Concentric metallic hollow spheres of radii $R$ and $4 R$ hold charges $Q _{1}$ and $Q _{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V ( R )- V (4 R )$ is

Three concentric spherical shells have radii $a, b$ and $c (a < b < c)$ and have surface charge densities $\sigma ,-\;\sigma $ and $\;\sigma \;$ respectively. If  $V_A,V_B$ and $V_C$  denote the potentials of the three shells, then, for $c = a +b,$ we have

Draw a graph showing variation of potential with $r$ distance for a uniformly charged spherical shell.

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.

Ten electrons are equally spaced and fixed around a circle of radius $R$. Relative to $V = 0$ at infinity, the electrostatic potential $V$ and the electric field $E$ at the centre $C$ are

Calculate potential on the axis of a disc of radius $R$ due to a charge $Q$ uniformly distributed on its surface.