Write an equation for potential due to linear charge distribution. 

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

Consider two points $1$ and $2$ in a region outside a charged sphere. Two points are not very far away from the sphere. If $E$ and $V$ represent the electric field vector and the electric potential, which of the following is not possible

A cube of side $b$ has a charge $q$ at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

$1000$ small water drops each of radius $r$ and charge $q$ coalesce together to form one spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $ + q$ and $ - q$. The potential difference between the centres of the two rings is