Question

A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is not given a charge of $-3Q$, the new potential difference between the same two surfaces is :

• A. $V$
  
• B. $2V$
  
• C. $4V$
  
• D. $-2V$
  

Answer 1

The correct option is D $-2V$

Let radius of solid sphere $=r_1$ and radius of shell $=r_2$

In first case, potential at the surface of solid sphere is $V_1=\frac{kQ}{r_1}$

and potential at the surface of shell is $V_2=\frac{kQ}{r_2}$

Here, $V=V_1-V_2=\frac{kQ}{r_1}-\frac{kQ}{r_2}....\left(1\right)$

When -3Q is added to shell, potential at the surface of solid sphere is $V_1^{\prime }=\frac{k(Q-3Q)}{r_1}=\frac{-2kQ}{r_1}$ and

potential at the surface of shell is $V_2^{\prime }=\frac{k(Q-3Q)}{r_2}=\frac{-2kQ}{r_2}$

New potential difference , $V^{\prime }=V_1^{\prime }-V_2^{\prime }=\frac{-2kQ}{r_1}-\frac{-2kQ}{r_2}=-2V$ using (1)