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

A charge is spread non-uniformly on the surface of a hollow sphere of radius $R$, such that the charge density is given by $\sigma=\sigma_0(1-\sin \theta)$, where $\theta$ is the usual polar angle. The potential at the centre of the sphere is

Potential at a point $x$-distance from the centre inside the conducting sphere of radius $R$ and charged with charge $Q$ is

An electric charge ${10^{ - 3}}\,\mu \,C$ is placed at the origin $(0, 0)$ of $X -Y$ co-ordinate system. Two points $A$ and $B$ are situated at $\left( {\sqrt {2\,} \,,\,\,\sqrt 2 } \right)$  and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be......$volt$

$27$ identical drops are charged at $22\, V\,\,each.$ They combine to form a bigger drop. The potential of the bigger drop will be............ $V.$

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region: $Image$

$(A)$ the electrostatic field is zero

$(B)$ the electrostatic potential is constant

$(C)$ the electrostatic field is constant in magnitude

$(D)$ the electrostatic field has same direction