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 charge on solid sphere is

• A. $-\frac{q}{2}$
• B. $-\frac{q}{4}$
• C. $-\frac{q}{8}$
• D. $-\frac{q}{16}$

Answer 1

The correct option is B $-\frac{q}{4}$

The net charge on isolated outer sphere is zero.

Let, the charge on the inner sphere is $q_A$.

Now, potential on the inner sphere due to charge $q$ and $q_A$ will be,

$V_m=\frac{q_A}{4\pi {ϵ}_{0}a}+\frac{q}{4\pi {ϵ}_0\left(4a\right)}$

The inner sphere is grounded, hence its potential is zero.So,

$V_m=0$

$\Rightarrow \frac{1}{4\pi {ϵ}_0}\frac{q_A}{a}+\frac{1}{4\pi {ϵ}_0}\frac{q}{4a}=0$

$\Rightarrow \frac{q_A}{a}=-\frac{q}{4a}$

$\therefore q_A=-\frac{q}{4}$

Hence, option (b) is correct answer.