Define $1 \ eV$.

There are two thin wire rings,each of radius $R$,whose axes coincide. The charges of the rings are $q$ and $-q$. The magnitude of potential difference between the centres of the rings separated by a distance $\sqrt{3} R$ is

Two charges $q_1$ and $q_2$ are separated by a distance of $30\ cm$. $A$ third charge $q_3$,initially at $C$ as shown in the figure,is moved along the circular path of radius $40\ cm$ from $C$ to $D$. If the difference in potential energy due to the movement of $q_3$ from $C$ to $D$ is given by $\frac{q_3 K}{4 \pi \epsilon_0}$,find the value of $K$.

Three concentric metallic shells $A, B$ and $C$ of radii $a, b$ and $c$ $(a < b < c)$ have surface charge densities $+\sigma, -\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

The electric charges $+2q$, $+2q$, $-2q$ and $-2q$ are placed at the corners of a square of side $2L$ as shown in the figure. The electric potential at point $A$, midway between the two charges $+2q$ and $+2q$, is $(\epsilon_0 = \text{permittivity of free space})$