Q 12-02-200JEE MainJEE Main 2018 (8 Apr)Medium
Three concentric metal shells $A$, $B$ and $C$ of respective radii $a$, $b$ and $c$ $(a < b < c)$ have surface charge densities $+\sigma$, $-\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is:
Answer: (C) $\dfrac{\sigma}{\varepsilon_0}\left[\dfrac{a^2 - b^2}{b} + c\right]$
The charges are $q_A = 4\pi a^2\sigma$, $q_B = -4\pi b^2\sigma$, $q_C = 4\pi c^2\sigma$. At radius $b$, shells $A$ and $B$ act as point charges at the centre, while shell $C$ (outside) contributes its surface potential:
$$V_B = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_A + q_B}{b} + \frac{q_C}{c}\right) = \frac{\sigma}{\varepsilon_0}\left(\frac{a^2 - b^2}{b} + c\right)$$
Solution by Sreeraj P, M.Sc Physics