ELECTRIC CHANGES AND FIELDS

Ans. A dipole of dipole moment $\vec{P}$ in a uniform electric field$\vec{E}$. A force $qE$ on $+q$ and a force $ -qE$ is $-q$ charge.

The forces actat different points, resulting in a torque on the dipole.

Magnitude of torque = magnitude of each force X perpendicular distance between two forces$$\begin{aligned}\\&\tau=q\mathrm{E}\times2\mathrm{a\sin\theta}\\&\tau=2\mathrm{qa}\: \mathrm{E}\mathrm{\sin\theta}\\&\tau=\mathrm{P}\: \mathrm{E}\:\mathrm{\sin\theta}\\&\vec{\tau}=\vec{\mathrm{P}}\times\vec{\mathrm{E}}\quad(\because\vec{\mathrm{P}}=2\mathrm{qa})\end{aligned}$$