Two point charges $-Q$ and $+Q / \sqrt{3}$ are placed in the xy-plane at the origin $(0,0)$ and a point $(2,0)$, respectively, as shown in the figure. This results in an equipotential circle of radius $R$ and potential $V =0$ in the $xy$-plane with its center at $(b, 0)$. All lengths are measured in meters.

($1$) The value of $R$ is. . . . meter.

($2$) The value of $b$ is. . . . . .meter.

A regular hexagon of side $10\; cm$ has a charge $5 \;\mu\, C$ at each of its vertices. Calculate the potential at the centre of the hexagon.

In a uniform electric field, the potential is $10$ $V $ at the origin of coordinates, and $8$ $V$ at each of the points $(1, 0, 0), (0, 1, 0) $ and $(0, 0, 1)$. The potential at the point $(1, 1, 1)$ will be....$V$

A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

If the electric potential of the inner metal sphere is $10$ $ volt$ $\&$ that of the outer shell is $5$ $volt$, then the potential at the centre will be ......$volt$

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 $\left( {\frac{1}{{4\pi { \in _0}}} = k} \right).$