Question

Two thin conducting shells of radii $R$ and $3R$ are shown in figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. The inner shell is earthed with the help of switch $S$. Find the charge attained by the inner shell.

• A. $\frac{Q}{5}$
• B. $-\frac{Q}{6}$
• C. $\frac{Q}{9}$
• D. $-\frac{Q}{3}$

Answer 1

The correct option is D $-\frac{Q}{3}$

As the inner shell is earthed, the net potential of this shell must be zero.
Let $q$ be the charge of inner shell.
$\therefore V_{\text{inner}}=0$
$\Rightarrow \frac{Kq}{R}+\frac{KQ}{3R}=0$
$\Rightarrow q=-\frac{Q}{3}$
Hence, option $\left(A\right)$ is correct.