The electric field in a region surrounding the origin is uniform and along the $x$ - axis. A small circle is drawn with the centre at the origin cutting the axes at points $A, B, C, D$ having co-ordinates $(a, 0), (0, a), (-a, 0), (0, -a)$; respectively as shown in figure then potential in minimum at the point

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is

Consider three concentric metallic spheres $A, B$ and $C$ of radii $a , b, c$, respectively where $a < b < c$. $A$ and $B$ are connected, whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$, then the charge on the sphere $C$ is

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

Three charges $q, \sqrt 2q, 2q$ are placed at the corners $A, B$ and $C$ respectively of the square $ABCD$ of side $'a'$ then potential at point $'D'$

$1000$ small water drops each of radius $r$ and charge $q$ coalesce together to form one spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of