A charge $ + q$ is fixed at each of the points $x = {x_0},\,x = 3{x_0},\,x = 5{x_0}$..... $\infty$, on the $x - $axis and a charge $ - q$ is fixed at each of the points $x = 2{x_0},\,x = 4{x_0},x = 6{x_0}$,..... $\infty$. Here ${x_0}$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi {\varepsilon _0}r)$. Then, the potential at the origin due to the above system of charges is

Point charge ${q_1} = 2\,\mu C$ and ${q_2} = - 1\,\mu C$ are kept at points $x = 0$ and $x = 6$ respectively. Electrical potential will be zero at points

A conducting sphere of radius $R$ is given a charge $Q.$ The electric potential and the electric field at the centre of the sphere respectively are

Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta $ from the vertical. If the mass of each charge is $m,$ then the electrostatic potential at the centre of line joining them will be $\left( {\frac{1}{{4\pi { \in _0}}} = k} \right).$

Electric charges having same magnitude of electricicharge $q$ coulombs are placed at $x=1 \,m , 2 \,m , 4 \,m$, $8 \,m$....... so on. If any two consecutive charges have opposite sign but the first charge is necessarily positive, what will be the potential at $x=0$ ?

The electric potential at the surface of an atomic nucleus $(z=50)$ of radius $9 \times 10^{-13} \mathrm{~cm}$ is ________$\times 10^6 \mathrm{~V}$.