Consider a dipole with charges `q_1 = +q` and `q_2 = -q` placed in a uniform electric field E, as shown in Fig. As seen in a uniform electric field, the dipole experiences no net force; but experiences a torque `tau` given by

`tau = PxxE`

which will tend to rotate it (unless p is parallel or antiparallel to E). Suppose an external torque τ is applied in such a manner that it just neutralises this torque and rotates it in the plane of paper from angle `θ_0` to angle `θ_1` at an infinitesimal angular speed and without angular acceleration. The amount of work done by the external torque will be given by

`W = int_(theta_0)^(theta_1) tau_(ext) dθ = int_(theta_0)^(theta_1) pE sinθ dθ`

`= pE(costheta_0 - costheta_1)`

This work is stored as the potential energy of the system. We can then associate potential energy U(θ ) with an inclination θ of the dipole. Similar to other potential energies, there is a freedom in choosing the angle where the potential energy U is taken to be zero. A natural choice is to take `θ_0 = π / 2.`

`U(theta) = pE(cosπ/2 - costheta) = -pEcostheta = -p.E`