Question

derive an expression for the work done in rotating an electric dipole in a uniform electric field

Answer 1

The work done in rotating a dipole in uniform magnetic field is pE(Cosθ₀-Cosθ₁)

• Let a dipole of dipole moment p is placed in a electric field of magnitude E making an angle θ with the feild direction

• Torque of the dipole in magnetic field is

        $T=q\times 2a \times E \times Sin\theta$

        $T = pESin\theta$

• Work done in rotating the dipole from θ₀ to θ₁ is

        $W=\int\limits{T} \, d\theta$

        $W=\int\limit{pESin\theta} \, d\theta$

        $W=pE(Cos\theta_{0}-Cos\theta_{1} )$

• The work done is   $W=pE(Cos\theta_{0}-Cos\theta_{1} )$