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 induced on inner and outer surface 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 charge on inner surface of $S_2$ cannot be calculated with given information

Answer 1

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

Charges induced on inner and outer surface of $S_2$ is -Q and +Q respectively
Total electric field at A is zero
Electric field at C due to induced charge on inner surface of $S_2$ cannot be calculated with given information

For gaussian surface inside the conductor $S_2$
$\oint E.ds=\frac{\sum q_{in}}{{ϵ}_0}$
But in conductor $E=0$
So, $\sum q_{in}=0$
$Q_{s_1}+Q_{inner{s}_2}=0$
$Q_{inner{s}_2}=-Q_{s_1}=-Q$
But net charge on $S_2$ is zero So
$Q_{in{s}_2}+Q_{out{s}_2}=0$
There is no electric field inside the cavity of conductor due to the charge outside of the conductor.
So, $E_A=0$