Question

The torque acting on a dipole of momentum $\overrightarrow{p}$ in an electric field $\overrightarrow{E}$:

• A. $\overrightarrow{p}\times \overrightarrow{E}$
• B. $\overrightarrow{p}.\overrightarrow{E}$
• C. zero
• D. $\overrightarrow{E}\times \overrightarrow{p}$

Answer 1

The correct option is A $\overrightarrow{p}\times \overrightarrow{E}$

Force acting on dipole due to electric field is given by,

$F=qE$

Torque on a dipole in an electric field is given by,

$T=F\times d=Fdsin\theta =qEdsin\theta$. .....(i)

But dipole moment is given by,

$P=qd$ ....(ii)

By (i) and (ii) we get,

$\therefore$ $T=pEsin\theta =\overrightarrow{p}\times \overrightarrow{E}$