$A$ charge $q$ is placed at the centre $O$ of a circle of radius $R$. Two other charges $q$ and $q$ are placed at the ends of the diameter $AB$ of the circle. The work done to move the charge at point $B$ along the circumference of the circle to a point $C$ as shown in the figure is

$A$ solid conducting sphere with charge $Q$ is surrounded by an uncharged concentric conducting spherical shell. Let $V$ be the potential difference between the surface of the solid sphere and the outer surface of the shell. If the shell is now given a charge of $-3Q$,the new potential difference between the two surfaces is .........$V$.

Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively.
$(a)$ Give the signs of the potential difference $V_{P}-V_{Q}$ and $V_{B}-V_{A}$.
$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$,and $A$ and $B$.
$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.
$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.
$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A$?

The work done to assemble the three charges in a configuration as shown in the figure is

$A$ hollow metal sphere of radius $5\, cm$ is charged such that the potential on its surface is $10\, V$. The potential at the centre of the sphere is

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