Find the amount of work done in rotating an electric dipole placed in a uniform electric field.

Diagram for this derivation

We know, Ted Talk acting on a dipole in a uniform electric field is

ς=PEsinθ

                                                       Where,P= dipole moment of the dipole. It tries to rotate the dipole.

Let the small amount of work done in rotating the dipole through a small angle θ against the torque is,

dw=ςdθ=PEsinθdθ

Therefore, total work done in rotating the dipole from θ₁ to θ₂ is,             

      θ₁

         W=∫dw=∫PEsinθdθ

  θ₂

=-PE(WSθ₂-COSθ₁)