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 is situated in an electric field as shown in the figure. The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to the paper at point $A$ in an anti-clockwise direction. If the angle of rotation is measured with respect to the direction of the electric field,then the torque for different values of the angle of rotation $\theta$ is correctly represented by which graph among $a, b, c, d$ given in the figure?

An electric dipole has a fixed dipole moment $\vec{P}$ which makes an angle $\theta$ with respect to the $x$-axis. When subjected to an electric field $\vec{E_1} = E\hat{i}$,it experiences a torque $\vec{T_1} = \tau\hat{k}$. When subjected to another electric field $\vec{E_2} = \sqrt{3}E\hat{j}$,it experiences a torque $\vec{T_2} = -\vec{T_1}$. The angle $\theta$ is .......$^o$.

The electric dipole is situated in an electric field as shown in figure $(i)$. The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to the paper at point $A$ in an anticlockwise direction. If the angle of rotation is measured with respect to the direction of the electric field,then the torque for different values of the angle of rotation $\theta$ will be as represented in Fig. $(ii)$.

An electric dipole with dipole moment $5 \times 10^{-6} \ Cm$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5 \ N/C$. The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is (in $J$)

An electric dipole is placed at an angle of $30^\circ$ with an electric field intensity of $2 \times 10^5 \, \text{NC}^{-1}$. It experiences a torque equal to $4 \, \text{Nm}$. The charge on the dipole,if the dipole length is $2 \, \text{cm}$,is: