Consider three concentric metallic spheres $A, B$ and $C$ of radii $a , b, c$, respectively where $a < b < c$. $A$ and $B$ are connected, whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$, then the charge on the sphere $C$ is

Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta $ from the vertical. If the mass of each charge is $m,$ then the electrostatic potential at the centre of line joining them will be $\left( {\frac{1}{{4\pi { \in _0}}} = k} \right).$

Assertion : For a non-uniformly charged thin circular ring with net charge is zero, the electric field at any point on axis of the ring is zero.

Reason : For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is zero.

Uniform electric field of magnitude $ 100$ $V/m$ in space is directed along the line $y$ $=$ $3$ $+$ $x$. Find .........$V$ the potential difference between point $A (3, 1)$ $ \&$ $ B$ $ (1, 3)$

There are four concentric shells $A, B, C $ and $D $ of radii $ a, 2a, 3a$  and $4a$ respectively. Shells $B$ and $D$ are given charges $+q$ and $-q$ respectively. Shell $C$ is now earthed. The potential difference $V_A - V_C $ is : 

Find the potential $V$ of an electrostatic field $\vec E = a\left( {y\hat i + x\hat j} \right)$, where $a$ is a constant.