Question

A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.


The potential of outer shell is:

• A. $\frac{q}{32\pi {ϵ}_{0}a}$
• B. $\frac{q}{16\pi {ϵ}_{0}a}$
• C. $\frac{q}{8\pi {ϵ}_{0}a}$
• D. $\frac{q}{4\pi {ϵ}_{0}a}$

Answer 1

The correct option is A $\frac{q}{32\pi {ϵ}_{0}a}$

Let the potential of the outer shell be $V_B$.

Potential at outer shell due to point charge is given by $$V_1=\frac{kq}{4a}$$
Potential at outer shell due to inner sphere is given by $$V_2=-\frac{k{q}^{\prime }}{2a}$$$\therefore V_B=V_1+V_2$

$\Rightarrow V_B=\frac{kq}{4a}+(-\frac{kq}{8a})$

$\Rightarrow V_B=\frac{q}{32\pi {\epsilon }_{0}a}$

Hence, option (a) is the correct answer.