An electric dipole of moment p is placed in an electric field of...

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 An electric dipole of moment p is placed in an electric field of intensity E . The dipole acquires a position such that

An electric dipole of moment p is placed in an electric field of intensity E . The dipole acquires a position such that

Options

A $p E \sin \theta,-p E \cos \theta$
B $p E \sin \theta,-2 p E \cos \theta$
C $p E \sin \theta, 2 p E \cos \theta$
D $p E \cos \theta,-p E \sin \theta$

Correct answer

A. $p E \sin \theta,-p E \cos \theta$

Step-by-step solution

Here, Torque

\tau=p E \sin \theta

Potential energy of the dipole

\begin{aligned} U & =-\int \tau d \theta \\ & =-\int_{\pi / 2}^0 p E \sin \theta d \theta=p E[\cos \theta-0] \\ & =-p E \cos \theta \end{aligned}

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