Question
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.
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Answer
Work done against the restoring torque
$\text{dW} = \tau\text{ d}\theta$
$\text{dW} = \text{pE}\sin\theta\text{ d}\theta$
$\therefore , \text{W} = \text{pE}\int^{\theta1}_{\theta0}\sin\theta\text{d}\theta$
$ = \text{pE}\cos\theta_{0} -\cos\theta_{1}.$
$\text{dW} = \tau\text{ d}\theta$
$\text{dW} = \text{pE}\sin\theta\text{ d}\theta$
$\therefore , \text{W} = \text{pE}\int^{\theta1}_{\theta0}\sin\theta\text{d}\theta$
$ = \text{pE}\cos\theta_{0} -\cos\theta_{1}.$
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