Question 484: Electrostatics & Capacitance

Question

Two point charges q
1
$$\left( {\sqrt {10} \mu C} ight)$$ and q
2
($$-$$ 25 $$\mu $$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take $${1 \over {4\pi { \in _0}}}$$ = 9 $$ 	imes $$ 10
9
Nm
2
C
$$-$$2
]

Accepted Answer

Electric field due to $$\sqrt {10} \,\mu C$$ charge :
$$\overrightarrow {{E_1}}  =  - $$ E
1
sin$$	heta $$
1
$$\widehat i$$ + E
1
cos$$	heta $$
1
$$\widehat j$$
Where,
E
1
$$ = {1 \over {4\pi {\varepsilon _0}}} 	imes {{\left| {{q_1}} ight|} \over {{r_1}^2}}$$
$$ = 9 	imes {10^9} 	imes {{\sqrt {10}  	imes {{10}^{ - 6}}} \over {{{\left( {\sqrt {{1^2}}  + {3^2}} ight)}^2}}}$$
$$ = {{9 	imes {{10}^3}} \over {\sqrt {10} }}\,v/m$$
sin $$	heta $$
1
$$=$$ $${1 \over {\sqrt {10} }}$$
and  cos$$	heta $$
1
= $${3 \over {\sqrt {10} }}$$
$$ 	herefore $$   $$\overrightarrow {{E_1}}  = {{9 	imes {{10}^3}} \over {\sqrt {10} }}\,\left( { - {1 \over {10}}\widehat i + {3 \over {\sqrt {10} }}\widehat j} ight)$$
$$ = 9 	imes {10^2}\left( { - \widehat i + 3\widehat j} ight)$$
Electric field due to $$-$$ 25 $$\mu $$C charge,
$$\overrightarrow {{E_2}}  = $$ E
2
sin$$	heta $$
2
$$\widehat i$$ $$-$$ E
2
cos$$	heta $$
2
$$\widehat j$$
where
E
2
$$ = {1 \over {4\pi {\varepsilon _0}}} 	imes {{\left| {{9_2}} ight|} \over {r_2^2}}$$
$$ = 9 	imes {10^9} 	imes {{25 	imes {{10}^{ - 6}}} \over {{{\left( {\sqrt {{4^2} + {3^2}} } ight)}^2}}}$$
$$ = 9 	imes {10^3}$$ V/m
sin$$	heta $$
2
= $${4 \over 5}$$
and  cos$$	heta $$
2
= $${3 \over 5}$$
$$ 	herefore $$   $$\overrightarrow {{E_2}}  = 9 	imes {10^3}\,\,\left( {{4 \over 5}\widehat i - {3 \over 5}\widehat j} ight)$$
$$ = 18 	imes {10^2}\left( {4\widehat i - 3\widehat j} ight)$$
$$ 	herefore $$   Net electric field,
$$\overrightarrow E $$ = $${\overrightarrow E _1}$$ + $${\overrightarrow E _2}$$
$$ = \left( {63\widehat i - 27\widehat j} ight) 	imes {10^2}\,\,V/m$$

Answer

$$\left( {63\widehat i - 27\widehat j} ight) 	imes {10^2}$$

Answer

$$\left( { - 63\widehat i + 27\widehat j} ight) 	imes {10^2}$$

Answer

$$\left( {81\widehat i - 81\widehat j} ight) 	imes {10^2}$$

Answer

$$\left( { - 81\widehat i + 81\widehat j} ight) 	imes {10^2}$$

Electrostatics & Capacitance

Two point charges q 1 $\left( {\sqrt {10} \mu C} \right) and q 2 (- 25 \mu C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, [take {1 \over {4\pi { \in _0}}} = 9 \times 10 9 Nm 2 C -$2 ]

Choose the correct answer: