Question

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

Answer 1

Answer:

Consider a dipole placed in a uniform electric field. The torque acting on the dipole about the centre.

\tau =qE\times d

=qE\times 2a\; \sin \theta

=PE\sin \theta

work done in rotating a dipole from \theta _{0} to \theta _{1}

dw=\tau d\theta

w=\int_{\theta _{0}}^{\theta _{1}}\tau d\theta =\int_{\theta _{0}}^{\theta _{1}}PE\sin \theta d\theta =PE\left [ \cos \theta _{0}-\cos \theta _{1} \right ]