When an electric dipole of dipole moment p is at an angle θ with the electric field E, the torque on the dipole is
τ = pE sin θ
Work done in rotating the dipole through dθ,
dw = τ.dθ = pE sinθ.dθ
The total work done in rotating the dipole through an angle θ is W = ∫dw
W = pE ∫sinθ.dθ = –pE cos θ
This work done is the potential energy (U) of the dipole.
so, U = – pE cos θ
When the dipole is aligned parallel to the field, θ = 00
so, U = –pE
This shows that the dipole has a minimum potential energy when it is aligned with the field. A dipole in the electric field experiences a torque (τ = p * E) which tends to align the dipole in the field direction, dissipating its potential energy in the form of heat to the surroundings.