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

Consider a Gaussian spherical surface covering a dipole of charge $q$ and $-q,$ then

Two large thin conducting plates with a small gap in between are placed in a uniform electric field $E$ (perpendicular to the plates). The area of each plate is $A,$ and charges $+Q$ and $-Q$ are given to these plates as shown in figure. If $R, S,$ and $T$ are three points in space, then the