If $E_{a}$ and $E_{q}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance $r$ from the centre of the dipole,then

An electric dipole is placed on the $x$-axis as shown in the figure. Consider a spherical closed surface around it. Then,

Obtain the equation for the electric field produced by an electric dipole at a point on its equatorial plane.

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

An electric dipole is placed at an angle of $30^{\circ}$ in a non-uniform electric field. The electric dipole will experience:

The torque acting on a dipole of moment $\overrightarrow{P}$ in an electric field $\overrightarrow{E}$ is: