Question

An electric dipole of moment p is kept along an electric field E. The work done in rotating it from an equilibrium position by an angle $\theta$ is :

• A. PE(1 - cos $\theta$)
• B. PE(1 - sin $\theta$)
• C. PE cos $\theta$
• D. PE sin $\theta$

Answer 1

The correct option is A PE(1 - cos $\theta$)

Electric field will produce a torque on the dipole.
Torque , $\tau =pE\sin \theta$
The work done in rotating it from an equilibrium position by an angle $\theta$ is $W={\int }_0^{\theta }\tau d\theta =pE{\int }_0^{\theta }\sin \theta d\theta =-pE(\cos \theta -\cos 0)=pE(1-\cos \theta )$