Question

Suppose an external torque $\tau_{\text {ext }}$ is applied on dipole and rotates it in the plane of paper from angle $\theta_{0}$ to an angle $\theta_{1}$ at an infinitesimal angular speed and without angular acceleration. The amount of work done by the external torque will be given by

• A. $p E\left(\cos \theta_{1}-\cos \theta_{0}\right)$
• B. $-2 p E\left(\cos \theta_{1}-\cos \theta_{0}\right)$
• C. $p E\left(\cos \theta_{0}-\cos \theta_{1}\right)$
• D. $-2 p E\left(\cos \theta_{0}-\cos \theta_{1}\right)$

Answer 1

Answer: (C)

The amount of work done by the external torque will be given by
$W=\int\limits_{\theta_{0}}^{\theta_{1}} \tau_{\text {ext }}(\theta) d \theta=\int\limits_{\theta_{0}}^{\theta_{1}} p E \sin \theta d \theta=p E\left(\cos \theta_{0}-\cos \theta_{1}\right)$