A solid coducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge $-3Q$, the new potential difference between the same two surface is :-........$V$
$1$
$2$
$4$
$-2$
A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose centre coincides with the given sphere. The flux related to imaginary sphere is
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
The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$ where $r$ is the distance from the centre $a,\,b$ are constants. Then the charge density inside the ball is
Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of the spheres $\sigma _1/\sigma _2$ will be
In the circuit shown, a potential difference of $30\, V$ is applied across $AB$ . The potential difference between the points $M$ and $N$ is....$V$