Question

A solid conducting sphere having a charge $Q$ is surrounded by an uncharged Concentric conducting spherical shell. The potential difference between the surface of solid sphere and the shell is $V$. The shell is now given a charge $-3Q$. The shell potential difference between the same surfaces will be

• A. - 2v
• B. 4V
• C. V
• D. 2V

Answer 1

Answer: (C)

The difference of potential between the solid sphere and the hollow spherical shell depends only on their radii and the charge on the inner solid sphere
$V \propto \frac{Q}{R_1} - \frac{Q}{R_2}$
When charge -3Q is placed on outer sphere, the potential of inner sphere is $\frac{Q}{R_1} - \frac{3Q}{R_2}$ and that of outer sphere is $\frac{- Q}{R_2} - \frac{3Q}{R_2} = - \frac{4Q}{R_2}$
difference is again $\frac{Q}{R_1} + \frac{Q}{R_2}$