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

Three concentric spherical shells have radii $a, b$ and $c (a < b < c)$ and have surface charge densities $\sigma ,-\;\sigma $ and $\;\sigma \;$ respectively. If  $V_A,V_B$ and $V_C$  denote the potentials of the three shells, then, for $c = a +b,$ we have

A hollow conducting sphere of radius $R$ has a charge $( + Q)$ on its surface. What is the electric potential within the sphere at a distance $r = \frac{R}{3}$ from its centre

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between in the limits $589.0\,V$ to $589.8\, V$. What is the potential at a point on the sphere whose radius vector makes an angle of $60^o$ with the direction of the field ?........$V$

Twenty seven drops of same size are charged at $220\, \mathrm{~V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop. (In $\mathrm{~V}$)

Two identical positive charges are placed at $x =\, -a$ and $x = a$ . The correct variation of potential $V$ along the $x-$ axis is given by