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

$+\frac{q}{3}$

Let q' be the charge on inner shell when it is earthed.

V_inner = 0

∴ $\frac{1}{4 \pi \epsilon_0}\left[\frac{q^{\prime}}{r}+\frac{q}{3 r}\right]=0$

∴ q' = −q / 3

i.e. $+\frac{q}{3}$ charge will flow froms inner shell to earth.