**Potential Energy of an Electric Dipole in a Uniform Electric Field **

Work done in bringing an electric dipole from infinity to some point inside the field is equal to the potential energy of an electric dipole in an electric field.

Letus bring an electric dipole from infinity into a uniform electric filed E insuch a way that the dipole moment P is always along the direction of the field.

From the above figure, as the dipole is brought from infinity into the filed, thecharge -q covers 2l distances more than the net work done by the system inbringing the dipole from infinity into the field.

W = Force on Charge (-q) x Extra distance moved

W = – qE x 2l = – pE

W = – qE x 2l = – pE

Where,

p = Dipole moment of the electric dipole.

According to the law of conservation of energy, this work will be stored in the form of potential energy of the electric dipole. It is represented by U. Hence,

U = – pE

In this position, the electric dipole will be in stable equilibrium inside the field. If we now rotate the dipole in the field through an angle θ, then the Work done on the dipole is:

W = pE (1 – cosθ)

This will result in an increase in the potential energy of the dipole. Hence, the potential energy of an electric dipole in the position θ is given by:

U₀ = U + W = – pE + pE (1 – cosθ) = – pE cosθ \(=-\overrightarrow{p}.\overrightarrow{E}\).

\({{U}_{o}}=-pE\cos \theta=-\overrightarrow{p}.\overrightarrow{E}\).