An electric dipole with dipole moment $5 \times 10^{-7} \text{ C m}$ is placed in an electric field of $2 \times 10^4 \text{ N C}^{-1}$ at an angle of $60^{\circ}$ with the direction of the electric field. The torque acting on the dipole is:

Two short electric dipoles are placed as shown. The energy of electric interaction between these dipoles will be

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

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: $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$)

The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2r$ on the equatorial line from the mid-point of the dipole. Then,the value of $x$ is

Explain the positions (orientations) of a dipole in stable equilibrium,unstable equilibrium,and when the potential energy is zero.