Question

A solid sphere of radius $R$ has a charge $+2Q$. A hollow spherical shell of radius $3R$ placed concentric with the first sphere has net charge $-Q$. If the inner sphere is earthed, what will be the charge on it?

• A. $\frac{2Q}{3}$
• B. $\frac{-Q}{3}$
• C. $\frac{Q}{3}$
• D. $\frac{-2Q}{3}$

Answer 1

The correct option is C $\frac{Q}{3}$

Let the inner sphere has charge $q$. Now the potential at the surface of small sphere is

$\frac{k(-Q)}{3R}+\frac{kq}{R}=0$

Therefore, $q=\frac{Q}{3}$