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
$\frac{\pi}{3}$
$\frac{\pi}{3} + \tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$
$\frac{2 \pi}{3}$
$\tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$
Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then
A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$
Two spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of electric field of the spheres is
A hollow cylinder has a charge $q$ coulomb within it. If $\phi $ is the electric flux in units of voltmete associated with the curved surface $B$ , the flux linked with the plane surface $A$ in units of volt-meter will be
Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges in them repel each other with a force $F$ when kept apart at some some distance. $A$ third spherical conductor having same radius as that of $B$ but uncharged, is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is-