If the electric field at a distance $x$ on the axis of an electric dipole is equal to the electric field at a distance $y$ on its equatorial line,what is the ratio $x : y$?

$A$ system of three charges is placed as shown in the figure. If $D >> d$,the potential energy of the system is best given by:

An electric dipole of length $2 \ cm$ is placed with its axis making an angle of $60^{\circ}$ to a uniform electric field of $10^{5} \ N/C$. If it experiences a torque of $8 \sqrt{3} \ Nm$,calculate the magnitude of the charge on the dipole. (Given: $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$)

An electric dipole will have minimum potential energy when it subtends an angle with the direction of the electric field.

An electric dipole having each charge of magnitude $2 \mu C$ is placed in an electric field of intensity $8 \times 10^{4} \ N/C$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \ N \cdot m$,the length of the dipole is: (in $mm$)

The electric field at point $A$ due to an electric dipole with dipole moment $p$ is perpendicular to the dipole moment vector $p$. The angle $\theta$ is: