Question

derive and expression for energy stored in a dipole in a uniform electric field?

Answer 1

This is the field due to dipole on axial line

Answer 2

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