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

Obtain an expression for electric field at the surface of a charged conductor.

A point charge $q$ is placed in a cavity in a metal block. If a charge $Q$ is brought outside the metal, then the electric force experienced by $q$ is

$A$ and $B$ are concentric conducting spherical shells. $A$ is given a positive charge while $B$ is earthed. Then :-

Two uniformly charged spherical conductors $A$ and $B$ of radii $5 mm$ and $10 mm$ are separated by a distance of $2 cm$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $A$ and $B$ will be .

The dielectric strength of air at $NTP$ is $3 \times {10^6}\,V/m$ then the maximum charge that can be given to a spherical conductor of radius $3\, m$ is