# Two concentric shells of radii d and 2d respectively are placed far away from a parallel plate capacitor. Each plate of the capacitor is a square of side d and the separation between the plates is $\large\frac{d}{4 \pi}$. The charge on the plates are q and -q. Then the keys $K_1$ and $K_2$ are closed, find the charges on the shells and electric potential energy left in the parallel plate capacitor in equilibrium.

Charge on the outer shell $= (q- q_1)$
$\qquad= \large\frac{2}{3}$$q$
Charge on the inner shell $= \large\frac{-2q}{3}$
$\qquad= \large\frac{1}{2}\frac{q_1^2}{C}$
$\qquad= \large\frac{q^2}{72 \pi \in_0 d}$