A wheel having mass $m$ has charges $+q $ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of uniform vertical electric field $E =$  

A capacitor of capacitance $C_0$ is charged to a potential $V_0$ and is connected with another capacitor of capacitance $C$ as shown. After closing the switch $S$, the common potential across the two capacitors becomes $V$. The capacitance $C$ is given by

A metallic shell has a point charge $'q'$ kept inside its cavity. Which one of the following diagrams correctly represents the electric field lines

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ 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.......$V$

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-