$A$ hollow metal sphere of radius $15 \,cm$ is charged such that the potential on its surface is $20 \,V$. Then, the potential at the centre of the sphere is (in $V$)

$A$ charge $+q$ is fixed at each of the points $x = x_0, x = 3x_0, x = 5x_0, \dots$ up to $\infty$ on the $X$-axis and a charge $-q$ is fixed at each of the points $x = 2x_0, x = 4x_0, x = 6x_0, \dots$ up to $\infty$. Here $x_0$ is a positive constant. Taking the potential at a point due to a charge $Q$ at a distance $r$ from it to be $\frac{Q}{4\pi\varepsilon_0 r}$,find the potential at the origin due to the above system of charges.

Consider a sphere of radius $R$ having charge $q$ uniformly distributed inside it. At what minimum distance from its surface is the electric potential half of the electric potential at its centre?

The electrostatic potential on the surface of a uniformly charged spherical shell of radius $R = 10 \ cm$ is $120 \ V$. The potential at the centre of the shell,at a distance $r = 5 \ cm$ from the centre,and at a distance $r = 15 \ cm$ from the centre of the shell respectively,are:

Two electric charges $12\,\mu C$ and $-6\,\mu C$ are placed $20\, cm$ apart in air. There will be a point $P$ on the line joining these charges and outside the region between them,at which the electric potential is zero. The distance of $P$ from the $-6\,\mu C$ charge is.......$m$.

Out of two copper spheres of the same size,$x$ is hollow while $y$ is solid. If they are charged at the same potential,what can be said about the charges on them?