Write the relation between the electric field of an electric charge and electrostatic potential at any point.

Derive an expression for electric potential at a point due to a system of $\mathrm{N}$ charges.

Four charges $ + Q,\, - Q,\, + Q,\, - Q$ are placed at the corners of a square taken in order. At the centre of the square

Figure shows a solid hemisphere with a charge of $5\ nC$ distributed uniformly through its volume. The hemisphere lies on a plane and point $P$ is located on this plane, along a radial line from the centre of curvature at distance $15\ cm$. The electric potential at point $P$ due to the hemisphere, is .....$V$

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K=\frac{1}{4 \pi \varepsilon_0} \frac{q}{L^2}$, which of the following statement $(s)$ is (are) correct?

$(A)$ the elecric field at $O$ is $6 K$ along $O D$

$(B)$ The potential at $O$ is zero

$(C)$ The potential at all points on the line $PR$ is same

$(D)$ The potential at all points on the line $ST$ is same.

Two spheres $A$ and $B$ of radius $a$ and $b$ respectively are at same electric potential. The ratio of the surface charge densities of $A$ and $B$ is