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

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?

$A$ charge of $10 \,\mu C$ is placed at the origin of an $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volts will be

Eight charges,each of magnitude $q$,are placed at the vertices of a cube placed in a vacuum. The electric potential at the centre of the cube due to this system of charges is . . . . . . . ($\varepsilon_0 = $ permittivity of vacuum,$a = $ length of each side of the cube.)

Calculate the potential energy of a point charge $-q$ placed along the axis due to a charge $+Q$ uniformly distributed along a ring of radius $R$. Sketch the potential energy $(P.E.)$ as a function of axial distance $z$ from the centre of the ring. Looking at the graph,can you determine what would happen if $-q$ is displaced slightly from the centre of the ring along the axis?

The electric potential on the surface of a hollow sphere of radius $5 \ cm$ is $10 \ V$. What is the electric potential at its center?