Question

A solid conducting sphere of radius ${}^{\prime }{a}^{\prime }$ 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 found to be
$\frac{q}{n\pi {\epsilon }_{0}a}$

Answer 1

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$

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

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

Comparing this with the data given in the question we get, $n=32$