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 $S$. The charge attained by the inner shell is $-Q/x$.Find $x$.

Answer 1

Let $q$ be the charge attained by the inner shell.
As the inner shell is earthed so potential at any point on the surface of the shell is zero.
i.e, $V=0=V_{in}+V_{out}=\frac{kq}{R}+\frac{kQ}{3R}$
$\therefore q=-\frac{Q}{3}$