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 $\theta = 90^o$ , the torque and the potential energy of the dipole will respectively be
AIPMT 2012, Easy
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Here, torque $\tau=p E \sin \theta,$ here $\theta$ is the anlge between electric field and dipole moment Potential energy of the dipole
$U = - \int {\tau \,} d\theta $
$=-\int_{\pi / 2}^{0} p E \,\sin \theta d \theta=p E[\cos \theta-0]$
$=-p E\, \cos \theta$
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