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

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

Tardigrade Admin · Accepted Answer

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{3 Q}{R _{2}}

and that of outer sphere is

\frac{- Q}{R _{2}} - \frac{3 Q}{R _{2}} = - \frac{4 Q}{R _{2}}

difference is again

\frac{Q}{R _{1}} + \frac{Q}{R _{2}}