Assume that an electric field $\overrightarrow E  = 30{x^2}\hat i$ exists in space. Then the potential difference $V_A -V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\, m$ is

$N$ identical spherical drops charged to the same potential $V$ are combined to form a big drop. The potential of the new drop will be

Three charges $q, \sqrt 2q, 2q$ are placed at the corners $A, B$ and $C$ respectively of the square $ABCD$ of side $'a'$ then potential at point $'D'$

A neutral spherical copper particle has a radius of $10 \,nm \left(1 \,nm =10^{-9} \,m \right)$. It gets charged by applying the voltage slowly adding one electron at a time. Then, the graph of the total charge on the particle versus the applied voltage would look like

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.

A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is