Question

A charge $q$ is distributed uniformly on the surface of a solid sphere of radius $R$. It is covered by a concentric hollow conducting sphere of radius $2R$. The charge on outer surface of hollow sphere if it is earthed is

• A. $q$
• B. $-q$
• C. $0$
• D. $2q$

Answer 1

The correct option is C $0$

The charge on the inner surface of the hollow sphere should be $-q$ because if we draw a closed Gaussian surface through the material of the hollow sphere, the total charge enclosed by this Gaussian surface should be zero as inside the material of shell, electric field is zero.


By Gauss's law,
$\oint \overrightarrow{E}\cdot \overrightarrow{A}=\frac{q_{\text{enclosed}}}{{ϵ}_0}$

So, if $\overrightarrow{E}=0$ then $q_{\text{enclosed}}=0$

Let $q^{\prime }$ be the charge on the outer surface of the hollow sphere.

$V_B=\frac{kq}{2R}+\frac{k(-q)}{2R}+\frac{k{q}^{\prime }}{2R}$

Further, $V_B=0\left[\text{B is earthed}\right]$

$\Rightarrow \frac{kq}{2R}+\frac{k(-q)}{2R}+\frac{k{q}^{\prime }}{2R}=0$

$\Rightarrow q^{\prime }=0$

Therefore, option $\left(c\right)$ is correct.

Why this question? key idea- This question is intended to test your understanding and application of Gauss's law.