Question

$S_1$ and $S_2$ are two conducting surfaces. Between $S_1$ and $S_2$ and inside$S_1$ is air. $S_1$ is spherical with $A$ as its centre. $S_1$ has total charge $Q$ and $S_2$ is uncharged. Then, which of the following options are correct?

• A. Charges included on inner and outer surfaces of $S_2$ is $-Q$ and $+Q$ respectively
• B. Total electric field at $A$ is zero.
• C. Electric field at $B$ due to induced charges on outer surface of $S_2$ cannot be calculated with given information.
• D. Electric field at $C$ due to induced charges on inner surface of $S_2$ cannot be calculated with given information.

Answer 1

Answer: (A), (B), (D)

Electric field at $C$ due to induced charges on inner surface of $S_2$ cannot be calculated with given information.

(1) Using gaussian law on conductor $S_2$,

$\oint Eds=\frac{\sum q_{in}}{{ϵ}_0}$

$\because$ On conductor $E=0$

So, $\sum q_{in}=0$

$\Rightarrow Q_{S_1}+Q_{inner{S}_2}=0$

$Q_{inner{S}_2}=-Q_{S_1}=-Q$

$\because$ conductor $S_2$ is a uncharged one. So net charge on $S_2$ is zero.

$Q_{inner{S}_2}+Q_{out{S}_2}=0$

$Q_{out{S}_2}=-Q_{inner{S}_2}=+Q$

(2)We know that, there is no electric field inside the cavity of conductor due to the charge outside of the conductor.
So, $E_A=0$.

(3)At point $B$ is $E_B\ne 0$ as net charge enclosed by a gaussian surface drawn at $B$ is $Q$.

(4)Electric field due to inner surface of $S_2$ at point $C$ cannot be calculated, because it is not any symmetrical surface.

Hence, options $A,B$ and $D$ are correct.