Question

An electric dipole when placed in a uniform electric field e will have minimum potential energy, when the angle made by dipole moment with field e is

Answer 1

Zero

Use formula

U = - pE costheta

use theta =o

Answer 2

answer : zero , dipole is parallel to uniform electric field.

explanation : suppose an electric dipole of dipole moment P is placed in uniform electric field in such a way that, dipole makes an angle $\theta$ with electric field.

then, torque, $\tau=P.Esin\theta$

now, when dipole is rotated infinitesimally small angle $d\theta$ due to external electric field. then workdone of dipole , $W=P.E\int\limits^{\theta_0}_{\theta_1}{sin\theta}\,d\theta$

$=P.E(cos\theta_0-cos\theta_1)$

now taking , $\theta=90^{\circ}$ and $\theta_1=\theta$

then, potential energy, U = $-P.Ecos\theta$

now you can easily say that at $\theta=0^{\circ}$ potential energy will be minimum.