question_answer

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 \[\theta ={{90}^{0}},\] the torque and the potential energy of the dipole will respectively be [AIPMT (S) 2012]

A) \[pE\sin \theta ,\,-pE\cos \theta \]

B) \[pE\sin \theta ,-2\,pE\cos \theta \]

C) \[pE\sin \theta ,-2pE\cos \theta \]

D) \[pE\cos \theta ,-pE\sin \theta \]

Correct Answer: A

Solution :

[a] Here,

Torque  \[\tau =pE\sin \theta \]

Potential energy of the dipole \[U=-\int_{{}}^{{}}{\tau \,d\theta }\]

\[=-\int_{\pi /2}^{0}{pE\sin \theta d\theta =pE[\cos \theta -0]}\]

\[=-pE\cos \theta \]