Question

An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle 0 with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta ={90}^0$, the torque and the potential energy of the dipole will respectively be:

• A. $pEsin\theta ,2pEcos\theta$
• B. $pEcos\theta ,-pEsin\theta$
• C. $pEsin\theta ,-pEcos\theta$
• D. $pEsin\theta ,-2pEcos\theta$

Answer 1

The correct option is C $pEsin\theta ,-pEcos\theta$

Potential energy of the dipole

$U=-\int TdB$

$=-{\int }_{\pi /2}^{\theta }PE\sin \theta d\theta$

$=PE(\cos \theta -0)=-PE\cos \theta$

and potential energy $=PE\sin \theta$.