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  • Derive an expression for the work done in rotating a dipole from the angle  to <img alt="\theta _{1}" src="https://entrancecorner.codecogs.com/gi

Derive an expression for the work done in rotating a dipole from the angle \theta _{0} to \theta _{1} in a uniform electric field E.

 

 

 

 
 
 
 
 

Answers (1)

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 ]

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