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 $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta= 90^{\circ}$, the torque and the potential energy of the dipole will respectively be

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

Answer 1

Answer: (A)

Potential energy of the dipole
$U =-\int T dB =-\int\limits_{\pi / 2}^{\theta} PE \sin \theta d \theta$
$= PE (\cos \theta-0)=- PE \cos \theta$
and potential energy $= PE \sin \theta$.