The work done in carrying a charge $Q$ once around a circle of radius $r$ about a charge $q$ at the centre is

Calculate the potential energy of a point charge $-q$ placed along the axis due to a charge $+Q$ uniformly distributed along a ring of radius $R$. Sketch the potential energy $(P.E.)$ as a function of axial distance $z$ from the centre of the ring. Looking at the graph,can you determine what would happen if $-q$ is displaced slightly from the centre of the ring along the axis?

In the following diagram,the work done in moving a point charge from point $P$ to points $A$,$B$,and $C$ is $W_A$,$W_B$,and $W_C$ respectively. Then:

$A$ potential at a point $A$ is $-3 \ V$ and that at another point $B$ is $5 \ V$. What is the work done in carrying a charge of $5 \ mC$ from $B$ to $A$?

Assertion $(A)$: The work done by the electrostatic force is zero when a point charge moves in a circular path around another charge.
Reason $(R)$: The dot product of force and displacement vectors gives work done.

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance $R$ $(a < R < b)$ from the centre of the shell is (where $K = \frac{1}{4\pi\varepsilon_0}$):