Two spherical conductors $A$ and $B$ of radii $1\ mm$ and $2\  mm$ are separated by a distance of $5\ cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is

Consider the shown system of two concentric thin metal shells. The inner hell has charge $Q$, while the outer shell is neutral. Potential difference between the shells is $V$. If the shell are joined by metal wire, then potential of the inner shell is

The adjacent diagram shows a charge $+Q$ held on an insulating support $S$ and enclosed by a hollow spherical conductor. $O$ represents the centre of the spherical conductor. and $P$ is a point such that $OP = x $ and $SP = r$ . The electric field at point $P$  will be

A conducting sphere $A$ of radius $a$, with charge $Q$, is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$. 

Sixty four conducting drops each of radius $0.02 m$ and each carrying a charge of $5 \,\mu C$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be …………