If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$,then the torque acting on it is given by:

$A$ point electric dipole placed at the origin has a potential given by $V(r, \theta) = \frac{p \cos \theta}{4 \pi \varepsilon_0 r^2}$,where $\theta$ is the angle made by the position vector with the direction of the dipole. Then,

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

Electric field at the equator of a dipole is $E$. If both dipole moment and distance are doubled,then the electric field will be $:-$

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of an $(x, y)$ coordinate system. Then:

An electric dipole with dipole moment $2 \times 10^{-10} \text{ C m}$ is aligned at an angle $30^{\circ}$ with the direction of a uniform electric field of $10^4 \text{ N C}^{-1}$. The magnitude of the torque acting on the dipole is: