \sigma_2$ is
Options:
A) 5: 4
B) 3: 2
C) 4: 3
D) 2: 1
877
MediumMHT CET2021
An electron of mass '$m' and charge 'q' is accelerated from rest in a uniform electric field of strength 'E'. The velocity acquired by the electron when it travels a distance 'L$' is
Options:
A) \sqrt{\frac{2 \mathrm{qE}}{\mathrm{mL}}}
B) \sqrt{\frac{2 \mathrm{Em}}{\mathrm{qL}}}
C) \sqrt{\frac{2 \mathrm{qEL}}{\mathrm{m}}}
D) \times \sqrt{\frac{\mathrm{qE}}{\mathrm{mL}}}
878
MediumMHT CET2021
Two particles $A and B having same mass have charge +q and +4 q respectively. When they are allowed to fall from rest through same electric potential difference, the ratio of their speeds 'V_A' to '\mathrm{V}_{\mathrm{B}}$' will become
Options:
A) 1: 2
B) 2: 1
C) 1: 4
D) 4: 1
879
MediumMHT CET2021
A point charge $\mathrm{Q} is placed at the centre of the line joining two equal point charges +\mathrm{q} and +\mathrm{q}. The value of Q$ if the system of the charges is in equilibrium, is
Options:
A) \frac{-q}{2}
B) -\frac{9}{4}
C) \frac{+q}{4}
D) \frac{+q}{2}
880
MediumMHT CET2021
When a piece of polythene is rubbed with wool, a negative charge of $4 \times 10^{-7} \mathrm{C} is developed on the polythene. The number of electrons transferred from wool to polythene is [e=1.6 \times\left.10^{-19} \mathrm{C}\right]
Options:
A) 1.5 \times 10^{12}
B) 3.5 \times 10^{13}
C) 2.5 \times 10^{13}
D) 2.5 \times 10^{12}
881
MediumMHT CET2021
A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a distance '3r' from its centre is 'V'. The electric intensity at the distance '3r' from the centre of the sphere will be :
Options:
A) \mathrm{\frac{V}{3r}}
B) 3Vr
C) \mathrm{\frac{V}{r}}
D) \mathrm{\frac{V}{6r}}
882
MediumMHT CET2021
'$\mathrm{F}' is the force between the two identical charged particles placed at a distance '\mathrm{Y}$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes
Options:
A) \frac{F}{4}
B) 4 \mathrm{~F}
C) 2 \mathrm{~F}
D) \frac{\mathrm{F}}{2}
883
MediumMHT CET2021
A uniformly charged semicircular arc of radius '$r' has linear charge density (\lambda), is the electric field at its centre? ( \in_0=$ permittivity of free space)
Options:
A) \frac{\lambda}{4 \epsilon_0 r}
B) \frac{2 \pi \epsilon_0}{\lambda}
C) \frac{\lambda}{4 \epsilon_0}
D) \frac{2 \epsilon_0}{\lambda}
884
MediumMHT CET2021
A hollow charged metal sphere has radius 'R'. If the potential difference between its surface and a point at a distance '5 R' from the centre is $\mathrm{V}$, then magnitude of electric field Intensity at a distance '5R' from the centre of sphere is
Options:
A) \frac{V}{2 R}
B) \frac{\mathrm{V}}{20 \mathrm{R}}
C) 10 \mathrm{VR}
D) 20 \mathrm{VR}
885
MediumMHT CET2021
An electric dipole having dipole moment $\mathrm{P}=\mathrm{q} \times 2 \ell is placed in a uniform electric field '\mathrm{E}$'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively
Options:
A) \mathrm{qE}$ and minimum
B) \mathrm{qE}$ and maximum
C) 2 \mathrm{qE}$ and minimum
D) zero and minimum
886
MediumMHT CET2021
A uniformly charged half ring of a radius ' R ' has linear charge density '$\sigma'. The electric potential at the centre of the half ring is ( \epsilon_0=$ permittivity of free space)
Options:
A) \frac{\sigma}{6 \epsilon_0}
B) \frac{\sigma}{2 \epsilon_0}
C) \frac{\sigma}{\epsilon_0}
D) \frac{\sigma}{4 \epsilon_0}
887
MediumMHT CET2021
A spherical conducting shell of inner radius 'r$_1' and outer radius 'r_2' has a charge 'Q'. A charge -$q is placed at the centre of the shell. The surface charge density on the inner and outer surface of the shell will be
Options:
A) \frac{q}{4 \pi r_1^2} and \frac{\mathrm{Q}-\mathrm{q}}{4 \pi \mathrm{r}_2^2}
B) \frac{q}{4 \pi r_1^2} and \frac{Q}{4 \pi r_2^2}
C) \frac{-q}{4 \pi r_1^2} and \frac{Q+q}{4 \pi r_2^2}
D) zero and $\frac{\mathrm{Q}-\mathrm{q}}{4 \pi \mathrm{r}_2^2}
888
MediumMHT CET2021
A charge of magnitude '2e' and mass '4m' is moving in an electric field $\overrightarrow E $. The acceleration imparted to the above charge is
Options:
A) \mathrm{\frac{2m}{3Ee}}
B) \mathrm{\frac{Ee}{2m}}
C) \mathrm{\frac{2Ee}{3m}}
D) \mathrm{\frac{3m}{2Ee}}
889
MediumMHT CET2020
Van de Graaff generator produces
Options:
A) high voltage and high current
B) high voltage and low current
C) low voltage and low current
D) low voltage and high current
890
MediumMHT CET2020
A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and increases in size, the total electric flux coming out of the surface
Options:
A) increases
B) remains unchanged
C) becomes zero
D) decreases
891
MediumMHT CET2020
Surface density of charge on a charged conducting sphere of radius $R in terms of electric field intensity E at a distance r in free space is (r>R, \varepsilon_0=$ permittivity of free space)
Options:
A) \varepsilon_0 E\left(\frac{R}{r}\right)^2
B) \varepsilon_0 E \frac{R}{r}
C) \varepsilon_0 E\left(\frac{r}{R}\right)^2
D) \varepsilon_0 E \frac{r}{R}
892
MediumMHT CET2019
In case of dimensions of electric field and electric dipole moment the power of mass is reswpectively,
Options:
A) 1, 1
B) 1, 0
C) 0, 1
D) 0, 0
893
MediumMHT CET2019
A charged conductor produces an electric field of intensity 10^3 \mathrm{~V} / \mathrm{m} just outside its surface in vacuum. Then, it produces the electric field of intensity E just outside its surface, when it is placed in a medium of dielectric constant 4. The value of E will be
Options:
A) 400 \mathrm{~V} / \mathrm{m}
B) 450 \mathrm{~V} / \mathrm{m}
C) 250 \mathrm{~V} / \mathrm{m}
D) 150 \mathrm{~V} / \mathrm{m}
894
MediumMHT CET2019
Which of the following is the dimensional formula for electric polarisation?
Options:
A) \left[M^P L^{-2} T^1 I^1\right]
B) \left[M^{-1} L^{-2} T^1 I^{-1}\right]
C) \left[M^P L^{-1} T^{-1} I^1\right]
D) \left[M^1 L^{-2} T^1 I^1\right]
895
MediumMHT CET2019
Which of the following molecules is a polar molecule?
Options:
A)
B)
C)
D)
896
EasyNEET2025
An electric dipole with dipole moment 5 \times 10^{-6} \mathrm{Cm} is aligned with the direction of a uniform electric field of magnitude 4 \times 10^5 \mathrm{~N} / \mathrm{C}. The dipole is then rotated through an angle of 60^{\circ} with respect to the electric field. The change in the potential energy of the dipole is:
Options:
A) 1.2 J
B) 1.5 J
C) 0.8 J
D) 1.0 J
897
MediumNEET2025
Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (Radii of A and B are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as:
Options:
A) \frac{F}{2}
B) \frac{3 F}{8}
C) \frac{3 F}{5}
D) \frac{2 F}{3}
898
MediumNEET2024
A metal cube of side $5 \mathrm{~cm} is charged with 6 \mu \mathrm{C}$. The surface charge density on the cube is
Options:
A) 0.125 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2}
B) 0.25 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2}
C) 4 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2}
D) 0.4 \times 10^{-3} \mathrm{C} \mathrm{m}^{-2}
899
MediumNEET2024
The value of electric potential at a distance of $9 \mathrm{~cm} from the point charge 4 \times 10^{-7} \mathrm{C} is [Given \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 \mathrm{C}^{-2}$] :
Options:
A) 4 \times 10^2 \mathrm{~V}
B) 44.4 \mathrm{~V}
C) 4.4 \times 10^5 \mathrm{~V}
D) 4 \times 10^4 \mathrm{~V}
900
MediumNEET2024
A thin spherical shell is charged by some source. The potential difference between the two points $C and P (in V) shown in the figure is: (Take \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ SI units)
Options:
A) 3 \times 10^5
B) 1 \times 10^5
C) 0.5 \times 10^5
D) Zero
901
MediumNEET2024
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The potential (V) at any axial point, at $2 \mathrm{~m} distance (r) from the centre of the dipole of dipole moment vector \vec{P} of magnitude, 4 \times 10^{-6} \mathrm{C} \mathrm{m}, is \pm 9 \times 10^3 \mathrm{~V}. (Take \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI} units) Reason R: V= \pm \frac{2 P}{4 \pi \epsilon_0 r^2}, where r is the distance of any axial point, situated at 2 \mathrm{~m}$ from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:
Options:
A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true and R is NOT the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.
902
MediumNEET2023
According to Gauss law of electrostatics, electric flux through a closed surface depends on :
Options:
A) the area of the surface
B) the quantity of charges enclosed by the surface
C) the shape of the surface
D) the volume enclosed by the surface
903
MediumNEET2023
A charge $\mathrm{Q} ~\mu \mathrm{C}$ is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit) :
Options:
A) \frac{Q}{\epsilon_0} \times 10^{-6}
B) \frac{2 \mathrm{Q}}{3 \epsilon_0} \times 10^{-3}
C) \frac{\mathrm{Q}}{6 \epsilon_0} \times 10^{-3}
D) \frac{\mathrm{Q}}{6 \epsilon_0} \times 10^{-6}
904
MediumNEET2023
If a conducting sphere of radius $\mathrm{R} is charged. Then the electric field at a distance \mathrm{r}(\mathrm{r} > \mathrm{R}) from the centre of the sphere would be, (\mathrm{V}=$ potential on the surface of the sphere)
Options:
A) \frac{r V}{R^2}
B) \frac{R^2 V}{r^3}
C) \frac{R V}{r^2}
D) \frac{\mathrm{V}}{\mathrm{r}}
905
MediumNEET2023
An electric dipole is placed at an angle of $30^{\circ} with an electric field of intensity 2 \times 10^{5} \mathrm{NC}^{-1}. It experiences a torque equal to 4 ~\mathrm{N~m}. Calculate the magnitude of charge on the dipole, if the dipole length is 2 \mathrm{~cm}$.
Options:
A) 6 mC
B) 4 mC
C) 2 mC
D) 8 mC
906
MediumNEET2023
If $\oint_\limits{s} \vec{E} \cdot \overrightarrow{d S}=0$ over a surface, then:
Options:
A) the magnitude of electric field on the surface is constant.
B) all the charges must necessarily be inside the surface.
C) the electric field inside the surface is necessarily uniform.
D) the number of flux lines entering the surface must be equal to the number of flux lines leaving it.
907
MediumNEET2023
An electric dipole is placed as shown in the figure. The electric potential (in 102 V) at point P due to the dipole is ($\in_0 = permittivity of free space and \frac{1}{4 \pi \epsilon_{0}}$ = K) :
Options:
A) \left(\frac{5}{8}\right) \mathrm{qK}
B) \left(\frac{8}{5}\right) \mathrm{qK}
C) \left(\frac{8}{3}\right) \mathrm{qK}
D) \left(\frac{3}{8}\right) \mathrm{qK}
908
MediumNEET2022
Six charges +q, $-q, +q, -q, +q, and -q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q0 to the centre of the hexagon from infinity is ({\varepsilon _0}$ - permittivity of free space)
Options:
A) {{ - {q^2}} \over {4\pi {\varepsilon _0}d}}\left( {6 - {1 \over {\sqrt 2 }}} \right)
B) Zero
C) {{ - {q^2}} \over {4\pi {\varepsilon _0}d}}
D) {{ - {q^2}} \over {4\pi {\varepsilon _0}d}}\left( {3 - {1 \over {\sqrt 2 }}} \right)
909
MediumNEET2022
The angle between the electric lines of force and the equipotential surface is
Options:
A) 0$^\circ
B) 45$^\circ
C) 90$^\circ
D) 180$^\circ
910
MediumNEET2022
Two hollow conducting spheres of radii R1 and R2 (R1 >> R2) have equal charges. The potential would be
Options:
A) More on bigger sphere
B) More on smaller sphere
C) Equal on both the spheres
D) Dependent on the material property of the sphere
911
MediumNEET2022
Two point charges $-$q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R(R >> L) varies as:
Options:
A) {1 \over {{R^2}}}
B) {1 \over {{R^3}}}
C) {1 \over {{R^4}}}
D) {1 \over {{R^6}}}
912
MediumNEET2021
Polar molecules are the molecules :
Options:
A) having a permanent electric dipole moment
B) having zero dipole moment
C) acquire a dipole moment only in the presence of electric field due to displacement of charges
D) acquire a dipole moment only when magnetic field is absent
913
MediumNEET2021
A dipole is placed in an electric field as shown. In which direction will it move?
Options:
A) towards the right as its potential energy will increase.
B) towards the left as its potential energy will increase.
C) towards the right as its potential energy will decrease.
D) towards the left as its potential energy will decrease.
914
MediumNEET2021
Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres ($\sigma1 / \sigma$2) is :
Options:
A) {{R_1^2} \over {R_2^2}}
B) {{R_1^{}} \over {R_2^{}}}
C) {{R_2^{}} \over {R_1^{}}}
D) \sqrt {\left( {{{{R_1}} \over {{R_2}}}} \right)}
915
MediumNEET2021
Twenty seven drops of same size are charged at 220V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
Options:
A) 1980 V
B) 660 V
C) 1320 V
D) 1520 V
916
MediumNEET2020
A short electric dipole has a dipole moment of 16 $ \times 10-9 Cm. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60^\circ with the dipole axis is :\left( {{1 \over {4\pi {\varepsilon _0}}} = 9 \times {{10}^9}N{m^2}/{C^2}} \right)
Options:
A) 200 V
B) 400 V
C) zero
D) 50 V
917
MediumNEET2020
In a certain region of space with volume 0.2 m3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :
Options:
A) 0.5 N/C
B) 1 N/C
C) 5 N/C
D) zero
918
MediumNEET2020
A spherical conductor of radius 10 cm has a charge of 3.2 $ \times 10-7 C distributed uniformly. That is the magnetude of electric field at a point 15 cm from the centre of the sphere?\left( {{1 \over {4\pi {\varepsilon _0}}} = 9 \times {{10}^9}N{m^2}/{c^2}} \right)
Options:
A) 1.28 $ \times $ 105 N/C
B) 1.28 $ \times $ 106 N/C
C) 1.28 $ \times $ 107 N/C
D) 1.28 $ \times $ 104 N/C
919
MediumNEET2019
A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre :
Options:
A) zero as r increases for r < R, decreases as r increases for r > R
B) zero as r increases for r < R, increases as r increases for r > R.
C) decreases as r increases for r < R and for r > R.
D) increases as r increases for r < R and for r > R.
920
MediumNEET2019
Two point charges A and B, having charges +Q and – Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :
Options:
A) F
B) {{16F} \over 9}
C) {{9F} \over {16}}
D) {{4F} \over 3}
921
MediumNEET2019
Two parallel infinite line charges with linear charge densities +$\lambda C/m and -\lambda $ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?
Options:
A) {{2\lambda } \over {\pi {\varepsilon _0}R}}$ N/C
B) zero
C) {\lambda \over {\pi {\varepsilon _0}R}}$ N/C
D) {\lambda \over {2\pi {\varepsilon _0}R}}$ N/C
922
MediumNEET2018
A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow E . Due to the force q\overrightarrow E $ , its velocity increases from 0 to 6 m s–1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively
Options:
A) 2 m s–1, 4 m s–1
B) 1 m s–1, 3 m s–1
C) 1 m s–1, 3.5 m s–1
D) 1.5 m s–1, 3 m s–1
923
MediumNEET2018
An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is
Options:
A) smaller
B) 5 times greater
C) 10 times greater
D) equal
924
MediumNEET2017
Suppose the charge of a proton and an electron differ slightly. One of them is $-e, the other is (e + \Delta e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch greater than atomic size) apart is zero, then \Delta e is of the order of [Given : mass of hydrogen mh = 1.67 \times 10-$27 kg]
Options:
A) 10$-$23 C
B) 10$-$37 C
C) 10$-$47 C
D) 10$-$20 C
925
MediumNEET2017
The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram.
Options:
A) In all the four cases the work done is the same.
B) Minimum work is required to move q in figure(I).
C) Maximum work is required to move q in figure (II).
D) Maximum work is required to move q in figure (III)
926
MediumNEET2016
An electric dipole is placed at an angle of 30o with an electric field intensity 2 $ \times 105 N C-$1. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is
Options:
A) 8 mC
B) 2 mC
C) 5 mC
D) 7 $\mu $C
927
MediumNEET2016
Two identical charged spheres suspended from a common point by two massless strings of lengths $l, are initially at a distance d(d < < l$) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as
Options:
A) v $ \propto x-$1/2
B) v $ \propto x-$1
C) v $ \propto $ x1/2
D) v $ \propto $ x
928
MediumNEET2015
If potential (in volts) in a region is expressed as V(x, y, z) = 6xy $-$ y + 2yz, the electric field (in N/C) at point (1, 1, 0) is
Options:
A) - \left( {2\widehat i + 3\widehat j + \widehat k} \right)
B) - \left( {6\widehat i + 9\widehat j + \widehat k} \right)
C) - \left( {3\widehat i + 5\widehat j + 3\widehat k} \right)
D) - \left( {6\widehat i + 5\widehat j + 2\widehat k} \right)
929
MediumNEET2015
The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by
Options:
A) 4\pi {\varepsilon _0}A{a^3}
B) {\varepsilon _0}A{a^3}
C) 4\pi {\varepsilon _0}A{a^2}
D) A{\varepsilon _0}{a^2}
930
MediumNEET2014
In a region, the potential is represented by V(x, y, z) = 6x $- 8xy - 8y + 6yz, where V$ is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is
Options:
A) 6\sqrt 5 $ N
B) 30 N
C) 24 N
D) 4\sqrt {35} $ N
931
MediumNEET2014
A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere rrespectively are
Options:
A) zero and ${Q \over {4\pi {\varepsilon _0}{R^2}}}
B) {Q \over {4\pi {\varepsilon _0}R}}$ and zero
C) {Q \over {4\pi {\varepsilon _0}R}} and {Q \over {4\pi {\varepsilon _0}{R^2}}}
D) both are zero
932
MediumNEET2013
An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90o is
Options:
A) p2 E
B) pE
C) infinity
D) pE2
933
MediumNEET2013
A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to
Options:
A) -$Q/4
B) Q/4
C) -$Q/2
D) Q/2
934
MediumNEET2013
Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become
Options:
A) \left( {{{2r} \over {\sqrt 3 }}} \right)
B) \left( {{{2r} \over 3}} \right)
C) {\left( {{1 \over {\sqrt 2 }}} \right)^2}
D) \left( {{r \over {\root 3 \of 2 }}} \right)
935
MediumNEET2013
A, B and C are three points in a uniform electric field. The electric potential is
Options:
A) maximum at C
B) same at all the three points A, B and C
C) maximum at A
D) maximum at B
936
MediumNEET2012
Two metallic spheres of radii 1 cm and 3 cm are given charges of $-1 \times 10-2 C and 5 \times 10-$2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
Options:
A) 2 $ \times 10-$2 C
B) 3 $ \times 10-$2 C
C) 4 $ \times 10-$2 C
D) 1 $ \times 10-$2 C
937
MediumNEET2012
What is the flux through a cube of side $a$ if a point charge of q is at one of its corner?
Options:
A) {{2q} \over {{\varepsilon _0}}}
B) {q \over {8{\varepsilon _0}}}
C) {q \over {{\varepsilon _0}}}
D) {q \over {2{\varepsilon _0}}}6{a^2}
938
MediumNEET2012
Four point charges $-Q, -$q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is
Options:
A) Q = $-$q
B) Q = $ - {1 \over q}
C) Q = q
D) Q = ${1 \over q}
939
MediumNEET2012
An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta with the direction of the field. Assuming that the potential energy of the dipole to be zero when \theta $ = 90o, the torque and the potential energy of the dipole will respectively be
Options:
A) pEsin$\theta , -pEcos\theta
B) pEsin$\theta , -2pEcos\theta
C) pEsin$\theta , 2pEcos\theta
D) pEcos$\theta , -pEsin\theta
940
MediumNEET2011
Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2$a$. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is
Options:
A) {{3qQ} \over {4\pi {\varepsilon _0}a}}
B) {{3qQ} \over {8\pi {\varepsilon _0}a}}
C) {{qQ} \over {4\pi {\varepsilon _0}a}}
D) zero
941
MediumNEET2011
The electric potential V at any point (x, y, z), all in metres in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/meter, is
Options:
A) 8 along negative X-axis
B) 8 along positive X-axis
C) 16 along negative X-axis
D) 16 along positive X-axis
942
MediumNEET2011
A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will
Options:
A) increase four times
B) be reduced to half
C) remain the same
D) be doubled
943
MediumNEET2011
Four electric charges +q, +q, $- q and -$ q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges + q and +q, is
Options:
A) {1 \over {4\pi {\varepsilon _0}}}{{2q} \over L}\left( {1 + \sqrt 5 } \right)
B) {1 \over {4\pi {\varepsilon _0}}}{{2q} \over L}\left( {1 + {1 \over {\sqrt 5 }}} \right)
C) {1 \over {4\pi {\varepsilon _0}}}{{2q} \over L}\left( {1 - {1 \over {\sqrt 5 }}} \right)
D) zero
944
MediumNEET2010
The electric field at a distance ${{3R} \over 2} from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance {R \over 2}$ from the centre of the sphere is
Options:
A) zero
B) E
C) {E \over 2}
D) {E \over 3}
945
MediumNEET2010
Two positives ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)
Options:
A) {{4\pi {\varepsilon _0}F{d^2}} \over {{e^2}}}
B) \sqrt {{{4\pi {\varepsilon _0}F{e^2}} \over {{d^2}}}}
C) \sqrt {{{4\pi {\varepsilon _0}F{d^2}} \over {{e^2}}}}
D) {{4\pi {\varepsilon _0}F{d^2}} \over {{q^2}}}
946
MediumNEET2010
A square surface of side L meter in the plane of the paper is placed in a uniform electric field $E(volt/m) acting along the same plane at an angle \theta $ with the horizontal side of the square as shown in figurre. The electric flux linked to the surface, in units of volt m is
Options:
A) EL2
B) EL2cos$\theta
C) EL2sin$\theta
D) zero
947
MediumNEET2009
The electric potential at a point (x, y, z) is given by V = $-x2y -$ xz3 + 4 The electric field at that point is
Options:
A) \overrightarrow E = \widehat i2xy + \widehat j\left( {{x^2} + {y^2}} \right) + \widehat k\left( {3xz - {y^2}} \right)
B) \overrightarrow E = \widehat i{z^3} + \widehat jxyz + \widehat k{z^2}
C) \overrightarrow E = \widehat i\left( {2xy - {z^3}} \right) + \widehat jx{y^2} + \widehat k3{z^2}x
D) \overrightarrow E = \widehat i\left( {2xy + {z^3}} \right) + \widehat j{x^2} + \widehat k3x{z^2}
948
MediumNEET2009
Three concentric spherical shells have radii a, b and c (a < b < c) anf have surface charge densities $\sigma , -\sigma and \sigma $ respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have
Options:
A) VC = VB $ \ne $ VA
B) VC $ \ne VB \ne $ VA
C) VC = VB = VA
D) VC = VA $ \ne $ VB
949
MediumNEET2008
A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is
Options:
A) E along KO
B) 3E along OK
C) 3E along KO
D) E along OK
950
MediumNEET2008
The electric potential at a point in free space due to charge Q coulomb is Q $ \times $ 1011 volts. The electric field at that point is
Options:
A) 4\pi {\varepsilon _0}Q \times {10^{20}}$ volt/m
B) 12$\pi 0Q \times $ 1022 volt/m
C) 4\pi {\varepsilon _0}Q \times {10^{22}}$ volt/m
D) 12\pi {\varepsilon _0}Q \times {10^{20}}$ volt/m
951
MediumNEET2007
Charges +q and $-$q are placed at points A and B respectively which are a distance 2L apart, C is the midnight between A and B. The work done in moving a charge + Q along the semicircle CRD is
Options:
A) {{qQ} \over {2\pi {\varepsilon _0}L}}
B) {{qQ} \over {6\pi {\varepsilon _0}L}}
C) - {{qQ} \over {6\pi {\varepsilon _0}L}}
D) {{qQ} \over {4\pi {\varepsilon _0}L}}
952
MediumNEET2007
A hollow cylinder has a charge q coulomb within it. If $f$ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of V-m will be
Options:
A) {q \over {2{\varepsilon _0}}}
B) {\phi \over 3}
C) {q \over {{\varepsilon _0}}} - \phi
D) {1 \over 2}\left( {{q \over {{\varepsilon _0}}} - \phi } \right)
953
MediumNEET2007
Three point charges +q, $- 2q and + q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a$, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
Options:
A) \sqrt 2 qa along the line joining points (x = 0, y = 0, z = 0) and (x = a$, y = a, z = 0)
B) q$a along the line joining points (x = 0, y = 0, z = 0) and (x = a$, y = a, z = 0)
C) \sqrt 2 qa$ along +x direction
D) \sqrt 2 qa$ along +y direction.
954
MediumNEET2006
A square surface of side L metres is in the plane of the paper. A uniform electric field $\overrightarrow E $ (volt/m), also in the plane of the paper is limited only to the lower half of the square surface (see figure). The electric flux in SI inits associated with the surface is
Options:
A) EL2
B) EL2/2$\varepsilon $0
C) EL2/2
D) zero
955
MediumNEET2006
An electric dipole of moment $\overrightarrow p is lying along a uniform electric field \overrightarrow E $. The work done in rotating the dipole by 90o is
Options:
A) pE
B) \sqrt 2 pE
C) pE/2
D) 2pE
956
MediumNEET2005
As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge $-Q from the point A [coordinates (0, a$)] to another point B
Options:
A) zero
B) \left( {{{qQ} \over {4\pi {\varepsilon _0}}}{1 \over {{a^2}}}} \right).\sqrt 2 a
C) \left( {{{ - qQ} \over {4\pi {\varepsilon _0}}}{1 \over {{a^2}}}} \right).\sqrt 2 a
D) \left( {{{qQ} \over {4\pi {\varepsilon _0}}}{1 \over {{a^2}}}} \right).{a \over {\sqrt 2 }}
957
MediumNEET2005
Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is ${{{q_3}} \over {4\pi {\varepsilon _0}}}$ where k is
Options:
A) 8q1
B) 6q1
C) 8q2
D) 6q2
958
MediumNEET2004
A bullet of mass 2 g is having a charge of 2 $\mu $C. Through what potential difference must it be accelerated, starting from rst, to acquire a speed of 10 m/s ?
Options:
A) 5 kV
B) 50 kV
C) 5 V
D) 50 V
959
MediumNEET2004
An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively
Options:
A) 2q.E and minimum
B) q.E and p.E
C) zero and minimum
D) q.E and maximum
960
MediumNEET2003
A charge q is located at the centre of a cube. The electric flux through any face is
Options:
A) {{2\pi q} \over {6\left( {4\pi {\varepsilon _0}} \right)}}
B) {{4\pi q} \over {6\left( {4\pi {\varepsilon _0}} \right)}}
C) {{\pi q} \over {6\left( {4\pi {\varepsilon _0}} \right)}}
D) {q \over {6\left( {4\pi {\varepsilon _0}} \right)}}
961
MediumNEET2002
Identical charges ($-$q) are placed at each corners of cube of side b then electrostatic potential energy of charge (+q) which is placed at centre of cube will be
Options:
A) {{ - 4\sqrt 2 {q^2}} \over {\pi {\varepsilon _0}b}}
B) {{ - 8\sqrt 2 {q^2}} \over {\pi {\varepsilon _0}b}}
C) {{ - 4\,{q^2}} \over {\sqrt 3 \,\pi {\varepsilon _0}b}}
D) {{8\sqrt 2 \,{q^2}} \over {4\,\pi {\varepsilon _0}b}}
962
MediumNEET2002
Some charge is being given to a conductor. Then its potential is
Options:
A) maximum at surface
B) maximum at centre
C) remain same throughout the conductor
D) maximum somewhere between surface and centre.
963
MediumNEET2001
A charge Q$\mu $C is placed at the centre of a cube, the flux coming out from each face will be
Options:
A) {Q \over {6{\varepsilon _0}}} \times {10^{ - 6}}
B) {Q \over {6{\varepsilon _0}}} \times {10^{ - 3}}
C) {Q \over {24{\varepsilon _0}}}
D) {Q \over {8{\varepsilon _0}}}
964
MediumNEET2001
A dipole of dipole moment $\overrightarrow p is placed in uniform electric field \overrightarrow E $ then torque acting on it is given by
Options:
A) \overrightarrow \tau = \overrightarrow p .\overrightarrow E
B) \overrightarrow \tau = \overrightarrow p \times \overrightarrow E
C) \overrightarrow \tau = \overrightarrow p + \overrightarrow E
D) \overrightarrow \tau = \overrightarrow p - \overrightarrow E
965
MediumNEET2000
A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is
Options:
A) {Q \over {6{\varepsilon _0}}}
B) {Q \over {8{\varepsilon _0}}}
C) {Q \over {{\varepsilon _0}}}
D) {Q \over {2{\varepsilon _0}}}
966
MediumNEET2000
Electric field at centre O of semicircle of radius $a having linear charge density \lambda $ given as
Options:
A) {{2\lambda } \over {{\varepsilon _0}a}}
B) {{\lambda \pi } \over {{\varepsilon _0}a}}
C) {\lambda \over {2\pi {\varepsilon _0}a}}
D) {\lambda \over {\pi {\varepsilon _0}a}}
967
MediumVITEEE2024
Eight dipoles of charges of magnitude e each are placed inside a cube. The total electric flux coming out of the cube will be
Options:
A) \frac{8 e}{\varepsilon_0}
B) \frac{16 e}{\varepsilon_0}
C) \frac{e}{\varepsilon_0}
D) zero
968
MediumVITEEE2024
The work done in moving a charge particle of charge 2 \times 10^{-8} \mathrm{C} between two points having potential difference of 36 V is
Options:
A) 1.8 \mu \mathrm{~V}
B) 0.72 \mu \mathrm{~V}
C) 3.6 \mu \mathrm{~V}
D) 1.44 \mu \mathrm{~V}
969
MediumVITEEE2024
Three charges, each of +4 \mu \mathrm{C}, are placed at the corners A, B, C of a square A B C D of side 1 m . What is the magnitude (in \mathrm{NC}^{-1} ) of electric field at point O towards point D ?
Options:
A) 66000
B) 72000
C) 51000
D) 64000
970
MediumVITEEE2024
Two point charges of +3 \mu \mathrm{C} and -3 \mu \mathrm{C} are placed at a certain distance apart from each other. Electric potential at a distance 60 cm from the mid-point of dipole on axial line is 150 V , then the value of dipole length is
Options:
A) 2 \times 10^{-3} \mathrm{~m}
B) 2 \times 10^{-4} \mathrm{~m}
C) 10^{-3} \mathrm{~m}
D) 10^{-4} \mathrm{~m}
971
MediumVITEEE2023
Electric field in the region is given by $\mathbf{E}=\left(M / x^4\right) \hat{\mathbf{i}}$, then the correct expression for the potential in the region is (assume potential at infinity is zero)
Options:
A) M / 3 x^3
B) M x^3
C) M / 3 x^4
D) M / x^2
972
MediumVITEEE2021
The net electric force on a charge of $+3 \mu \mathrm{C} at the mid-point on the line joining two charges of magnitude +2 \mu \mathrm{C} and -2 \mu \mathrm{C} separated by the distance of 6 \mathrm{~mm}$, is
Options:
A) 6000 N
B) 500 N
C) 60 N
D) zero
973
MediumVITEEE2021
A hollow sphere of radius $0.1 \mathrm{~m} has a charge of 5 \times 10^{-8} \mathrm{C}. The potential at a distance of 5 \mathrm{cm} from the centre of the sphere is \left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)
Options:
A) 4000 V
B) 4500 V
C) 5000 V
D) 6000 V
974
MediumVITEEE2021
An electric charge does not have which of the following properties?
Options:
A) Total charge conservation
B) Quantisation of charge
C) Two type of charge
D) Circular line of force
974
Total Questions
114
Easy
837
Medium
23
Hard
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