$A$ charge $Q$ is placed at each corner of a cube of side $r$. The potential at the centre of the cube is ($\epsilon_0$ = permittivity of free space).

Two equal point charges are fixed at $x = -a$ and $x = +a$ on the $x$-axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$,when it is displaced by a small distance $x$ along the $x$-axis,is approximately proportional to

Two conducting spheres of radii $r_1$ and $r_2$ have the same electric field intensity near their surfaces. The ratio of their electric potentials is

$A$ charge of $5\,C$ is given a displacement of $0.5\,m$. The work done in the process is $10\,J$. The potential difference between the two points will be.......$V$

If four charges $+12 \text{ nC}, -20 \text{ nC}, +32 \text{ nC}$ and $-15 \text{ nC}$ are arranged at the four vertices of a square of side $\sqrt{2} \text{ m}$,then the net electric potential at the centre of the square due to these four charges is (in $\text{ V}$)

$A$ solid conducting sphere with charge $Q$ is surrounded by an uncharged concentric conducting spherical shell. Let $V$ be the potential difference between the surface of the solid sphere and the outer surface of the shell. If the shell is now given a charge of $-3Q$,the new potential difference between the two surfaces is .........$V$.