Question

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

• A. $q$
• B. $-q$
• C. $0$
• D. $2q$

Answer 1

The correct option is C $0$

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

Charge distribution on the various surfaces is shown in the figure.


Let us select a point $\text{P}$, a distance $r(R<r<2R)$ from centre.

As hollow sphere is grounded, $V_P=0$

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

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

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