Q 12-02-160JEE MainJEE Main 2020 (3 Sep, Shift 2)Medium
Concentric metallic hollow spheres of radii $R$ and $4R$ hold charges $Q_1$ and $Q_2$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V(R) - V(4R)$ is:
Answer: (C) $\dfrac{3Q_1}{16\pi\varepsilon_0R}$
The outer shell contributes the same potential at both radii, so only $Q_1$ matters:
$$V(R) - V(4R) = \frac{Q_1}{4\pi\varepsilon_0}\left(\frac1R - \frac1{4R}\right) = \frac{3Q_1}{16\pi\varepsilon_0R}$$
(Equal densities give $Q_2 = 16Q_1$, which does not appear in this answer.)
Solution by Sreeraj P, M.Sc Physics