Question

Drive an expression for the energy stored In a dipole in a uniform electric field

Answer 1

Suppose an electric dipole of dipole moment p is placed along a direction, making an angle θwith the direction of an external uniform electric field E. Then, the torque acting on the dipole is given by

t=pE sin Ø

If the dipole is rotated through an infinitesimally small angle dθ, against the torque acting on it, then the small work done is given by

dW=pdØ=pE sin dØ

If the dipole is oriented, making an angle θ1 to θ2 with the electric filed, then the total work done is given by

Fig1

W = pE (cos θ1 − cos θ2)

This work done is stored in the dipole in the form of its potential energy.

∴U = pE (cos 90° − cos θ)

U = − pE cos θ

U = −
p.E