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 charge on the solid sphere is $\frac{-q}{n}$. Find the value of $n$

Answer 1

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,

$V_m=0$

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

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

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

Comparing with the data given in the question, we get $n=4$

Accepted answers : $4,4.0,4.00$