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 now given a charge $-4Q$, the new potential difference between the same two surfaces is :

• A. 4 V
• B. 2 V
• C. -2 V
• D. V

Answer 1

The correct option is D V

We know that potential difference between two points (i.e $\Delta V$) is given by
$\Delta V=E.d$ (where $d$ is the distance between two points)

We know that electric field inside a hollow sphere is 0.
so, no matter how much charge we give to the outer shell, the potential difference will only be due to the electric field of the inner sphere.
$⟹\Delta V=E_{sphere}.d$
$⟹\Delta V=V$ will remain same.