Question

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

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

Answer 1

The correct option is D $+\frac{q}{3}$

Let $q^{\prime }$ be the charge on the inner shell when it is earthed.

Potential of inner shell will be zero as it is grounded.

So, $\frac{k{q}^{\prime }}{r}+\frac{kq}{3r}=0$

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

Therefore, $+\frac{q}{3}$ charge will flow from inner shell to earth.

Why this question? Concept- When an object is grounded, its potential become equal to potential of earth i.e $V=0$