Question

Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries charge $q$ and the inner shell is neutral. The amount of charge that flows from the inner shell to the earth after the key K is closed is equal to $(1/n{)}^{th}$ of the charge on the outer shell. What is the value of n?

Answer 1

Let charge appearing on the inner shell is $Q$.
When key K is closed , the inner shell will be earthed and its potential will be zero.
i.e, $\frac{kQ}{r}+\frac{q}{3r}=0$
$\therefore Q=-\left(q/3\right)$
Now charge that flows from the inner shell to the earth shall be $-Q=\left(q/3\right)$
thus, $n=3$