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 charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the  three charges will be in equilibrium, if $q$ is equal to

If on the concentric hollow spheres of radii $r$ and $R( > r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is

Four identical capacitors are connected in series with a battery of $emf$ $10\,V$. The point $X$ is earthed, then the potential of point $A$ is.....$V$

Two capacitor one of capacitance $C$ and other capacitance $C/2$ are connected with a battery of $V$ $volt$ then heat produced in connecting wire

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance, the new force will be