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

For a short dipole placed at origin $O$,the dipole moment $P$ is along the $x$-axis,as shown in the figure. If the electric potential and electric field at point $A$ (at distance $r$ on the $x$-axis) are $V_0$ and $E_0$,respectively,then the correct combination of the electric potential and electric field,respectively,at point $B$ (at distance $2r$ on the $y$-axis) is given by

An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole through $\frac{\pi}{3}$ radians is:

An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $60^{\circ}$ with a uniform electric field. It experiences a torque of $4 \sqrt{3} \ Nm$. Calculate the magnitude of the electric field. (The dipole has charges $\pm 8 \ nC$)

An electric dipole with dipole moment $4 \times 10^{-9} \text{ Cm}$ is aligned at $60^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \text{ NC}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

The net electric field at the given point $O$ due to all the four identical short electric dipoles of dipole moment $p$ each,as shown in the figure,is $\left( k = \frac{1}{4\pi \varepsilon_0} \right)$.