$A$ regular hexagon of side $6 \ cm$ has a charge of $2 \ \mu C$ at each of its vertices. What is the potential at the centre of the hexagon? $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \text{ SI units}\right]$

Write expressions for electric potential due to a continuous distribution of charges.

$A$ total charge $Q$ is distributed between two concentric spherical shells of radii $r$ and $R$ $(R > r)$ such that their surface charge densities are equal. What is the electric potential at their common center?

$A$ 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 minimum work needed to be done to bring a charge $q=6 \mu C$ from $\infty$ to a point $0.75 \ m$ from a charge $Q=30 \mu C$ is (in $J$)

Write an equation for the electric potential due to a volume charge distribution.