An electric dipole of length $0.5 \text{ }\mu\text{m}$ is placed with its axis making an angle of $30^{\circ}$ with a uniform electric field of $10^4 \text{ V/m}$. If it experiences a torque of $5 \times 10^{-9} \text{ Nm}$, the magnitude of the charge on the dipole is (given $\sin 30^{\circ} = 0.5$). (in $\text{ }\mu\text{C}$)

Two charges of $-4 \ \mu C$ and $+4 \ \mu C$ are placed at the points $A(1, 0, 4) \ m$ and $B(2, -1, 5) \ m$ located in an electric field $\vec{E} = 0.20 \ \hat{i} \ V/cm$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \ Nm$. Where $\alpha = $ . . . . . .

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:

The electric potential at a point on the axis of an electric dipole is proportional to $[r=$ distance between the centre of the electric dipole and the point].

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. $(ii)$.

What does an electric dipole experience when placed in a non-uniform electric field?