A parallel plate capacitor has plates with area $A$ and separation $d$ . A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d $ is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced is
$K$
$\frac {1}{K}$
$\frac {A}{d^2K}$
$\frac {d^2K}{A}$
Three identical dipoles are arranged as shown below. What will be the net electric field at $M$
An electric dipole is placed along the $x$ -axis at the origin $O.$ A point $P$ is at a distance of $20\, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$ -axis. If the electric field at $P$ makes an angle $\theta$ with the $x$ -axis, the value of $\theta$ would be
A thin spherical conducting shell of radius $R$ has charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is
What is the effective capacitance between points $X$ and $Y$ ?......$\mu F$
Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+ q$ and $-q$. The potential difference between the centres of the two rings is