Q 12-02-175JEE MainJEE Main 2019 (8 Apr, Shift 1)Easy
A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged 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 of $-4Q$, the new potential difference between the same two surfaces is
Answer: (C) $V$
Charge on the shell (on its outer surface) produces the same potential at every point inside and on the shell, so it adds equally to both potentials and cancels in the difference. The difference depends only on the inner charge $Q$:
$$V = kQ\left(\frac1a - \frac1b\right)$$
It stays $V$.
Solution by Sreeraj P, M.Sc Physics