Electric potential at any point is : $V = -5x + 3y + \sqrt {15} z$ ; then the magnitude of electric field is :-

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,

In the circuit shown, a potential difference of $60\,V$ is applied across $AB$. The potential difference between the point $M$ and $N$ is…..$V$

Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame in $xy$ plane as shown in figure. The plane of the frame is perpendicular to $z-$ axis. If a $-ve$ point charges is placed at a distance $z$ away from the above frame $(z << L)$ then

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