There are three co-centric conducting spherical shells $A, B$ and $C$ of radii $a, b$ and $c$ respectively ( $c > b > a$ ) and they are charged with charge $q_1, q_2$ and $q_3$ respectively. The potentials of the spheres $A, B$ and $C$ respectively, are :
Answer: (D) $\dfrac1{4\pi\epsilon_o}\left(\dfrac{q_1}a + \dfrac{q_2}b + \dfrac{q_3}c\right), \dfrac1{4\pi\epsilon_o}\left(\dfrac{q_1+q_2}b + \dfrac{q_3}c\right), \dfrac1{4\pi\epsilon_o}\left(\dfrac{q_1+q_2+q_3}c\right)$
A shell of charge $Q$ and radius $R$ gives potential $kQ/R$ inside it and $kQ/r$ outside ($k = \frac1{4\pi\varepsilon_0}$).
- $A$ (radius $a$) is inside $B$ and $C$: $V_A = k\left(\dfrac{q_1}a + \dfrac{q_2}b + \dfrac{q_3}c\right)$
- $B$ is outside $A$, inside $C$: $V_B = k\left(\dfrac{q_1+q_2}b + \dfrac{q_3}c\right)$
- $C$ is outside both: $V_C = k\,\dfrac{q_1+q_2+q_3}c$
This is option (D).
Solution by Sreeraj P, M.Sc Physics