Answer to Question #201478 in Electricity and Magnetism for Yashi

Question

Under what condition will the magnitude of the torque acting on an electric dipole in a uniform electric field be equal to its potential energy

Answer 1

Torque=$\tau$

Electric dipole moment =p

Uniform electric field =E

Dipole moment p=q.d

Torque$\tau=p\times E$

$\tau =pEsin\theta$

$\theta=90°$

sin90°=1

$\tau=pE$

Energy

$U=-p.E$

$U=-pEcos\theta$

$\theta=180°$

Cos180°=-1

U=pE

Then

$\theta=90°$ torque is equal to$\theta =180 °$ electric potential energy