An electric 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 $V$.

The potential difference $(V_A-V_B)$ in the arrangement shown in the figure is $(q=1 \mu C, x=2 \text{ cm}, y=3 \text{ cm})$.

$A$ 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)

The value of the electric potential at a point due to a point charge is:

$A$ 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.

Four equal point charges $Q$ are placed in the $xy$ plane at $(0, 2), (4, 2), (4, -2)$ and $(0, -2)$. The work required to put a fifth charge $Q$ at the origin of the coordinate system will be