Question

Derive an expression for the total work done in rotating the electric dipole through an angle theta in a uniform electric field.

Answer 1

Analogous to the work

W=FΔs

done by a force F over a distance Δs , there is also a work done by a torque T for a rotational movement

W=TΔθ

where Δθ is the angle of rotation. The torque experienced by an electric dipole with dipole moment p⃗ in an electric field E⃗ is

T⃗ =p⃗ ×E⃗ =pEsinθ

were θ is the angle between the dipole moment and the electric field. Thus the work performed during a rotation of a dipole from an angle θ=α to an angle θ=β is given by

W=∫βαT(θ)dθ=∫βαpEdθsinθ