A point charge $q$ of mass $m$ is suspended vertically by a string of length $\ell .$ A point dipole of dipole moment $\overrightarrow{p}$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N\times \left(mgh\right),$ where $g$ is the acceleration due to gravity, then the value of $N$ is (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta }$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces) 

In the figure the net torque acting on the dipole is

An electric dipole having point charges $+q$ and $-q$, separated by a fixed distance $d$ is kept under the influence of a uniform electric field $E$, such that the axis of the dipole is making an angle $\theta =45°$ with the direction of $E$, as shown in the figure. If the electric dipole is allowed to rotate in the $xy$-plane with its center being stationary, what is the magnitude of the net torque acting on the electric dipole?

A dipole is placed in a uniform electric field with its axis parallel to the field. It experiences:

There is an electric dipole in X-Y plane .Its dipole moment is $4\times {10}^{-9}\mathrm{Cm}$ On the same plane there is also a uniform

electric field of magnitude $5\times {10}^4{\mathrm{NC}}^{-1}$. If the axis of dipole makes an angle $30°$ with the electric field . Calculate the magnitude of torque acting on the dipole and also mention the direction of the torque

An electric dipole with dipole moment $4\times {10}^{-9} \mathrm{C} \mathrm{m}$ is inclined at $30°$ with the direction of a uniform electric field of magnitude ${\mathrm{5\times 10}}^4 \mathrm{N} {\mathrm{C}}^{-1}$. Calculate the magnitude of torque acting on the dipole.