A thin metallic spherical shell contains a charge $Q$ on it. A point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in fig. All  the three charges are positive. The force on the charge at the centre is :-

Five point charges each having magnitude $'q'$ are placed at the corners of regular hexagon as shown in figure. Net electric field at the centre $'O'$ is $\vec E$ . To get net electric field at $'O'$ to be $6\vec E$ , charge placed on the remaining sixth corner should be

A charge $q$ is placed at $O$ in the cavity in a spherical uncharge $d$ conductor. Point $S$ is outside the conductor. If the charge is displaced from $O$ towards $S$ still remaining with in the cavity,

The resultant capacitance between $A$ and $B$ in the fig. is.....$\mu F$

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-

A hollow metal sphere of radius $5\,cm$ is charged such that the potential on its surface is $10\,V$. The potential at a distance of $2\,cm$ from the centre of the sphere.......$V$