An electric point charge $10^{-3} \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be.....$volt$.

Draw a graph showing the variation of electric potential $V$ with distance $r$ from the center for a uniformly charged spherical shell of radius $R$.

Two concentric hollow conducting spheres of radius $r$ and $R$ $(r < R)$ are shown. The charge on the outer shell is $Q$. What charge $q$ should be given to the inner sphere so that the potential at any point $P$ at a distance $x$ $(x > R)$ from the center is zero?

$A$ neutral spherical copper particle has a radius of $10 \,nm$ $(1 \,nm = 10^{-9} \,m)$. 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:

The side length of an equilateral triangle is $d$. Three charges,each of magnitude $Q$,are placed at the three vertices. If $P$ is the midpoint of one side,find the electric potential $V_P$ at point $P$.

$A$ unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius $R$, having uniform positive charge density $\rho$. The initial and final positions of the charge are marked by $A$ and $B$ at distances $2R$ and $3R$ respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\frac{\rho R^2}{n \epsilon_0}$. The value of $n$ is : ($\epsilon_0$ is the permittivity of vacuum)