Three identical metal plates with large surface areas are kept parallel to each other as shown in the figure. The leftmost plate is given a charge $Q$, the rightmost a charge $-2Q$ and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

A cavity of radius $r$ is made inside a solid sphere. The volume charge density of the remaining sphere is $\rho$. An electron (charge $e$, mass $m$) is released inside the cavity from point $P$ as shown in the figure. The centre of sphere and the centre of the cavity arc is separated by a distance $a$. The time after which the electron again touches the sphere is

Consider Gauss's law:

$\oint \overrightarrow{E}·\overrightarrow{d}s=\frac{q}{{\epsilon }_0}$

Then, for the situation shown in figure at the Gaussian surface