Two point charges $q_1 = 4 \times 10^{-8} \ C$ and $q_2 = -6 \times 10^{-8} \ C$ are placed at points $A$ and $B$ respectively,which are $50 \ cm$ apart. At what distance from point $A$ on the line $AB$ is the electric potential zero (in $cm$)?

Four identical charges $+50\,\mu C$ each are placed,one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $+50\,\mu C$ from infinity to the centre of the square? (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\frac{N\cdot m^2}{C^2}$)

$A$ solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4\, Q$, the new potential difference between the same two surfaces is......$V$.

$A$ uniform electric field exists in the positive $x$-direction. Let $A$ be the origin. Point $B$ is at $x = +1 \ cm$ on the $x$-axis and point $C$ is at $y = +1 \ cm$ on the $y$-axis. Which of the following relations is correct regarding the potentials at $A, B,$ and $C$?

There are two thin wire rings,each of radius $R$,whose axes coincide. The charges of the rings are $q$ and $-q$. The magnitude of potential difference between the centres of the rings separated by a distance $\sqrt{3} R$ is

$64$ drops of mercury,each charged to a potential of $10\,V$,are combined to form one bigger drop. The potential of this bigger drop will be.......$V$ (Assume all the drops to be spherical).