$64$ identical drops each charged up to a potential of $10 \, mV$ are combined to form a bigger drop. The potential of the bigger drop will be $.......... \, mV$.

Statement-$1$: For a charged particle moving from point $P$ to point $Q$,the net work done by the electrostatic force is independent of the path connecting point $P$ to point $Q$.
Statement-$2$: The net work done by a conservative force on an object in a closed loop is zero.

Three concentric spherical metallic shells $X$,$Y$,and $Z$ of radii $a$,$b$,and $c$ respectively $[a < b < c]$ have surface charge densities $\sigma$,$-\sigma$,and $\sigma$,respectively. The shells $X$ and $Z$ are at the same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$,respectively,then the radius of shell $Z$ is $......\,cm$.

If on two concentric hollow spheres of radii $R$ and $r$ $(R < r)$,a total charge $Q$ is distributed such that their surface charge densities are equal,then the potential at their common centre is:

$A$ charge $q$ is placed at the centre $O$ of a circle of radius $R$. Two other charges $q$ and $q$ are placed at the ends of the diameter $AB$ of the circle. The work done to move the charge at point $B$ along the circumference of the circle to a point $C$ as shown in the figure is

$A$ charge $+q$ is placed at the origin $O$ of $X-Y$ axes as shown in the figure. The work done in taking a charge $Q$ from $A$ to $B$ along the straight line $AB$ is