Class 12 • Physics

EM waves

Chapter-8

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MediumBITSAT2023

The electric and the magnetic field associated with an E.M. wave, propagating along the $\mathrm{Z}$-axis can be represented by

Options:

A) \left(\mathbf{E}=E_0 \hat{\mathbf{i}}, \mathbf{B}=B_0 \hat{\mathbf{j}}\right)

B) \left(\mathbf{E}=E_0 \hat{k}, \mathbf{B}=B_0 \hat{\mathbf{i}}\right)

C) \left(\mathbf{E}=E_0 \hat{\mathbf{j}}, \mathbf{B}=B_0 \hat{\mathbf{i}}\right)

D) \left(\mathrm{E}=E_0 \hat{\mathrm{j}}, \mathrm{B}=B_0 \hat{\mathrm{k}}\right)

MediumBITSAT2022

An electromagnetic wave is propagating along X-axis. At x = 1 cm and t = 18s, its electric vector |E| = 8 V/m, then the magnitude of its magnetic vector is

Options:

A) 2.66 $\times 10-$8

B) 3 $\times 10-$7

C) 3.14 $\times 10-$8

D) 3.16 $\times 10-$7

MediumBITSAT2021

Choose the correct statement.

Options:

A) The speed of light in the meta-material is $v = c|n|$.

B) The speed of light in the meta-material is $v = {c \over {|n|}}$.

C) The speed of light in the meta-material is v = c.

D) The wavelength of the light in the meta-material ($\lambdam) is given by \lambdam = \lambda$air | n |.

MediumBITSAT2020

The magnetic field of a beam emerging from a fitter facing a flood light is given by B = 10 $\times 10-8 sin(1 \times 107z - 3.6 \times$ 1015t)T. The average intensity of the beam is

Options:

A) 1.82 W/m2

B) 1.19 W/m2

C) 1.18 W/m2

D) 1.17 W/m2

MediumCOMEDK2025

A plane electromagnetic wave with frequency 40 MHz travels in free space. At a particular point in space and time, the magnetic field is 2 \times 10^{-8} T. What will be the electric field at this point?

Options:

A) 16 \mathrm{Vm}^{-1}

B) 6 \mathrm{Vm}^{-1}

C) 8 \mathrm{Vm}^{-1}

D) 18 \mathrm{Vm}^{-1}

MediumCOMEDK2025

The electric and magnetic fields associated with an electromagnetic wave propagating along +z axis, can be represented by

Options:

A) E=E_0 i, \quad B=B_0 j

B) E=E_0 i, \quad B=B_0 k

C) E=E_0 k, \quad B=B_0 j

D) E=E_0 j, \quad B=B_0 k

MediumCOMEDK2024

Column - I lists the waves of the electromagnetic spectrum. Column - II gives approximate frequency range of these waves. Match Column - I and Column - II and choose the correct match from the given choices. Column I Column II (A) Radiowaves (P) $10^{18} \text { to } 10^{20} \mathrm{~Hz} (B) Microwaves (P) 10^{11} \text { to } 5 \times 10^{14} \mathrm{~Hz} (C) Infrared (R) 10^4 \text { to } 10^8 \mathrm{~Hz} (D) X-rays (S) 10^9 \text { to } 10^{12} \mathrm{~Hz}

Options:

A) (A)-(R) (B)-(P) (C)-(S) (D)-(Q)

B) (A)-(R) (B)-(S) (C)-(Q) (D)-(P)

C) (A)-(R) (B)-(S) (C)-(P) (D)-(Q)

D) (A)-(R) (B)-(Q) (C)-(S) (D)-(P)

MediumCOMEDK2024

An electromagnetic wave of frequency $3 \mathrm{~MHz} passes from vacuum into a dielectric medium (\mu_r=1)$ of relative permittivity 4.0. Then,

Options:

A) Wavelength is halved and frequency is doubled

B) Wavelength doubled and frequency remains unchanged

C) Wavelength and frequency are unchanged

D) Wavelength is halved and frequency remains unchanged

MediumCOMEDK2023

The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in vacuum is

Options:

A) reciprocal of speed of light in vacuum

B) the speed of light in vacuum

C) proportional to frequency of the electromagnetic wave

D) inversely proportional to the frequency of the electromagnetic wave

MediumCOMEDK2023

A plane electromagnetic wave of frequency $20 \mathrm{~MHz} travels through a space along x-direction. If the electric field vector at a certain point in space is 6 \mathrm{~Vm}^{-1}$, then what is the magnetic field vector at that point?

Options:

A) 2 \times 10^{-8} \mathrm{~T}

B) \frac{1}{2} \times 10^{-8} \mathrm{~T}

C) 2 \mathrm{~T}

D) \frac{1}{2} \mathrm{~T}

MediumCOMEDK2023

What feature of the infrared waves make it useful for the haze photography?

Options:

A) Since it is invisible

B) Since it has large wave length

C) Since it is absorbed by the medium

D) Since it has high frequency

MediumCOMEDK2022

Speed of electromagnetic wave in a medium having relative permittivity $\varepsilon_r and relative permeability \mu_r is (speed of light in air, c=3\times10^8$ m/s)

Options:

A) {1 \over {\sqrt {{\mu _r}{\varepsilon _r}} }}

B) {c \over {\sqrt {{\mu _r}{\varepsilon _r}} }}

C) c\sqrt {{{{\mu _r}} \over {{\varepsilon _r}}}}

D) {c \over {{\mu _r}{\varepsilon _r}}}

MediumCOMEDK2022

A 30 mW laser beam has a cross-sectional area of 15 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by [Permuittivity of space, $\varepsilon_0=9\times10^{-12} Speed of light, c=3\times10^8$ m/s]

Options:

A) 1.22 kV/m

B) 12 kV/m

C) 10 kV/m

D) 201 kV/m

MediumCOMEDK2021

The correct arrangement in increasing order of wavelength of X-rays, UV rays, microwave is

Options:

A) microwave, X-rays, UV rays

B) UV rays, X-rays, microwave

C) X-rays, UV rays, microwave

D) microwave, UV rays, X-rays

MediumCOMEDK2021

Which of the following waves are used to treatment of muscles ache?

Options:

A) Ultraviolet

B) Infrared

C) Microwave

D) X-rays

MediumCOMEDK2020

Which of the following has/have zero average value in a plane electromagnetic wave?

Options:

A) Electric field

B) Magnetic field

C) Both (a) and (c)

D) Magnetic energy

HardJee Advance2025

A cube of unit volume contains 35 \times 10^7 photons of frequency 10^{15} \mathrm{~Hz}. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is \alpha \times 10^{-9} \mathrm{~T}. Taking permeability of free space \mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}, Planck's constant h=6 \times 10^{-34} \mathrm{Js} and \pi=\frac{22}{7}, the value of \alpha is ____________.

Options:

MediumJee Advance2023

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by \vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Vm}^{-1}. Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, c=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1} ]

Options:

A) B_x=-2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Wb} \mathrm{m}^{-2}.

B) B_y=2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Wb} \mathrm{m}^{-2}.

C) The wave is polarized in the x y-plane with polarization angle 30^{\circ} with respect to the x-axis.

D) The refractive index of the medium is 2.

MediumJee Advance2015

In terms of potential difference V, electric current I, permittivity ${\varepsilon _0}, permeability {\mu _0}$ and speed of light c, the dimensionally correct equation(s) is(are) :

Options:

A) {\mu _0}{I^2} = {\varepsilon _0}{V^2}

B) {\varepsilon _0}I = {\mu _0}V

C) I = {\varepsilon _0}cV

D) {\mu _0}cI = {\varepsilon _0}V

EasyJee Advance2018

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E] and [B] stand for dimensions of electric and magnetic fields respectively, while \left[ {{\varepsilon _0}} \right] and \left[ {{\mu _0}} \right] stand for dimensions of the permittivity and permeability of free space respectively. \left[ L \right] and \left[ T \right] are dimensions of length and time respectively. All the quantities are given in SI units. The relation between \left[ {{\varepsilon _0}} \right] and \left[ {{\mu _0}} \right]$ is

Options:

A) \left[ {{\mu _0}} \right] = \left[ {{\varepsilon _0}} \right]{\left[ L \right]^2}{\left[ T \right]^{ - 2}}

B) \left[ {{\mu _0}} \right] = \left[ {{\varepsilon _0}} \right]{\left[ L \right]^{ - 2}}{\left[ T \right]^2}

C) \left[ {{\mu _0}} \right] = {\left[ {{\varepsilon _0}} \right]^{ - 1}}{\left[ L \right]^2}{\left[ T \right]^{ - 2}}

D) \left[ {{\mu _0}} \right] = {\left[ {{\varepsilon _0}} \right]^{ - 1}}{\left[ L \right]^{ - 2}}{\left[ T \right]^2}

EasyJee Advance2018

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E] and [B] stand for dimensions of electric and magnetic fields respectively, while \left[ {{\varepsilon _0}} \right] and \left[ {{\mu _0}} \right] stand for dimensions of the permittivity and permeability of free space respectively. \left[ L \right] and \left[ T \right] are dimensions of length and time respectively. All the quantities are given in SI units. The relation between [E] and [B]$ is

Options:

A) \left[ E \right] = \left[ B \right]\left[ L \right]\left[ T \right]

B) \left[ E \right] = \left[ B \right]{\left[ L \right]^{ - 1}}\left[ T \right]

C) \left[ E \right] = \left[ B \right]\left[ L \right]{\left[ T \right]^{ - 1}}

D) \left[ E \right] = \left[ B \right]{\left[ L \right]^{ - 1}}{\left[ T \right]^{ - 1}}

EasyJee Advance2013

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 $\times 108 ms-$1. The final momentum of the object is

Options:

A) 0.3 $\times 10-17 kg-ms-$1

B) 1.0 $\times 10-17 kg-ms-$1

C) 3.0 $\times 10-17 kg-ms-$1

D) 9.0 $\times 10-17 kg-ms-$1

MediumJEE Mains2014

If microwaves, X rays, infracted, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength :

Options:

A) R, M, I, V, U, X and G

B) M, R, V, X, U, G and I

C) G, X, U, V, I, M and R

D) I, M, R, U, V, X and G

MediumJEE Mains2014

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :

Options:

A) 1.34 V/m

B) 2.68 V/m

C) 4.02 V/m

D) 5.36 V/m

MediumJEE Mains2014

Match the List - I (Phenomenon associated with electromagnetic radiation) with List - II (Part of electromagnetic spectrum) and select the correct code from the choices given the lists : List - I List - II (I) Doublet of sodium (A) Visible radiation (II) Wavelengthcorresponding totemperature associatedwith the isotropicradiation filling all space (B) Microwave (III Wavelength emitted byatomic hydrogen ininterstellar space (C) Short radiowave (IV) Wavelength of radiationarising from two closeenergy levels in hydrogen (D) X - rays

Options:

A) (I)-(A), (II)-(B), (III)-(B), (IV)-(C)

B) (I)-(A), (II)-(B), (III)-(C), (IV)-(C)

C) (I)-(D), (II)-(C), (III)-(A), (IV)-(B)

D) (I)-(B), (II)-(A), (III)-(D), (IV)-(A)

MediumJEE Mains2014

An electromagnetic wave of frequency 1 $ \times 1014 hertz is propagating along z - axis. The amplitude of electric field is 4 V/m. If \in 0 = 8.8 \times 10-$12 C2/N-m2, then average energy density of electric field will be :

Options:

A) 35.2 $ \times 10-$10 J/m3

B) 35.2 $ \times 10-$11 J/m3

C) 35.2 $ \times 10-$12 J/m3

D) 35.2 $ \times 10-$13 J/m3

EasyJEE Mains2014

Match List I (Wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists.

Options:

A) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

B) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

C) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

D) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

EasyJEE Mains2015

For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for $\overrightarrow E and \overrightarrow B $ field respectively ?

Options:

A) \left( {\widehat i + 2\widehat j} \right)\,\, and \left( {2\widehat i - \widehat j} \right)

B) \left(-\, {2\widehat i - 3\widehat j} \right) and \left( {3\widehat i - 2\widehat j} \right)

C) \left( {2\widehat i + 3\widehat j} \right) and \left( {\widehat i + 2\widehat j} \right)

D) \left( {3\widehat i + 4\widehat j} \right) and \left( {4\widehat i - 3\widehat j} \right)

EasyJEE Mains2015

An electromagnetic wave travelling in the x-direction has frequency of 23 $ \times 1014 Hz and electric field amplitude of 27 Vm-$1. From the options given below, which one describes the magnetic field for this wave ?

Options:

A) \overrightarrow B (x, t) = (3 \times 10-8T) \widehat j sin [ 2\pi (1.5 \times 10-8x - 2 \times $ 1014t)]

B) \overrightarrow B (x, t) = (9 \times 10-8T) \widehat k sin [ 2\pi (1.5 \times 10-6x - 2 \times $ 1014t)]

C) \overrightarrow B (x, t) = (9 \times 10-8T) \widehat i sin [ 2\pi (1.5 \times 10-8x - 2 \times $ 1014t)]

D) \overrightarrow B (x, t) = (9 \times 10-8T) \widehat j sin [(1.5 \times 10-6 x - 2 \times $ 1014t)]

EasyJEE Mains2026

A plane electromagnetic wave is moving in free space with velocity c = 3 \times 10^8 m/s and its electric field is given as \vec{E}=54\sin(kz - \omega t)\,\hat{j} V/m, where \hat{j} is the unit vector along y-axis. The magnetic field vector \vec{B} of the wave is :

Options:

A) -1.8\times 10^{-7}\sin(kz - \omega t)\,\hat{i} T

B) +1.8\times 10^{-7}\sin(kz - \omega t)\,\hat{i} T

C) 1.4\times 10^{-7}\sin(kz - \omega t)\,\hat{k} T

D) 1.4\times 10^{-7}\sin(kz - \omega t)\,\hat{i} T

EasyJEE Mains2026

The electric field of an electromagnetic wave travelling through a medium is given by \vec{E}(x, t)=25 \sin \left(2.0 \times 10^{15} t-10^7 x\right) \hat{n} then the refractive index of the medium is \_\_\_\_ . (All given measurement are in SI units)

Options:

A) 2

B) 1.2

C) 1.5

D) 1.7

MediumJEE Mains2026

\text { Match the LIST-I with LIST-II } List-I List-II A. Radio-wave I. is produced by Magnetron valve B. Micro-wave II. due to change in the vibrational modes of atoms C. Infrared-wave III. due to inner shell electrons moving from higher energy level to lower energy level D. X-ray IV. due to rapid acceleration of electrons Choose the correct answer from the options given below:

Options:

A) A-IV, B-II, C-I, D-III

B) A-IV, B-III, C-I, D-II

C) A-IV, B-I, C-II, D-III

D) A-II, B-IV, C-III, D-I

EasyJEE Mains2026

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability of \mu=2 \mu_0, is ( \mu_0= permeability of vacuum)

Options:

A) 6: 1

B) 3: 2

C) \sqrt{6}: 1

D) 36: 1

EasyJEE Mains2026

\text { Match List - I with List - II. } List - IRelation List - IILaw A. \oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d a} I. Ampere's circuital law B. \oint \vec{B} \cdot \overrightarrow{d l}=\mu_0\left(I+\epsilon_0 \frac{d \phi_E}{d t}\right) II. Faraday's laws of electromagnetic induction C. \oint \vec{E} \cdot \overrightarrow{d a}=\frac{1}{\epsilon_0} \int_{\mathrm{v}} \rho \mathrm{dv} III. Ampere - Maxwell law D. \oint \vec{B} \cdot \overrightarrow{d l}=\mu_0 I$ IV. Gauss's law of electrostatics Choose the correct answer from the options given below :

Options:

A) A-I, B-IV, C-III, D-II

B) A-II, B-III, C-IV, D-I

C) A-IV, B-I, C-II, D-III

D) A-II, B-III, C-I, D-IV

MediumJEE Mains2026

A laser beam has intensity of 4.0 \times 10^{14} \mathrm{~W} / \mathrm{m}^2. The amplitude of magnetic field associated with beam is \_\_\_\_ T. (Take \epsilon_{\mathrm{o}}=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2 and \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s} )

Options:

A) 1.83

B) 2.0

C) 5.5

D) 18.3

EasyJEE Mains2026

The electric field in a plane electromagnetic wave is given by : $ E_y=69 \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right] \mathrm{V} / \mathrm{m} . The expression for magnetic field associated with this electromagnetic wave is \_\_\_\_$ T.

Options:

A) B_z=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right]

B) B_z=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x+1.8 \times 10^{11} t\right]

C) B_y=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right]

D) B_y=69 \sin \left[0.6 \times 10^3 x+1.8 \times 10^{11} t\right]

EasyJEE Mains2025

The unit of \sqrt{\frac{2I}{\varepsilon_0 c}} is :(I = intensity of an electromagnetic wave, c = speed of light)

Options:

A) Vm

B) NC-1

C) NC

D) Nm

EasyJEE Mains2025

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, \vec{E} and magnetic field, \vec{B} vectors associated with the wave in Cartesian frame are

Options:

A) E_x, B_y

B) E_y, B_x

C) E_y, B_z

D) E_z, B_y

EasyJEE Mains2025

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum.Reason (R) : Mass of a photon 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 true and (R) is the correct explanation of (A)

B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

C) (A) is false but (R) is true

D) (A) is true but (R) is false

MediumJEE Mains2025

The magnetic field of an E.M. wave is given by \vec{B} = \left( \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \right) 30 \sin \left[ \omega \left( t - \frac{z}{c} \right) \right] (S.I. Units).The corresponding electric field in S.I. units is:

Options:

A) \overrightarrow{\mathrm{E}}=\left(\frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{z}{\mathrm{c}}\right)\right]

B) \overrightarrow{\mathrm{E}}=\left(\frac{1}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}-\frac{z}{\mathrm{c}}\right)\right]

C) \overrightarrow{\mathrm{E}}=\left(\frac{\sqrt{3}}{2} \hat{i}-\frac{1}{2} \hat{j}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{z}{\mathrm{c}}\right)\right]

D) \overrightarrow{\mathrm{E}}=\left(\frac{3}{4} \hat{i}+\frac{1}{4} \hat{j}\right) 30 \mathrm{c} \cos \left[\omega\left(\mathrm{t}-\frac{z}{\mathrm{c}}\right)\right]

MediumJEE Mains2025

Due to presence of an em-wave whose electric component is given by E=100 \sin (\omega t-k x) \mathrm{NC}^{-1} a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Options:

A) 50 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}

B) 400 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}

C) 200 \sin (\omega t-k x) \mathrm{NC}^{-1}

D) 25 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}

EasyJEE Mains2025

Arrange the following in the ascending order of wavelength (\lambda) : (A) Microwaves \left(\lambda_1\right) (B) Ultraviolet rays \left(\lambda_2\right) (C) Infrared rays \left(\lambda_3\right) (D) X-rays \left(\lambda_4\right) Choose the most appropriate answer from the options given below :

Options:

A) \lambda_4<\lambda_3<\lambda_2<\lambda_1

B) \lambda_4<\lambda_2<\lambda_3<\lambda_1

C) \lambda_3<\lambda_4<\lambda_2<\lambda_1

D) \lambda_4<\lambda_3<\lambda_1<\lambda_2

EasyJEE Mains2025

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is \mathrm{E}_y=9.3 \mathrm{Vm}^{-1}. Then, the magnetic field vector of the wave at that point is

Options:

A) \mathrm{B}_z=1.55 \times 10^{-8} \mathrm{~T}

B) \mathrm{B}_z=6.2 \times 10^{-8} \mathrm{~T}

C) \mathrm{B}_z=3.1 \times 10^{-8} \mathrm{~T}

D) \mathrm{B}_z=9.3 \times 10^{-8} \mathrm{~T}

MediumJEE Mains2025

The electric field of an electromagnetic wave in free space is \overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C. The associated magnetic field in Tesla is

Options:

A) \overrightarrow{\mathrm{B}}=\frac{57}{3 \times 10^8} \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](\hat{k})

B) \overrightarrow{\mathrm{B}}=\frac{57}{3 \times 10^8} \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](5 \hat{k})

C) \overrightarrow{\mathrm{B}}=-\frac{57}{3 \times 10^8} \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](\hat{k})

D) \overrightarrow{\mathrm{B}}=-\frac{57}{3 \times 10^8} \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](5 \hat{k})

MediumJEE Mains2024

The magnetic field in a plane electromagnetic wave is $\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{T}$. The corresponding electric field will be :

Options:

A) E_z=105 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}

B) E_y=10.5 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}

C) E_y=1.17 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}

D) E_z=1.17 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{Vm}^{-1}

MediumJEE Mains2024

A plane EM wave is propagating along $x direction. It has a wavelength of 4 \mathrm{~mm}. If electric field is in y direction with the maximum magnitude of 60 \mathrm{~Vm}^{-1}$, the equation for magnetic field is :

Options:

A) \mathrm{B}_z=2 \times 10^{-7} \sin \left[\frac{\pi}{2}\left(x-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}

B) \mathrm{B}_z=2 \times 10^{-7} \sin \left[\frac{\pi}{2} \times 10^3\left(x-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}

C) \mathrm{B}_z=60 \sin \left[\frac{\pi}{2}\left(x-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}

D) \mathrm{B}_x=60 \sin \left[\frac{\pi}{2}\left(x-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{i}} \mathrm{T}

MediumJEE Mains2024

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{-4} \mathrm{~N}. If 360 \mathrm{~W} / \mathrm{cm}^2$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Options:

A) 20 \mathrm{~m}^2

B) 0.2 \mathrm{~m}^2

C) 0.1 \mathrm{~m}^2

D) 0.02 \mathrm{~m}^2

EasyJEE Mains2024

In the given electromagnetic wave $\mathrm{E}_{\mathrm{y}}=600 \sin (\omega t-\mathrm{kx}) \mathrm{Vm}^{-1}, intensity of the associated light beam is (in \mathrm{W} / \mathrm{m}^2 : (Given \epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

Options:

A) 486

B) 729

C) 243

D) 972

EasyJEE Mains2024

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$. The relative permeability of the medium is 2.0. The relative permittivity will be:

Options:

A) 4

B) 1

C) 2

D) 5

EasyJEE Mains2024

Match List I with List II : LIST IEM-Wave LIST IIWavelength Range A. Infra-red I. $<10^{-3} nm B. Ultraviolet II. 400 nm to 1 nm C. X-rays III. 1 mm to 700 nm D. Gamma rays IV. 1 nm to 10^{-3}$ nm Choose the correct answer from the options given below :

Options:

A) (A)-(I), (B)-(III), (C)-(II), (D)-(IV)

B) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)

C) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

D) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

EasyJEE Mains2024

Arrange the following in the ascending order of wavelength: A. Gamma rays $\left(\lambda_1\right) B. x - rays \left(\lambda_2\right) C. Infrared waves \left(\lambda_3\right) D. Microwaves \left(\lambda_4\right)$ Choose the most appropriate answer from the options given below

Options:

A) \lambda_1<\lambda_2<\lambda_3<\lambda_4

B) \lambda_2<\lambda_1<\lambda_4<\lambda_3

C) \lambda_4<\lambda_3<\lambda_2<\lambda_1

D) \lambda_4<\lambda_3<\lambda_1<\lambda_2

EasyJEE Mains2024

The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t}-z / \mathrm{c}) \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit) :

Options:

A) \overrightarrow{\mathrm{B}}=\hat{j} \frac{40}{\mathrm{c}} \cos \omega(\mathrm{t}-z / \mathrm{c})

B) \overrightarrow{\mathrm{B}}=\hat{i} \frac{40}{\mathrm{c}} \cos \omega(\mathrm{t}-z / \mathrm{c})

C) \vec{B}=\hat{j} 40 \cos \omega(t-z / c)

D) \overrightarrow{\mathrm{B}}=\hat{k} \frac{40}{\mathrm{c}} \cos \omega(\mathrm{t}-z / \mathrm{c})

EasyJEE Mains2024

If frequency of electromagnetic wave is 60 \mathrm{~MHz} and it travels in air along z direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \mathrm{m} ) is :

Options:

A) 2.5

B) 5

C) 10

D) 2

EasyJEE Mains2024

Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:

Options:

A) Statement I is incorrect but Statement II is correct.

B) Both Statement I and Statement II are correct.

C) Statement I is correct but Statement II is incorrect.

D) Both Statement I and Statement II are incorrect.

EasyJEE Mains2024

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \mathrm{~Hz} and an amplitude of 50 \mathrm{~Vm}^{-1}. The total average energy density of the electromagnetic field of the wave is : [Use \varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ ]

Options:

A) 4.425 \times 10^{-8} \mathrm{Jm}^{-3}

B) 2.212 \times 10^{-10} \mathrm{Jm}^{-3}

C) 2.212 \times 10^{-8} \mathrm{Jm}^{-3}

D) 1.106 \times 10^{-8} \mathrm{Jm}^{-3}

EasyJEE Mains2024

The electric field of an electromagnetic wave in free space is represented as $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \cos (\omega \mathrm{t}-\mathrm{kz}) \hat{i}$. The corresponding magnetic induction vector will be :

Options:

A) \overrightarrow{\mathrm{B}}=\mathrm{E}_0 \mathrm{C} \cos (\omega \mathrm{t}+\mathrm{k} z) \hat{j}

B) \overrightarrow{\mathrm{B}}=\frac{\mathrm{E}_0}{\mathrm{C}} \cos (\omega \mathrm{t}-\mathrm{kz}) \hat{j}

C) \overrightarrow{\mathrm{B}}=\mathrm{E}_0 \mathrm{C} \cos (\omega \mathrm{t}-\mathrm{k} z) \hat{j}

D) \overrightarrow{\mathrm{B}}=\frac{\mathrm{E}_0}{\mathrm{C}} \cos (\omega \mathrm{t}+\mathrm{kz}) \hat{j}

EasyJEE Mains2024

A plane electromagnetic wave of frequency $35 \mathrm{~MHz} travels in free space along the X-direction. At a particular point (in space and time) \vec{E}=9.6 \hat{j} \mathrm{~V} / \mathrm{m}$. The value of magnetic field at this point is :

Options:

A) 9.6 \hat{j} T

B) 3.2 \times 10^{-8} \hat{i} T

C) 9.6 \times 10^{-8} \hat{k} T

D) 3.2 \times 10^{-8} \hat{k} T

MediumJEE Mains2024

An object is placed in a medium of refractive index 3 . An electromagnetic wave of intensity $6 \times 10^8 \mathrm{~W} / \mathrm{m}^2 falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space =3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ) :

Options:

A) 6 \mathrm{~Nm}^{-2}

B) 36 \mathrm{~Nm}^{-2}

C) 18 \mathrm{~Nm}^{-2}

D) 2 \mathrm{~Nm}^{-2}

EasyJEE Mains2024

A plane electromagnetic wave propagating in $\mathrm{x}-direction is described by E_y=\left(200 \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 t-0.05 x\right] \text {; } The intensity of the wave is : (Use \epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$)

Options:

A) 35.4 \mathrm{~Wm}^{-2}

B) 53.1 \mathrm{~Wm}^{-2}

C) 26.6 \mathrm{~Wm}^{-2}

D) 106.2 \mathrm{~Wm}^{-2}

EasyJEE Mains2023

Match List I with List II of Electromagnetic waves with corresponding wavelength range : List I List II (A) Microwave (I) 400 \mathrm{~nm} to 1 \mathrm{~nm} (B) Ultraviolet (II) 1 \mathrm{~nm} to 10^{-3} \mathrm{~nm} (C) X-Ray (III) 1 \mathrm{~mm} to 700 \mathrm{~nm} (D) Infra-red (IV) 0.1 \mathrm{~m} to 1 \mathrm{~mm} Choose the correct answer from the options given below:

Options:

A) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

B) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

C) (A)-(IV), (B)-(I), (C)-(III), (D) -(II)

D) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

EasyJEE Mains2023

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $z-axis and magnetic field is along the positive x$-axis. Then the direction of propagation of electromagnetic wave is:

Options:

A) at $45^{\circ}$ angle from positive y-axis

B) positive $y$-axis

C) negative $\mathrm{y}$-axis

D) positive z-axis

EasyJEE Mains2023

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

Options:

A) \oint \overrightarrow{\mathrm{E}} \cdot \overrightarrow{d l}=0

B) \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I

C) \oint \vec{E} \cdot \overrightarrow{d l}=-\frac{\partial \phi_{B}}{\partial t}

D) \oint \vec{D} \cdot \overrightarrow{d A}=Q

MediumJEE Mains2023

Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below.

Options:

A) Both $\mathrm{A} and \mathrm{R} are true but \mathrm{R} is NOT the correct explanation of \mathrm{A}

B) \mathrm{A} is true but \mathrm{R}$ is false

C) Both $\mathrm{A} and \mathrm{R} are true and \mathrm{r} is the correct explanation of \mathrm{A}

D) \mathrm{A} is false but \mathrm{R}$ is true

EasyJEE Mains2023

A plane electromagnetic wave of frequency $20 ~\mathrm{MHz} propagates in free space along \mathrm{x}-direction. At a particular space and time, \overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}. What is \overrightarrow{\mathrm{B}}$ at this point?

Options:

A) -2.2 \times 10^{-8} \hat{i} T

B) 2.2 \times 10^{-8} \hat{i} T

C) 2.2 \times 10^{-8} \hat{k} T

D) -2.2 \times 10^{-8} \hat{k} T

EasyJEE Mains2023

The electric field in an electromagnetic wave is given as $\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1} where \omega and c are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of 5 \times 10^{-4} \mathrm{~m}^{3} will be (Given \varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$ )

Options:

A) 17 \cdot 7 \times 10^{-13} \mathrm{~J}

B) 28 \cdot 5 \times 10^{-13} \mathrm{~J}

C) 8 \cdot 85 \times 10^{-13} \mathrm{~J}

D) 88 \cdot 5 \times 10^{-13} \mathrm{~J}

EasyJEE Mains2023

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $6.0 \times 10^{-7} \mathrm{~T}$. The maximum value of electric field in the electromagnetic wave is

Options:

A) 6.0 \times 10^{-7} ~\mathrm{Vm}^{-1}

B) 5 \times 10^{14} ~\mathrm{Vm}^{-1}

C) 180 ~\mathrm{Vm}^{-1}

D) 2 \times 10^{15} ~\mathrm{Vm}^{-1}

EasyJEE Mains2023

The energy of an electromagnetic wave contained in a small volume oscillates with

Options:

A) double the frequency of the wave

B) the frequency of the wave

C) half the frequency of the wave

D) zero frequency

EasyJEE Mains2023

The energy density associated with electric field $\vec{E} and magnetic field \vec{B} of an electromagnetic wave in free space is given by \left(\epsilon_{0}-\right. permittivity of free space, \mu_{0}-$ permeability of free space)

Options:

A) U_{E}=\frac{\epsilon_{0} E^{2}}{2}, U_{B}=\frac{B^{2}}{2 \mu_{0}}

B) U_{E}=\frac{E^{2}}{2 \epsilon_{0}}, U_{B}=\frac{\mu_{0} B^{2}}{2}

C) U_{E}=\frac{\epsilon_{0} E^{2}}{2}, U_{B}=\frac{\mu_{0} B^{2}}{2}

D) U_{E}=\frac{E^{2}}{2 \epsilon_{0}}, U_{B}=\frac{B^{2}}{2 \mu_{0}}

EasyJEE Mains2023

For the plane electromagnetic wave given by $E=E_{0} \sin (\omega t-k x) and B=B_{0} \sin (\omega t-k x)$, the ratio of average electric energy density to average magnetic energy density is

Options:

A) 1

B) 4

C) 2

D) 1/2

EasyJEE Mains2023

The ratio of average electric energy density and total average energy density of electromagnetic wave is :

Options:

A) 1

B) 3

C) 2

D) \frac{1}{2}

EasyJEE Mains2023

Match List I with List II : List I List II A. Microwaves I. Radio active decay of the nucleus B. Gamma rays II. Rapid acceleration and deceleration of electron in aerials C. Radio waves III. Inner shell electrons D. X-rays IV. Klystron valve Choose the correct answer from the options given below :

Options:

A) A-I, B-III, C-IV, D-II

B) A-IV, B-III, C-II, D-I

C) A-IV, B-I, C-II, D-III

D) A-I, B-II, C-III, D-IV

EasyJEE Mains2023

Match List I with List II LIST I LIST II A. Microwaves I. Physiotherapy B. UV rays II. Treatment of cancer C. Infra-red light III. Lasik eye surgery D. X-ray IV. Aircraft navigation Choose the correct answer from the options given below:

Options:

A) A - IV, B - III, C - I, D - II

B) A - II, B - IV, C - III, D - I

C) A - III, B - II, C - I, D - IV

D) A - IV, B - I, C - II, D - III

MediumJEE Mains2023

A point source of 100 \mathrm{~W} emits light with 5 \% efficiency. At a distance of 5 \mathrm{~m} from the source, the intensity produced by the electric field component is:

Options:

A) \frac{1}{40 \pi} \frac{W}{m^2}

B) \frac{1}{10 \pi} \frac{W}{m^2}

C) \frac{1}{20 \pi} \frac{W}{m^2}

D) \frac{1}{2 \pi} \frac{W}{m^2}

EasyJEE Mains2023

Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as ${E_0} = \sqrt {{{{\mu _0}} \over {{\varepsilon _0}}}} {B_0}$. 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 true and Statement II is false

C) Both Statement I and Statement II are false

D) Statement I is false but Statement II is true

EasyJEE Mains2023

Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of the motion of the source. D. The speed of light in a medium is independent of intensity. Choose the correct answer from the options given below:

Options:

A) B and D only

B) B and C only

C) A and C only

D) C and D only

EasyJEE Mains2023

Match List I with List II List I List II A. Gauss's Law in Electrostatics I. $\oint {\overrightarrow E \,.\,d\overrightarrow l = - {{d{\phi _B}} \over {dt}}} B. Faraday's Law II. \oint {\overrightarrow B \,.\,d\overrightarrow A = 0} C. Gauss's Law in Magnetism III. \oint {\overrightarrow B \,.\,d\overrightarrow l = {\mu _0}{i_c} + {\mu _0}{ \in _0}{{d{\phi _E}} \over {dt}}} D. Ampere-Maxwell Law IV. \oint {\overrightarrow E \,.\,d\overrightarrow s = {q \over {{ \in _0}}}} $ Choose the correct answer from the options given below :

Options:

A) A-I, B-II, C-III, D-IV

B) A-III, B-IV, C-I, D-II

C) A-IV, B-I, C-II, D-III

D) A-II, B-III, C-IV, D-I

EasyJEE Mains2023

An electromagnetic wave is transporting energy in the negative $z direction. At a certain point and certain time the direction of electric field of the wave is along positive y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

Options:

A) Negative direction of $y

B) Positive direction of $z

C) Positive direction of $x

D) Negative direction $x

EasyJEE Mains2023

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by $\mathrm{{E_x} = {E_o}\sin (kz - \omega t)} \mathrm{{B_y} = {B_o}\sin (kz - \omega t)} Then the correct relation between E_0 and B_0$ is given by

Options:

A) \mathrm{{E_o}{B_o} = \omega k}

B) \mathrm{{E_0} = k{B_0}}

C) \mathrm{k{E_0} = \omega {B_0}}

D) \mathrm{\omega {E_0} = k{B_0}}

MediumJEE Mains2023

In $\overrightarrow E and \overrightarrow K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : (\omega$ - angular frequency) :

Options:

A) {1 \over \omega }\left( {\overline K \times \overline E } \right)

B) \overline K \times \overline E

C) \omega \left( {\overline K \times \overline E } \right)

D) \omega \left( {\overline E \times \overline K } \right)

EasyJEE Mains2022

Match List - I with List - II : List - I List - II (a) UV rays (i) Diagnostic tool in medicine (b) X-rays (ii) Water purification (c) Microwave (iii) Communication, Radar (d) Infrared wave (iv) Improving visibility in foggy days Choose the correct answer from the options given below :

Options:

A) (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

B) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

C) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

D) (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

MediumJEE Mains2022

Sun light falls normally on a surface of area $36 \mathrm{~cm}^{2} and exerts an average force of 7.2 \times 10^{-9} \mathrm{~N}$ within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

Options:

A) 25.92 \times 10^{2} \mathrm{~W} / \mathrm{cm}^{2}

B) 8.64 \times 10^{-6} \mathrm{~W} / \mathrm{cm}^{2}

C) 6.0 \mathrm{~W} / \mathrm{cm}^{2}

D) 0.06\mathrm{~W} / \mathrm{cm}^{2}

EasyJEE Mains2022

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. (A) In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. (B) The energy in electromagnetic wave is divided equally between electric and magnetic fields. (C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. (D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. (E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below :

Options:

A) (D) only

B) (B) and (D) only

C) (B), (C) and (E) only

D) (A), (B) and (E) only

MediumJEE Mains2022

A beam of light travelling along $X-axis is described by the electric field E_{y}=900 \sin \omega(\mathrm{t}-x / c). The ratio of electric force to magnetic force on a charge \mathrm{q} moving along Y-axis with a speed of 3 \times 10^{7} \mathrm{~ms}^{-1} will be : (Given speed of light =3 \times 10^{8} \mathrm{~ms}^{-1}$)

Options:

A) 1 : 1

B) 1 : 10

C) 10 : 1

D) 1 : 2

EasyJEE Mains2022

The oscillating magnetic field in a plane electromagnetic wave is given by $B_{y}=5 \times 10^{-6} \sin 1000 \pi\left(5 x-4 \times 10^{8} t\right) T$. The amplitude of electric field will be :

Options:

A) 15 \times 10^{2} \,\mathrm{Vm}^{-1}

B) 5 \times 10^{-6} \,\mathrm{Vm}^{-1}

C) 16 \times 10^{12} \,\mathrm{Vm}^{-1}

D) 4 \times 10^{2} \,\mathrm{Vm}^{-1}

EasyJEE Mains2022

A velocity selector consists of electric field $\vec{E}=E \,\hat{k} and magnetic field \vec{B}=B \,\hat{j} with B=12 \,m T. The value of E required for an electron of energy 728 \,\mathrm{e} V moving along the positive x-axis to pass undeflected is : (Given, mass of electron =9.1 \times 10^{-31} \mathrm{~kg}$ )

Options:

A) 192 \,\mathrm{kVm}^{-1}

B) 192 \,\mathrm{mVm}^{-1}

C) 9600 \,\mathrm{kVm}^{-1}

D) 16 \,\mathrm{kVm}^{-1}

EasyJEE Mains2022

The magnetic field of a plane electromagnetic wave is given by : $ \overrightarrow{\mathrm{B}}=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} \mathrm{t}\right) \,\hat{j} \mathrm{~T}$. The amplitude of the electric field would be :

Options:

A) 6\, \mathrm{Vm}^{-1} along x$-axis

B) 3\, \mathrm{Vm}^{-1} along z$-axis

C) 6\, \mathrm{Vm}^{-1} along z$-axis

D) 2 \times 10^{-8} \,\mathrm{Vm}^{-1} along z$-axis

EasyJEE Mains2022

Light wave travelling in air along x-direction is given by ${E_y} = 540\sin \pi \times {10^4}(x - ct)\,V{m^{ - 1}}. Then, the peak value of magnetic field of wave will be (Given c = 3 \times 108 ms-$1)

Options:

A) 18 $\times 10-$7 T

B) 54 $\times 10-$7 T

C) 54 $\times 10-$8 T

D) 18 $\times 10-$8 T

EasyJEE Mains2022

The rms value of conduction current in a parallel plate capacitor is $6.9 \,\mu \mathrm{A}. The capacity of this capacitor, if it is connected to 230 \mathrm{~V} ac supply with an angular frequency of 600 \,\mathrm{rad} / \mathrm{s}$, will be :

Options:

A) 5 pF

B) 50 pF

C) 100 pF

D) 200 pF

EasyJEE Mains2022

An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$\pi \times 103x - 3\pi \times 1011t) Vm-1 Then, the value of magnetic field amplitude will be : (Given : speed of light in Vacuum c = 3 \times 108 ms-$1)

Options:

A) 1 $\times 10-$6 T

B) 5 $\times 10-$6 T

C) 18 $\times$ 109 T

D) 21 $\times$ 109 T

EasyJEE Mains2022

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm$-$1. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

Options:

A) {E_y} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}} {B_z} = 2\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T

B) {E_y} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}} {B_z} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T

C) {E_y} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}} {B_z} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T

D) {E_y} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^4}(x - 4 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}} {B_z} = 60\sin \left[ {{\pi \over 4} \times {{10}^4}(x - 4 \times {{10}^8}t)} \right]\widehat k\,\,T

EasyJEE Mains2022

A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 $\times 10-$8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

Options:

A) 2.0 $\times 10-$5 s

B) 4.0 $\times 10-$5 s

C) 1.0 $\times 10-$5 s

D) 8.0 $\times 10-$5 s

EasyJEE Mains2022

Given below are two statements : Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves. Statement II : In a material medium, the EM wave travels with speed $v = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$. 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) Both Statement I and Statement II are false

C) Statement I is correct but Statement II is false

D) Statement I is incorrect but Statement II is true

EasyJEE Mains2022

Match List-I with List-II : List - I List - II (a) Ultraviolet rays (i) Study crystal structure (b) Microwaves (ii) Greenhouse effect (c) Infrared rays (iii) Sterilizing surgical instrument (d) X-rays (iv) Radar system Choose the correct answer from the options given below :

Options:

A) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)

B) (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

C) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

D) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

EasyJEE Mains2022

Which is the correct ascending order of wavelengths?

Options:

A) \lambdavisible < \lambdaX-ray < \lambdagamma-ray < \lambda$microwave

B) \lambdagamma-ray < \lambdaX-ray < \lambdavisible < \lambda$microwave

C) \lambdaX-ray < \lambdagamma-ray < \lambdavisible < \lambda$microwave

D) \lambdamicrowave < \lambdavisible < \lambdagamma-ray < \lambda$X-ray

MediumJEE Mains2022

If Electric field intensity of a uniform plane electromagnetic wave is given as $E = - 301.6\sin (kz - \omega t){\widehat a_x} + 452.4\sin (kz - \omega t){\widehat a_y}{V \over m}. Then magnetic intensity 'H' of this wave in Am-1 will be : [Given : Speed of light in vacuum c = 3 \times {10^8} ms-1, Permeability of vacuum {\mu _0} = 4\pi \times {10^{ - 7}} NA-$2]

Options:

A) + 0.8\sin (kz - \omega t){\widehat a_y} + 0.8\sin (kz - \omega t){\widehat a_x}

B) + 1.0 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_y} + 1.5 \times {10^{ - 6}}(kz - \omega t){\widehat a_x}

C) - 0.8\sin (kz - \omega t){\widehat a_y} - 1.2\sin (kz - \omega t){\widehat a_x}

D) - 1.0 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_y} - 1.5 \times {10^{ - 6}}\sin (kz - \omega t){\widehat a_x}

EasyJEE Mains2022

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size ${\lambda \over {100}}, where \lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be :

Options:

A) Reflection

B) Refraction

C) Diffraction

D) Scattering

EasyJEE Mains2022

The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

Options:

A) 2.25

B) 4.25

C) 6.25

D) 8.25

EasyJEE Mains2022

The electric field in an electromagnetic wave is given by E = 56.5 sin $\omega(t - x/c) NC-1. Find the intensity of the wave if it is propagating along x-axis in the free space. (Given : \varepsilon 0 = 8.85 \times 10-12C2N-1m-$2)

Options:

A) 5.65 Wm$-$2

B) 4.24 Wm$-$2

C) 1.9 $\times 10-7 Wm-$2

D) 56.5 Wm$-$2

MediumJEE Mains2022

An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.

Options:

A) 1.19 $\times 10-$8T

B) 1.71 $\times 10-$8T

C) 0.84 $\times 10-$8T

D) 3.36 $\times 10-$8T

100

MediumJEE Mains2022

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 $\times 10-2 Am-1 at a point, what will be the approximate magnitude of electric field intensity at that point? (Given : Permeability of free space \mu0 = 4\pi \times 10-7 NA-2, speed of light in vacuum c = 3 \times 108 ms-$1)

Options:

A) 16.96 Vm$-$1

B) 2.25 $\times 10-2 Vm-$1

C) 8.48 Vm$-$1

D) 6.75 $\times 106 Vm-$1

101

MediumJEE Mains2021

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20cos(2 $\times 1010 t - 200x) V/m. The dielectric constant of the medium is equal to : (Take \mu$r = 1)

Options:

A) 9

B) 2

C) {1 \over 3}

D) 3

102

MediumJEE Mains2021

The magnetic field vector of an electromagnetic wave is given by $B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t); where \widehat i,\widehat j represents unit vector along x and y-axis respectively. At t = 0s, two electric charges q1 of 4\pi coulomb and q2 of 2\pi coulomb located at \left( {0,0,{\pi \over k}} \right) and \left( {0,0,{{3\pi } \over k}} \right), respectively, have the same velocity of 0.5 c \widehat i$, (where c is the velocity of light). The ratio of the force acting on charge q1 to q2 is :-

Options:

A) 2\sqrt 2 :1

B) 1:\sqrt 2

C) 2 : 1

D) \sqrt 2 :1

103

EasyJEE Mains2021

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $- 10 \times$ 1010 t) V/m The velocity of electromagnetic wave in this medium is :(Given C = speed of light in vacuum)

Options:

A) {3 \over 2}$C

B) C

C) {2 \over 3}$C

D) {C \over 2}

104

MediumJEE Mains2021

A light beam is described by $E = 800\sin \omega \left( {t - {x \over c}} \right). An electron is allowed to move normal to the propagation of light beam with a speed of 3 \times 107 ms-$1. What is the maximum magnetic force exerted on the electron?

Options:

A) 1.28 $\times 10-$18 N

B) 1.28 $\times 10-$21 N

C) 12.8 $\times 10-$17 N

D) 12.8 $\times 10-$18 N

105

EasyJEE Mains2021

The relative permittivity of distilled water is 81. The velocity of light in it will be :(Given $\mu$r = 1)

Options:

A) 4.33 $\times$ 107 m/s

B) 2.33 $\times$ 107 m/s

C) 3.33 $\times$ 107 m/s

D) 5.33 $\times$ 107 m/s

106

EasyJEE Mains2021

A linearly polarized electromagnetic wave in vacuum is $E = 3.1\cos \left[ {(1.8)z - (5.4 \times {{10}^6})t} \right]\widehat iN/C$is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

Options:

A) The wavelength is 5.4 m

B) The frequency of electromagnetic wave is 54 $\times$ 104 Hz.

C) The transmitted wave will be $3.1\cos \left[ {(1.8)z - (5.4 \times {{10}^6})t} \right]\widehat iN/C

D) The reflected wave will be $3.1\cos \left[ {(1.8)z + (5.4 \times {{10}^6})t} \right]\widehat iN/C

107

EasyJEE Mains2021

Intensity of sunlight is observed as 0.092 Wm$-2 at a point in free space. What will be the peak value of magnetic field at the point?({\varepsilon _0} = 8.85 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}$)

Options:

A) 2.77 $\times 10-$8 T

B) 1.96 $\times 10-$8 T

C) 8.31 T

D) 5.88 T

108

EasyJEE Mains2021

In an electromagnetic wave the electric field vector and magnetic field vector are given as $\overrightarrow E = {E_0}\widehat i and \overrightarrow B = {B_0}\widehat k$ respectively. The direction of propagation of electromagnetic wave is along :

Options:

A) \left( {\widehat k} \right)

B) \widehat j

C) \left( { - \widehat k} \right)

D) \left( { - \widehat j} \right)

109

EasyJEE Mains2021

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $\left( {\overrightarrow E } \right) and magnetic field \left( {\overrightarrow B } \right)$ components.

Options:

A) Ex, Bz or Ez, Bx

B) Ex, By or Ey, Bx

C) Ey, By or Ez, Bz

D) Ey, Bx or Ex, By

110

EasyJEE Mains2021

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, $\overrightarrow B = 2.0 \times {10^{ - 8}}\widehat kT. (where, \widehat k is unit vector along z-direction) What is \overrightarrow E $ at this point?

Options:

A) 0.6 $\widehat j$ V/m

B) 6.0 $\widehat k$ V/m

C) 6.0 $\widehat j$ V/m

D) 0.6 $\widehat k$ V/m

111

EasyJEE Mains2021

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $\overrightarrow B = 8.0 \times 10-8 \widehat zT. The value of electric field at this point is :(speed of light = 3 \times 108 ms-1)\widehat x, \widehat y, \widehat z$ are unit vectors along x, y and z directions.

Options:

A) 2.6 $\widehat x$ V/m

B) -24 \widehat x$ V/m

C) 24 $\widehat x$ V/m

D) -2.6 \widehat y$ V/m

112

EasyJEE Mains2021

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is :

Options:

A) Ue = Um

B) Ue $\ne$ Um

C) Ue < Um

D) Ue > Um

113

EasyJEE Mains2021

Match List - I with List - II. List I List II (a) Source of microwave frequency (i) Radioactive decay of nucleus (b) Source of infrared frequency (ii) Magnetron (c) Source of Gamma Rays (iii) Inner shell electrons (d) Source of X-rays (iv) Vibration of atoms and molecules (v) LASER (vi) RC circuit Choose the correct answer from the options given below :

Options:

A) (a)-(vi), (b)-(v), (c)-(i), (d)-(iv)

B) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

C) (a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)

D) (a)-(vi), (b)-(iv), (c)-(i), (d)-(v)

114

MediumJEE Mains2020

For a plane electromagnetic wave, the magnetic field at a point x and time t is $\overrightarrow B \left( {x,t} \right) = \left[ {1.2 \times {{10}^{ - 7}}\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat k} \right] T The instantaneous electric field \overrightarrow E corresponding to \overrightarrow B $ is : (speed of light c = 3 × 108 ms–1)

Options:

A) \overrightarrow E \left( {x,t} \right) = \left[ {36\sin \left( {1 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat i} \right] {V \over m}

B) \overrightarrow E \left( {x,t} \right) = \left[ {36\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat k} \right]{V \over m}

C) \overrightarrow E \left( {x,t} \right) = \left[ {36\sin \left( {1 \times {{10}^3}x + 0.5 \times {{10}^{11}}t} \right)\widehat j} \right]{V \over m}

D) \overrightarrow E \left( {x,t} \right) = \left[ { - 36\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat j} \right]{V \over m}

115

MediumJEE Mains2020

The correct match between the entries in column I and column II are : I II Radiation Wavelength (a) Microwave (i) 100 m (b) Gamma rays (ii) 10–15 m (c) A.M. radio waves (iii) 10–10 m (d) X-rays (iv) 10–3 m

Options:

A) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

B) (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

C) (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

D) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)

116

MediumJEE Mains2020

An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is $\overrightarrow E = 30\widehat j\sin \left( {1.5 \times {{10}^7}t - 5 \times {{10}^{ - 2}}x} \right) V/m. The maximum magnetic force experienced by the electron will be : (given c = 3 \times 108 ms–1 and electron charge = 1.6 \times $ 10–19 C)

Options:

A) 4.8 $ \times $ 10–19 N

B) 2.4 $ \times $ 10–18 N

C) 3.2 $ \times $ 10–18 N

D) 1.6 $ \times $ 10–18 N

117

MediumJEE Mains2020

The electric field of a plane electromagnetic wave is given by $\overrightarrow E = {E_0}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$ Its magnetic field will be given by :

Options:

A) {{{E_0}} \over c}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)

B) {{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\sin \left( {kz - \omega t} \right)

C) {{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\cos \left( {kz - \omega t} \right)

D) {{{E_0}} \over c}\left( { - \widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)

118

MediumJEE Mains2020

Choose the correct option relating wave lengths of different parts of electromagnetic wave spectrum:

Options:

A) \lambda radio waves > \lambda micro waves > \lambda visible > \lambda $x-rays

B) \lambda visible > \lambda x-rays > \lambda radio waves > \lambda $micro waves

C) \lambda visible < \lambda micro waves < \lambda radio waves < \lambda $x-rays

D) \lambda x-rays < \lambda micro waves < \lambda radio waves < \lambda $visible

119

MediumJEE Mains2020

The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $\overrightarrow E = {E_0}\widehat j\cos \left( {\omega t - kx} \right). The magnetic field \overrightarrow B $ , at the moment t = 0 is :

Options:

A) \overrightarrow B = {{{E_0}} \over {\sqrt {{\mu _0}{ \in _0}} }}\cos \left( {kx} \right)\widehat j

B) \overrightarrow B = {{{E_0}} \over {\sqrt {{\mu _0}{ \in _0}} }}\cos \left( {kx} \right)\widehat k

C) \overrightarrow B = {E_0}\sqrt {{\mu _0}{ \in _0}} \cos \left( {kx} \right)\widehat k

D) \overrightarrow B = {E_0}\sqrt {{\mu _0}{ \in _0}} \cos \left( {kx} \right)\widehat j

120

MediumJEE Mains2020

The magnetic field of a plane electromagnetic wave is $\overrightarrow B = 3 \times {10^{ - 8}}\sin \left[ {200\pi \left( {y + ct} \right)} \right]\widehat i T where c = 3 \times $ 108 ms–1 is the speed of light. The corresponding electric field is :

Options:

A) \overrightarrow E = - {10^{ - 6}}\sin \left[ {200\pi \left( {y + ct} \right)} \right]\widehat k$ V/m

B) \overrightarrow E = - 9\sin \left[ {200\pi \left( {y + ct} \right)} \right]\widehat k$ V/m

C) \overrightarrow E = 9\sin \left[ {200\pi \left( {y + ct} \right)} \right]\widehat k$ V/m

D) \overrightarrow E = 3 \times {10^{ - 8}}\sin \left[ {200\pi \left( {y + ct} \right)} \right]\widehat k

121

MediumJEE Mains2020

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $\widehat k and 2\widehat i - 2\widehat j$, respectively. What is the unit vector along direction of propagation of the wave?

Options:

A) {1 \over {\sqrt 5 }}\left( {\widehat i + 2\widehat j} \right)

B) {1 \over {\sqrt 5 }}\left( {2\widehat i + \widehat j} \right)

C) {1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)

D) {1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)

122

MediumJEE Mains2020

A plane electromagnetic wave, has frequency of 2.0 $ \times 1010 Hz and its energy density is 1.02 \times 10–8 J/m3 in vacuum. The amplitude of the magnetic field of the wave is close to ( {1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}{{N{m^2}} \over {{C^2}}} and speed of light = 3 \times $ 108 ms–1)

Options:

A) 190 nT

B) 150 nT

C) 160 nT

D) 180 nT

123

MediumJEE Mains2020

A plane electromagnetic wave is propagating along the direction ${{\widehat i + \widehat j} \over {\sqrt 2 }} , with its polarization along the direction \widehat k$ . The correct form of the magnetic field of the wave would be (here B0 is an appropriate constant) :

Options:

A) {B_0}{{\widehat i - \widehat j} \over {\sqrt 2 }}\cos \left( {\omega t - k{{\widehat i + \widehat j} \over {\sqrt 2 }}} \right)

B) {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {\omega t - k{{\widehat i + \widehat j} \over {\sqrt 2 }}} \right)

C) {B_0}{{\widehat j - \widehat i} \over {\sqrt 2 }}\cos \left( {\omega t + k{{\widehat i + \widehat j} \over {\sqrt 2 }}} \right)

D) {B_0}\widehat k\cos \left( {\omega t - k{{\widehat i + \widehat j} \over {\sqrt 2 }}} \right)

124

MediumJEE Mains2020

The electric fields of two plane electromagnetic plane waves in vacuum are given by $\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right) and \overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right) At t = 0, a particle of charge q is at origin with a velocity \overrightarrow v = 0.8c\widehat j$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :

Options:

A) {E_0}q\left( {0.8\widehat i - \widehat j + 0.4\widehat k} \right)

B) {E_0}q\left( { - 0.8\widehat i + \widehat j + \widehat k} \right)

C) {E_0}q\left( {0.8\widehat i + \widehat j + 0.2\widehat k} \right)

D) {E_0}q\left( {0.4\widehat i - 3\widehat j + 0.8\widehat k} \right)

125

MediumJEE Mains2020

A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $\overrightarrow B = 5 \times {10^{ - 8}}\widehat jT. The corresponding electric field \overrightarrow E $ is (speed of light c = 3 × 108 ms–1)

Options:

A) 15 $\widehat i$V / m

B) -15 $\widehat i$V / m

C) 1.66 × 10–16 $\widehat i$V / m

D) -1.66 × 10–16 $\widehat i$V / m

126

MediumJEE Mains2020

The electric field of a plane electromagnetic wave is given by $\overrightarrow E = {E_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {kz + \omega t} \right) At t = 0, a positively charged particle is at the point (x, y, z) = \left( {0,0,{\pi \over k}} \right). If its instantaneous velocity at (t = 0) is {v_0}\widehat k$ , the force acting on it due to the wave is :

Options:

A) parallel to $\widehat k

B) parallel to ${{\widehat i + \widehat j} \over {\sqrt 2 }}

C) antiparallel to ${{\widehat i + \widehat j} \over {\sqrt 2 }}

D) zero

127

MediumJEE Mains2020

If the magnetic field in a plane electromagnetic wave is given by $\overrightarrow B = 3 \times 10-8 sin(1.6 \times 103x + 48 \times 1010t)\widehat j$ T, then what will be expression for electric field ?

Options:

A) \overrightarrow E = (9sin(1.6 \times 103x + 48 \times 1010t)\widehat k$ V/m)

B) \overrightarrow E = (60sin(1.6 \times 103x + 48 \times 1010t)\widehat k$ V/m)

C) \overrightarrow E = (3 \times 10-8 sin(1.6 \times 103x + 48 \times 1010t)\widehat i$ V/m)

D) \overrightarrow E = (3 \times 10-8 sin(1.6 \times 103x + 48 \times 1010t)\widehat j$ V/m)

128

MediumJEE Mains2019

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

Options:

A) \overrightarrow B = 2 × 10–7 sin(1.5 × 102 x + 0.5 × 1011t) \widehat j

B) \overrightarrow B = 60 sin(0.5 × 103x + 0.5 × 1011t) \widehat k

C) \overrightarrow B = 2 × 10–7 sin(0.5 × 103 z + 1.5 × 1011t) \widehat i

D) \overrightarrow B = 2 × 10–7 sin(0.5 × 103 z - 1.5 × 1011t) \widehat i

129

MediumJEE Mains2019

An electromagnetic wave is represented by the electric field $\overrightarrow E = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right] . Taking unit vectors in x, y and z directions to be \widehat i,\widehat j,\widehat k , the direction of propagation \widehat s$, is :

Options:

A) \widehat s = {{3\widehat i - 4\widehat j} \over 5}

B) \widehat s = {{ - 4\widehat k + 3\widehat j} \over 5}

C) \widehat s = \left( {{{ - 3\widehat j + 4\widehat k} \over 5}} \right)

D) \widehat s = {{4\widehat j - 3\widehat k} \over 5}

130

MediumJEE Mains2019

Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm–2. If the surface has an area of 25 cm2, the momentum transferred to the surface in 40 min time duration will be :

Options:

A) 6.3 × 10–4 Ns

B) 5.0 × 10–3 Ns

C) 1.4 × 10–6 Ns

D) 3.5 × 10–6 Ns

131

MediumJEE Mains2019

The electric field of a plane electromagnetic wave is given by $\overrightarrow E = {E_0}\widehat i\cos (kz)cos(\omega t) The corresponding magnetic field \overrightarrow B $ is then given by

Options:

A) \overrightarrow B = {{{E_0}} \over C}\widehat j\sin (kz)\sin (\omega t)

B) \overrightarrow B = {{{E_0}} \over C}\widehat j\sin (kz)\cos (\omega t)

C) \overrightarrow B = {{{E_0}} \over C}\widehat j\cos (kz)\sin (\omega t)

D) \overrightarrow B = {{{E_0}} \over C}\widehat k\sin (kz)\cos (\omega t)

132

MediumJEE Mains2019

50 W/m2 energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy (25%) is reflected from the surface and the rest is absorbed. The force exerted on 1m2 surface area will be close to (c = 3 × 108 m/s) :-

Options:

A) 20 × 10–8 N

B) 35 × 10–8 N

C) 10 × 10–8 N

D) 15 × 10–8 N

133

MediumJEE Mains2019

The magnetic field of a plane electromagnetic wave is given by : $$\overline B = {B_0}\widehat i\left[ {\cos (kz - \omega t)} \right] + {B_i}\widehat j\cos (kz + \omega t)$$ B0 = 3 × 10–5 T and B1 = 2 × 10–6 T. The rms value of the force experienced by a stationary charge Q = 10–4 C at z = 0 is closest to :

Options:

A) 0.6 N

B) 0.9 N

C) 3 × 10–2 N

D) 0.1 N

134

MediumJEE Mains2019

The magnetic field of an electromagnetic wave is given by :- $\mathop B\limits^ \to = 1.6 \times {10^{ - 6}}\cos \left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\mathop i\limits^ \wedge + \mathop j\limits^ \wedge } \right){{Wb} \over {{m^2}}}$ The associated electric field will be :-

Options:

A) \mathop E\limits^ \to = 4.8 \times {10^2}\cos \left( {2 \times {{10}^7}z - 6 \times {{10}^{15}}t} \right)\left( -2{\mathop i\limits^ \wedge + \mathop {j}\limits^ \wedge } \right){V \over m}

B) \mathop E\limits^ \to = 4.8 \times {10^2}\cos \left( {2 \times {{10}^7}z - 6 \times {{10}^{15}}t} \right)\left( 2{\mathop i\limits^ \wedge + \mathop {j}\limits^ \wedge } \right){V \over m}

C) \mathop E\limits^ \to = 4.8 \times {10^2}\cos \left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {\mathop i\limits^ \wedge - \mathop {2j}\limits^ \wedge } \right){V \over m}

D) \mathop E\limits^ \to = 4.8 \times {10^2}\cos \left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( -{\mathop i\limits^ \wedge + \mathop {2j}\limits^ \wedge } \right){V \over m}

135

MediumJEE Mains2019

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 V m–1 along y-direction. Its corresponding magnetic field component, B would be :

Options:

A) 2 × 10–8 T along y-direction

B) 6 × 10–8 T along z-direction

C) 2 × 10–8 T along z-direction

D) 6 × 10–8 T along x-direction

136

MediumJEE Mains2019

The mean intensity of radiation on the surface of the Sun is about 108 W/m2 . The rms value of the corresponding magnetic field is closet to :

Options:

A) 102 T

B) 10$-$2 T

C) 10$-$4 T

D) 1 T

137

MediumJEE Mains2019

A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be :

Options:

A) 6 V/m

B) 10 V/m

C) 30 V/m

D) 24 V/m

138

MediumJEE Mains2019

A 27 mW laser beam has a cross-sectional area of 10 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by : [Given permittivity of space $ \in 0 = 9 \times 10–12 SI units, Speed of light c = 3 \times $ 108 m/s]

Options:

A) 2 kV/m

B) 1 kV/m

C) 1.4 kV/m

D) 0.7 kV/m

139

MediumJEE Mains2019

An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:

Options:

A) \left( {{1 \over {\sqrt n }},{1 \over {\sqrt n }}} \right)

B) \left( {\sqrt n ,\sqrt n } \right)

C) \left( {\sqrt n ,{1 \over {\sqrt n }}} \right)

D) \left( {{1 \over {\sqrt n }},\sqrt n } \right)

140

MediumJEE Mains2019

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression $\overrightarrow E \left( {x,y} \right) = 10\widehat j\cos \left[ {\left( {6x + 8z} \right)} \right]. The magnetic field \overrightarrow B (x,z, t) is given by -$ (c is the velocity of light)

Options:

A) {1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]

B) {1 \over c}\left( {6\widehat k - 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]

C) {1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]

D) {1 \over c}\left( {6\hat k - 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]

141

MediumJEE Mains2019

If the magnetic field of a plane electromagnetic wave is given by (the speed of light = 3 × 108 B = 100 × 10–6 sin $\left[ {2\pi \times 2 \times {{10}^{15}}\left( {t - {x \over c}} \right)} \right]$ then the maximum electric field associated with it is -

Options:

A) 4.5 $ \times $ 104 N/C

B) 4 $ \times $ 104 N/C

C) 6 $ \times $ 104 N/C

D) 3 $ \times $ 104 N/C

142

MediumJEE Mains2019

The energy associated with electric field is (UE) and with magnetic field is (UB) for an electromagnetic wave in free space. Then :

Options:

A) {U_E} = {{{U_B}} \over 2}

B) {U_E} > {U_B}

C) {U_E} < {U_B}

D) {U_E} = {U_B}

143

MediumJEE Mains2019

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, $\overrightarrow E = 6.3\widehat j\,V/m. The corresponding magnetic field \overrightarrow {B,} $ at that point will be :

Options:

A) 18.9 $ \times 10-8 \widehat k$T

B) 2.1 $ \times 10-8 \widehat k$T

C) 6.3 $ \times 10-8 \widehat k$T

D) 18.9 $ \times 108 \widehat k$T

144

MediumJEE Mains2018

A plane electromagnetic wave of wavelength $\lambda $ has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :

Options:

145

MediumJEE Mains2018

An EM wave from air enters a medium. The electric fields are $\overrightarrow {{E_1}} = {E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right] in air and \overrightarrow {{E_2}} = {E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right] in medium, where the wave number k and frequency \nu refer to their values in air. The medium is non-magnetic. If {\varepsilon _{{r_1}}} and {\varepsilon _{{r_2}}}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

Options:

A) {{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 4

B) {{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 2

C) {{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 4}

D) {{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 2}

146

MediumJEE Mains2018

A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1. The next zero that occurs in its neighbourhood is at z2. The frequency of the electroagnetic wave is :

Options:

A) {{3 \times {{10}^8}} \over {\left| {{z_2} - {z_1}} \right|}}

B) {{1.5 \times {{10}^8}} \over {\left| {{z_2} - {z_1}} \right|}}

C) {{6 \times {{10}^8}} \over {\left| {{z_2} - {z_1}} \right|}}

D) {1 \over {{t_1} + {{\left| {{z_2} - {z_1}} \right|} \over {3 \times {{10}^8}}}}}

147

MediumJEE Mains2018

A monochromatic beam of light has a frequency $v = {3 \over {2\pi }} \times {10^{12}}Hz and is propagating along the direction {{\widehat i + \widehat j} \over {\sqrt 2 }}. It is polarized along the \widehat k$ direction. The acceptable form for the magnetic field is :

Options:

148

MediumJEE Mains2017

The electric field component of a monochromatic radiation is given by $\overrightarrow E = 2 E0 \widehat i cos kz cos \omega t Its magnetic field \overrightarrow B $ is then given by :

Options:

A) {{2{E_0}} \over c} \widehat j sin kz cos \omega $t

B) - {{2{E_0}} \over c} \widehat j sin kz sin \omega $t

C) {{2{E_0}} \over c} \widehat j sin kz sin \omega $t

D) {{2{E_0}} \over c} \widehat j cos kz cos \omega $t

149

MediumJEE Mains2017

Magnetic field in a plane electromagnetic wave is given by $\overrightarrow B = B0 sin (k x + \omega t) \widehat j\,T$ Expression for corresponding electric field will be : Where c is speed of light.

Options:

A) \overrightarrow E = B0 c sin (k x + \omega t) \widehat k$ V/m

B) \overrightarrow E = {{{B_0}} \over c} sin (k x + \omega t) \widehat k$ V/m

C) \overrightarrow E = - B0 c sin (kx +\omega t) \widehat k$ V/m

D) \overrightarrow E = B0 c sin (kx -\omega t) \widehat k$ V/m

150

MediumJEE Mains2016

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

Options:

A) For an electromagnetic wave propagating in +x direction the electric field is $\vec E = {1 \over {\sqrt 2 }}{E_{yz}}{\mkern 1mu} \left( {x,t} \right)\left( {\hat y - \hat z} \right) and the magnetic field is \vec B = {1 \over {\sqrt 2 }}{B_{yz}}{\mkern 1mu} \left( {x,t} \right)\left( {\hat y + \hat z} \right)

B) For an electromagnetic wave propagating in +x direction the electric field is $\vec E = {1 \over {\sqrt 2 }}{E_{yz{\mkern 1mu} }}\left( {y,z,t} \right)\left( {\hat y + \hat z} \right) and the magnetic field is \vec B = {1 \over {\sqrt 2 }}{B_{yz{\mkern 1mu} }}\left( {y,z,t} \right)\left( {\hat y + \hat z} \right)

C) For an electromagnetic wave propagating in + y direction the electric field is $\overrightarrow E = {1 \over {\sqrt 2 }}{E_{yz{\mkern 1mu} }}\left( {x,t} \right)\widehat y and the magnetic field is \vec B = {1 \over {\sqrt 2 }}{B_{yz{\mkern 1mu} }}\left( {x,t} \right)\widehat z

D) For an electromagnetic wave propagating in + y direction the electric field is $\overrightarrow E = {1 \over {\sqrt 2 }}{E_{yz{\mkern 1mu} }}\left( {x,t} \right)\widehat z and the magnetic field is \overrightarrow B = {1 \over {\sqrt 2 }}{B_{z{\mkern 1mu} }}\left( {x,t} \right)\widehat y

151

MediumJEE Mains2016

Microwave oven acts on the principle of :

Options:

A) transferring electrons from lower to higher energy levels in water molecule

B) giving rotational energy to water molecules

C) giving vibrational energy to water molecules

D) giving translational energy to water molecules

152

MediumJEE Mains2016

Arrange the following electromagnetic radiations per quantum in the order of increasing energy : A : Blue light B : Yellow light C : X-ray D : Radiowave.

Options:

A) C, A, B, D

B) B, A, D, C

C) D, B, A, C

D) A, B, D, C

153

MediumJEE Mains2014

During the propagation of electromagnetic waves in a medium :

Options:

A) Electric energy density is double of the magnetic energy density.

B) Electric energy density is half of the magnetic energy density.

C) Electric energy density is equal to the magnetic energy density.

D) Both electric and magnetic energy of densities are zero.

154

MediumJEE Mains2014

Match List - $1 (Electromagnetic wave type ) with List - 2$ (Its association/application) and select the correct option from the choices given below the lists:

Options:

A) 1 - iv,\,\,2 - iii,\,\,3 - ii,\,\,4 - i

B) 1 - i,\,\,2 - ii,\,\,3 - iv,\,\,4 - iii

C) 1 - iii,\,\,2 - ii,\,\,3 - i,\,\,4 - iv

D) 1 - i,\,\,2 - ii,\,\,3 - iii,\,\,4 - iv

155

MediumJEE Mains2013

The magnetic field in a travelling electromagnetic wave has a peak value of $20 nT$. The peak value of electric field strength is :

Options:

A) 3V/m

B) 6V/m

C) 9V/m

D) 12V/m

156

MediumJEE Mains2012

An electromagnetic wave in vacuum has the electric and magnetic field $\mathop E\limits^ \to and \mathop B\limits^ \to , which are always perpendicular to each other. The direction of polarization is given by \mathop X\limits^ \to and that of wave propagation by \mathop k\limits^ \to $. Then

Options:

A) \mathop X\limits^ \to ||\mathop B\limits^ \to and \mathop X\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to

B) \mathop X\limits^ \to ||\mathop E\limits^ \to and \mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to

C) \mathop X\limits^ \to ||\mathop B\limits^ \to and \mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to

D) \mathop X\limits^ \to ||\mathop E\limits^ \to and \mathop k\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to

157

MediumJEE Mains2006

The $rms value of the electric field of the light coming from the Sun is 720 N/C.$ The average total energy density of the electromagnetic wave is

Options:

A) 4.58 \times {10^{ - 6}}\,J/{m^3}

B) 6.37 \times {10^{ - 9}}\,J/{m^3}

C) 81.35 \times {10^{ - 12}}\,J/{m^3}

D) 3.3 \times {10^{ - 3}}\,J/{m^3}

158

MediumJEE Mains2004

An electromagnetic wave of frequency $v=3.0 MHz passes from vacuum into a dielectric medium with permittivity \in = 4.0.$ Then

Options:

A) wave length is halved and frequency remains unchanged

B) wave length is doubled and the frequency becomes half

C) wave length is doubled and the frequency remains unchanged

D) wave length and frequency both remain unchanged.

159

MediumJEE Mains2004

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

Options:

A) Ec

B) 2E/c

C) E/c

D) E/{c^2}

160

MediumJEE Mains2002

Electromagnetic waves are transverse in nature is evident by

Options:

A) polarization

B) interference

C) reflection

D) diffraction

161

MediumJEE Mains2002

Which of the following are not electromagnetic waves?

Options:

A) cosmic rays

B) gamma rays

C) \beta $-rays

D) X$-rays

162

MediumJEE Mains2026

The equation of the electric field of an electromagnetic wave propagating through free space is given by : E=\sqrt{377} \sin \left(6.27 \times 10^3 t-2.09 \times 10^{-5} x\right) \mathrm{N} / \mathrm{C} The average power of the electromagnetic wave is \left(\frac{1}{\alpha}\right) \mathrm{W} / \mathrm{m}^2. The value of \alpha is $ \left(\text { Take } \sqrt{\frac{\mu_0}{\varepsilon_o}}=377 \text { in SI units }\right)

Options:

163

MediumJEE Mains2026

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $ E_{\mathrm{y}}=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m} (where x, \mathrm{t} and other values have S.I. units). The dielectric constant of the medium is \_\_\_\_ (speed of light in free space is 3 \times 10^8 \mathrm{~m} / \mathrm{s}$ )

Options:

164

MediumJEE Mains2026

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, \sigma = 10 \,\mathrm{mho} / \mathrm{m}. The ratio of maximum conduction current density to maximum displacement current density is \_\_\_\_. $ \left[\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\, \mathrm{Nm}^2 / \mathrm{C}^2\right]

Options:

165

EasyJEE Mains2025

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5 \mu \mathrm{~F}. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _________ \mathrm{Vs}^{-1}.

Options:

166

EasyJEE Mains2025

A parallel plate capacitor of area A=16 \mathrm{~cm}^2 and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area \mathrm{A}_0=3.2 \mathrm{~cm}^2 inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through \mathrm{A}_0 is __________ mA .

Options:

167

EasyJEE Mains2023

In a medium the speed of light wave decreases to $0.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is x: 1. The value of x is _________. (Given speed of light in free space =3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1} and for the given medium \mu_{\mathrm{r}}=1$)

Options:

168

MediumJEE Mains2023

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $24 \mathrm{~W}. The radius of curvature of hemisphere is 10 \mathrm{~cm} and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____________ \times~10^{-8} \mathrm{~N}$.

Options:

169

EasyJEE Mains2022

Nearly 10% of the power of a $110 \mathrm{~W} light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 \mathrm{~m} from the bulb to a distance of 5 \mathrm{~m} is a \times 10^{-2} \mathrm{~W} / \mathrm{m}^{2}$. The value of 'a' will be _________.

Options:

170

MediumJEE Mains2022

The displacement current of 4.425 $\muA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs-1. The area of each plate of the capacitor is 40 cm2. The distance between each plate of the capacitor is x \times 10-3 m. The value of x is __________. (Permittivity of free space, E0 = 8.85 \times 10-12 C2 N-1 m-$2).

Options:

171

MediumJEE Mains2022

The intensity of the light from a bulb incident on a surface is 0.22 W/m2. The amplitude of the magnetic field in this light-wave is ______________ $\times 10-9 T. (Given : Permittivity of vacuum \in0 = 8.85 \times 10-12 C2 N-1-m-2, speed of light in vacuum c = 3 \times 108 ms-$1)

Options:

172

MediumJEE Mains2021

The electric field in an electromagnetic wave is given by E = (50 NC$-1) sin\omega (t - x/c)The energy contained in a cylinder of volume V is 5.5 \times 10-12 J. The value of V is _____________ cm3. (given \in0 = 8.8 \times 10-12C2N-1m-$2)

Options:

173

EasyJEE Mains2021

A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x $\times 10-$8 T. The value of x is ___________.

Options:

174

MediumJEE Mains2021

The electric field in a plane electromagnetic wave is given by $\overrightarrow E = 200\cos \left[ {\left( {{{0.5 \times {{10}^3}} \over m}} \right)x - \left( {1.5 \times {{10}^{11}}{{rad} \over s} \times t} \right)} \right]{V \over m}\widehat j. If this wave falls normally on a perfectly reflecting surface having an area of 100 cm2. If the radiation pressure exerted by the E.M. wave on the surface during a 10 minute exposure is {x \over {{{10}^9}}}{N \over {{m^2}}}$. Find the value of x .

Options:

175

EasyJEE Mains2021

The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by the radiation coming from 60W at the same distance is $\sqrt {{x \over 5}} $E. Where the value of x = ____________.

Options:

176

HardJEE Mains2021

Seawater at a frequency f = 9 $\times 102 Hz, has permittivity \varepsilon = 80\varepsilon 0 and resistivity \rho = 0.25 \Omegam. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t) = V0 sin(2\pift). Then the conduction current density becomes 10x times the displacement current density after time t = {1 \over {800}}s. The value of x is _____________. (Given : {1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9} Nm2C-$2)

Options:

177

EasyJEE Mains2021

If 2.5 $\times 10-$6 N average force is exerted by a light wave on a non-reflecting surface of 30 cm2 area during 40 minutes of time span, the energy flux of light just before it falls on the surface is ___________ W/cm2. (Round off to the Nearest Integer)(Assume complete absorption and normal incidence conditions are there)

Options:

178

MediumJEE Mains2021

A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x $\times 10-1 V/m. Value of x is ___________. (Rounded off to the nearest integer) [Take {\varepsilon _0} = 8.85 \times {10^{ - 12}} C2N-1 m-2, c = 3 \times {10^8} ms-$1]

Options:

179

MediumJEE Mains2021

The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is ${x \over {10}}\sqrt {{{{\mu _0}c} \over \pi }} {V \over m}$. The efficiency of the bulb is 10% and it is a point source. The value of x is ___________.

Options:

180

MediumJEE Mains2021

The wavelength of an X-ray beam is 10$\mathop A\limits^o . The mass of a fictitious particle having the same energy as that of the X-ray photons is {x \over 3}h$ kg. The value of x is __________. (h = Planck's constant)

Options:

181

MediumJEE Mains2021

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ $\times 10-$2 cm.

Options:

182

EasyJEE Mains2021

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ $\times$ 107 m/s.

Options:

183

MediumJEE Mains2020

Suppose that intensity of a laser is ${{315} \over \pi } W/m2. The rms electric field, in units of V/m associated with this source is close to the nearest integer is __________. \in $0 = 8.86 × 10–12 C2 Nm–2; c = 3 × 108 ms–1)

Options:

184

MediumMHT CET2023

Select the 'WRONG' statement out of the following.

Options:

A) Electromagnetic waves do not require any medium for their propagation.

B) Electromagnetic waves can travel through vacuum waves speed of light

C) Material medium is necessary for propagation of electromagnetic waves.

D) Electromagnetic waves are transverse in nature.

185

MediumMHT CET2023

An electromagnetic wave, whose wave normal makes an angle of $45^{\circ} with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through 15^{\circ}. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is 3 \times 10^8 \mathrm{~m} / \mathrm{s} ? \left(\sin 30^{\circ}=0.5, \sin 45^{\circ}=\frac{1}{\sqrt{2}}\right)

Options:

A) \frac{\sqrt{2}}{3} \times 10^8 \mathrm{~m} / \mathrm{s}

B) 1.5 \times 10^8 \mathrm{~m} / \mathrm{s}

C) 2.1 \times 10^8 \mathrm{~m} / \mathrm{s}

D) 2.5 \times 10^8 \mathrm{~m} / \mathrm{s}

186

MediumMHT CET2023

A charge '$q' moves with velocity 'v$' through electric (E) as well as magnetic field (B). Then the force acting on it is

Options:

A) \mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})

B) \mathrm{q}(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{v}})

C) \mathrm{q}(\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{v}})

D) \overrightarrow{\mathrm{qE}}+\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})

187

MediumMHT CET2020

In amplitude modulation,

Options:

A) amplitude remains constant but frequency . changes according to information signal

B) amplitude of carrier wave changes according to information signal

C) both amplitude and frequency changes according to information signal

D) both amplitude and frequency do not change according to information signal

188

MediumNEET2025

The electric field in a plane electromagnetic wave is given by $ E_z=60 \cos \left(5 x+1.5 \times 10^9 t\right) \mathrm{V} / \mathrm{m}$ Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

Options:

A) B z=60 \cos \left(5 x+1.5 \times 10^9 t\right) T

B) B_y=60 \sin \left(5 x+1.5 \times 10^9 t\right) T

C) B_y=2 \times 10^{-7} \cos \left(5 x+1.5 \times 10^9 t\right) T

D) B_x=2 \times 10^{-7} \cos \left(5 x+1.5 \times 10^9 t\right) T

189

MediumNEET2024

The electromagnetic radiation which has the smallest wavelength are

Options:

A) X-rays

B) Gamma rays

C) Ultraviolet rays

D) Microwaves

190

MediumNEET2024

If the ratio of relative permeability and relative permittivity of a uniform medium is $1: 4. The ratio of the magnitudes of electric field intensity (E) to the magnetic field intensity (H) of an EM wave propagating in that medium is (Given that \sqrt{\frac{\mu_0}{\varepsilon_0}}=120 \pi$):

Options:

A) 30 \pi: 1

B) 1: 120 \pi

C) 60 \pi: 1

D) 120 \pi: 1

191

MediumNEET2024

The property which is not of an electromagnetic wave travelling in free space is that:

Options:

A) They are transverse in nature

B) The energy density in electric field is equal to energy density in magnetic field

C) They travel with a speed equal to $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}

D) They originate from charges moving with uniform speed

192

MediumNEET2023

In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of $2.0 \times 10^{10} \mathrm{~Hz} and amplitude 48 ~\mathrm{Vm}^{-1}. Then the amplitude of oscillating magnetic field is : (Speed of light in free space =3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$ )

Options:

A) 1.6 \times 10^{-8} \mathrm{~T}

B) 1.6 \times 10^{-7} \mathrm{~T}

C) 1.6 \times 10^{-6} \mathrm{~T}

D) 1.6 \times 10^{-9} \mathrm{~T}

193

MediumNEET2022

The magnetic field of a plane electromagnetic wave is given by $\overrightarrow B = 3 \times {10^{ - 8}}\cos (1.6 \times {10^3}x + 48 \times {10^{10}}t)\widehat j$, then the associated electric field will be :

Options:

A) 9\cos (1.6 \times {10^3}x + 48 \times {10^{10}}t)\widehat k$ V/m

B) 3 \times {10^{ - 8}}\cos (1.6 \times {10^3}x + 48 \times {10^{10}}t)\widehat i$ V/m

C) 3 \times {10^{ - 8}}\sin (1.6 \times {10^3}x + 48 \times {10^{10}}t)\widehat i$ V/m

D) 9\sin (1.6 \times {10^3}x - 48 \times {10^{10}}t)\widehat k$ V/m

194

MediumNEET2022

The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability ${\mu _0} and permittivity {\varepsilon _0}$ is (Given that c - velocity) of light in free space

Options:

A) {{\sqrt {{\mu _0}{\varepsilon _0}} } \over c}

B) c

C) {1 \over c}

D) {c \over {\sqrt {{\mu _0}{\varepsilon _0}} }}

195

MediumNEET2022

Match List - I with List - II List - I(Electromagnetic waves) List - II(Wavelength) (a) AM radio waves (i) ${10^{ - 10}} m (b) Microwaves (ii) {10^2} m (c) Infrared radiations (iii) {10^{ - 2}} m (d) X-rays (iv) {10^{ - 4}}$ m Choose the correct answer from the options given below

Options:

A) (a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)

B) (a) - (iii), (b) - (ii), (c) - (i), (d) - (iv)

C) (a) - (iii), (b) - (iv), (c) - (ii), (d) - (i)

D) (a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)

196

MediumNEET2022

When light propagates through a material medium of relative permittivity $\varepsilon r and relative permeability \mu$r, the velocity of light, v is given by (c-velocity of light in vacuum)

Options:

A) v = c

B) v = \sqrt {{{{\mu _r}} \over {{\varepsilon _r}}}}

C) v = \sqrt {{{{\varepsilon _r}} \over {{\mu _r}}}}

D) v = {c \over {\sqrt {{\varepsilon _r}{\mu _r}} }}

197

MediumNEET2021

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

Options:

A) - \widehat j + \widehat k, - \widehat j + \widehat k

B) \widehat j + \widehat k, \widehat j + \widehat k

C) - \widehat j + \widehat k, - \widehat j - \widehat k

D) \widehat j + \widehat k, - \widehat j - \widehat k

198

MediumNEET2020

The ratio of contributions made by the electric field and magnetic field components to the intensity of and electromagnetic wave is : (c = speed of electromagnetic waves)

Options:

A) 1 : 1

B) 1 : c

C) 1 : c2

D) c : 1

199

MediumNEET2019

Which colour of the light has the longest wavelength?

Options:

A) blue

B) violet

C) red

D) green

200

MediumNEET2018

An EM wave is propagating in a medium with a velocity $\overrightarrow v = v\widehat i$. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along

Options:

A) z direction

B) +z direction

C) –y direction

D) –x direction

201

MediumNEET2017

In an electromagnetic wave in free space that root mean square value of the electric field is Erms = 6 V m$-$1. The peak value of the magnetic field is

Options:

A) 2.83 $ \times 10-$8 T

B) 0.70 $ \times 10-$8 T

C) 4.23 $ \times 10-$8 T

D) 1.41 $ \times 10-$8 T

202

MediumNEET2016

Out of the following options which one can be used to produce a propagating electromagnetic wave ?

Options:

A) A chargeless particle

B) An accelerating charge

C) A charge moving at constant velocity

D) A stationary charge

203

MediumNEET2015

The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong ?

Options:

A) Ultraviolet rays

B) \gamma - rays

C) X-rays

D) Infra-red rays

204

MediumNEET2015

A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C = Velocity of light)

Options:

A) {{2E} \over {{C^2}}}

B) {E \over {{C^2}}}

C) {E \over C}

D) {{2E} \over C}

205

MediumNEET2014

Light with an energy flux of 25 $ \times 104 W m-$2 falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm2, the average force exerted on the surface is

Options:

A) 1.25 $ \times 10-$6 N

B) 2.50 $ \times 10-$6 N

C) 1.20 $ \times 10-$6 N

D) 3.0 $ \times 10-$6 N

206

MediumNEET2013

An electromagnetic wave of frequency $\upsilon = 3.0 MHz passes from vaccum into a dielectric medium with relative permittivity {{\varepsilon _r}}$ = 4.0. Then

Options:

A) Wavelength is doubled and frequency becomes half.

B) Wavelength is halved and frequency remains unchanged.

C) Wavelength and frequency both remain unchanged.

D) Wavelength is doubled and frequency unchanged.

207

MediumNEET2013

The condition under which a microwave oven heats up a food item containing water molecules most efficiently is

Options:

A) Microwaves are heat waves, so always produce heating.

B) Infra-red waves produce heating in a microwave oven.

C) The frequency of the microwaves must match the resonant frequency of the water molecules.

D) The frequency of the microwaves has no relation with natural frequency of water molecules.

208

MediumNEET2012

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagatting in vacuum is equal to

Options:

A) the speed of light in vacuum

B) reciprocal of speed of light in vacuum

C) the ratio of magnetic permeability to the electric susceptibility of vacuum

D) unity

209

MediumNEET2012

The electric field associated with an em wave in vacuum is given by E = $\widehat i 40 cos (kz - 6 \times $ 108 t) where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is

Options:

A) 2 m$-$1

B) 0.5 m$-$1

C) 6 m$-$1

D) 3 m$-$1

210

MediumNEET2011

The electric and the magnetic field, associated with an e.m. wave, propagating along the +z-axis, can be represented by

Options:

A) \left[ {\overrightarrow E = {E_0}\widehat i,\overrightarrow B = {B_0}\widehat j} \right]

B) \left[ {\overrightarrow E = {E_0}\widehat k,\overrightarrow B = {B_0}\widehat i} \right]

C) \left[ {\overrightarrow E = {E_0}\widehat j,\overrightarrow B = {B_0}\widehat i} \right]

D) \left[ {\overrightarrow E = {E_0}\widehat j,\overrightarrow B = {B_0}\widehat k} \right]

211

MediumNEET2011

The decreasing order of wavelength of infrared, microwave, ultraviolet and gamma rays is

Options:

A) microwave, infrared, ultraviolet, gamma rays

B) gamma rays, ultraviolet, infraref, microwaves

C) microwaves, gamma rays, infrared, ultraviolet

D) infrared, microwave, ultraviolet, gamma rays

212

MediumNEET2010

The electric field of an electromagnetic wave in free space is given by $\overrightarrow E = 10\cos ({10^7}t + kx)\widehat j\,\,V/m, where t and x are in seconds and metres respectively. It can be inferred that (1) the wavelength \lambda $ is 188.4 m. (2) the wave number k is 0.33 rad/m. (3) the wave amplitude is 10 V/m. (4) the wave is propagating along +x direction. Which one of the following pairs of statements is correct ?

Options:

A) (3) and (4)

B) (1) and (2)

C) (2) and (3)

D) (1) and (3)

213

MediumNEET2010

Which of the following statement is false for the properties of electromagnetic waves ?

Options:

A) Both electric and magnetic field vectors attain the maxima and minima at the same place and same time.

B) The energy in electromagnetic wave is divided equally between electric and magnetic vectors.

C) Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave.

D) These waves do not require any material medium for propagation.

214

MediumNEET2009

The electric field part of an electromagnetic wave in a medium is represented by Ex = 0; ${E_y} = 2.5{N \over C}\cos \left[ {\left( {2\pi \times {{10}^6}{{rad} \over m}} \right)t - \left( {\pi \times {{10}^{ - 2}}{{rad} \over s}} \right)x} \right];$ Ez = 0.

Options:

A) moving along x direction with frequency 106 Hz and wavelength 100 m.

B) moving along x direction with frequency 106 Hz and wavelength 200 m.

C) moving along $-$x direction with frequency 106 Hz and wavelength 200 m.

D) moving along y direction with frequency $2\pi \times {10^6}\,Hz$ and wavelength 200 m.

215

MediumNEET2008

The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon 0 and permeability \mu $0 is given by

Options:

A) {1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}

B) \sqrt {{{{\mu _0}} \over {{\varepsilon _0}}}}

C) \sqrt {{{{\varepsilon _0}} \over {{\mu _0}}}}

D) \sqrt {{\mu _0}{\varepsilon _0}}

216

MediumNEET2007

The electric and magnetic field of an electromagnetic wave are

Options:

A) in opposite phase and perpendicular to each other

B) in opposite phase and parallel to each other

C) in phase and perpendicular to each other

D) in phase and parallel to each other.

217

MediumNEET2005

If $\lambda v, \lambda x and \lambda $m represent the wavelengths of visible light, X-rays and microwaves respectively, then

Options:

A) {\lambda _m} > {\lambda _x} > {\lambda _v}

B) {\lambda _m} > {\lambda _v} > {\lambda _x}

C) {\lambda _v} > {\lambda _x} > {\lambda _m}

D) {\lambda _v} > {\lambda _m} > {\lambda _x}

218

MediumNEET2003

Which of the following rays are not electromagnetic waves ?

Options:

A) X-rays

B) \gamma $-rays

C) \beta $-rays

D) heat rays

219

MediumNEET2003

We consider the radiation emitted by the human body. Which one of the following statements is true?

Options:

A) The radiation emitted is in the infra-red region

B) The radiation emitted only during the day

C) The radiation is emitted during the summers and absorbed during the winters

D) The radiation emitted lies in the ultraviolet region and hence is not visible

220

MediumNEET2002

What is the cause of Green house effect ?

Options:

A) infra-red rays

B) ultra violet rays

C) X-rays

D) radio waves.

221

MediumNEET2002

The velocity of electromagnetic wave is parallel to

Options:

A) \overrightarrow B \times \overrightarrow E

B) \overrightarrow E \times \overrightarrow B

C) \overrightarrow E

D) \overrightarrow B

222

MediumNEET2001

Biological inportance of ozone layer is

Options:

A) it stops ultraviolet rays

B) ozone layer reduces green house effect

C) ozone layer reflects radio waves

D) ozone layer controls O2/H2 ratio in atmosphertte.

223

MediumNEET2000

The frequency order for $\gamma $-rays (a), X-rays (b), UV rays (c) is

Options:

A) b $> a >$ c

B) a $> b >$ c

C) c $> b >$ a

D) a $> c >$ b

224

MediumVITEEE2024

The magnetic field in a electromagnetic wave is given by $B_y=2 \times 10^{-7} \sin \left(0.5+10^3 x+1.5 \times 10^{11} t\right) \mathrm{T}$ The frequency of the wave is (in GHz)

Options:

A) 1.26 GHz

B) 2.39 GHz

C) 12.6 GHz

D) 23.9 GHz

225

MediumVITEEE2024

An electromagnetic wave with poynting vector 6 \mathrm{Wm}^{-2} is absorbed by a surface area 12 \mathrm{~m}^2. The force on the surface is

Options:

A) 24 \times 10^{-8} \mathrm{~N}

B) 30 \times 10^{-5} \mathrm{M}

C) 2.4 \times 10^{-12} \mathrm{~N}

D) 3.6 \times 10^8 \mathrm{M}

226

MediumVITEEE2021

Which component of electromagnetic spectrum have maximum wavelength?

Options:

A) Radio waves

B) Visible spectrum

C) Gamma rays

D) X-rays

226

Total Questions

Easy

146

Medium

Hard

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