Question

An electrical dipole of dipole moment ${}^{\prime }{p}^{\prime }$ is placed in an electric field of intensity ${}^{\prime }{E}^{\prime }$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with electric field. Assuming that the potential energy of the dipole to be zero when $\theta ={90}^{\circ }$, the torque on dipole and the potential energy of the dipole will be respectively

• A. $pE\sin \theta ,2pE\cos \theta$
• B. $pE\cos \theta ,-pE\sin \theta$
• C. $pE\sin \theta ,-pE\cos \theta$
• D. $pE\sin \theta ,-2pE\cos \theta$

Answer 1

The correct option is C $pE\sin \theta ,-pE\cos \theta$


The formula for potential energy of dipole placed in uniform electric field,

$U=-\overrightarrow{p}.\overrightarrow{E}=-pE\cos \theta$

Torque experienced by dipole is,

$|\overrightarrow{\tau }|=|\overrightarrow{p}\times \overrightarrow{E}|=pE\sin \theta$

Option (3) is correct.

Why this question: Formula of potential energy and torque on dipole is used.