derive an expression for potential energy of an electric dipole in a uniform electric field .

Potential Energy of an Electric Dipole, When Placed in a Uniform Electric Field

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

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

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

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 = −