Question

Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries $q$ while inner shell is neutral and is connected to earth by a switch $S$. Find the charge that will flow from earth to inner shell after the switch $S$ is closed.

• A. $-\frac{q}{3}$
• B. $-\frac{q}{2}$
• C. $\frac{q}{3}$
• D. $\frac{2q}{3}$

Answer 1

The correct option is A $-\frac{q}{3}$

Let $q^{\prime }$ be the charge on the inner shell when it is earthed (switch $S$ is closed).

Since the shell is grounded , potential of inner shell, $V_{inner}=0$

$V_{inner}=V_1+V_2$

Where, $V_1\to$ Potential due to outer shell on the inner shell.

$V_2\to$ Potential due to charge present on the inner shell.

$V_{inner}=\frac{1}{4\pi {\epsilon }_o}[\frac{q^{{}^{\prime }}}{r}+\frac{q}{3r}]=0$

$\Rightarrow q^{{}^{\prime }}=-\frac{q}{3}$

Hence, option (a) is the correct answer.

Why this question: This question will check the basic understanding on application of concept of earthing.