Two concentric conducting spherical shells of radii $30 \, cm$ and $5 \, cm$ are charged. If the outer shell has a charge of $3 \, \mu C$ and the inner shell has a charge of $0.5 \, \mu C$,what is the electric potential on the outer spherical shell?

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

The figure shows the electric field lines of a positive and a negative charge,respectively. Determine the sign of the potential difference $V_Q - V_P$ and $V_B - V_A$.

$A$ regular hexagon of side $10 \; cm$ has a charge $5 \; \mu C$ at each of its vertices. Calculate the potential at the centre of the hexagon.

$A$ charge $+q$ is distributed over a thin ring of radius $r$ with line charge density $\lambda = q \sin^2 \theta / (\pi r)$. Note that the ring is in the $XY$-plane and $\theta$ is the angle made by the position vector with the $X$-axis. The work done by the electric force in displacing a point charge $+Q$ from the centre of the ring to infinity is

$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric of inner radius $a$,outer radius $b$ and dielectric constant $k$. If sphere $A$ is given a charge $Q$,the potential at the outer surface of the dielectric (at radius $b$) is: