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. $pE\left(\cos {\theta }_1-\cos {\theta }_0\right)$
• B. $-2pE\left(\cos {\theta }_1-\cos {\theta }_0\right)$
• C. $pE\left(\cos {\theta }_0-\cos {\theta }_1\right)$
• D. $-2pE\left(\cos {\theta }_0-\cos {\theta }_1\right)$

Answer 1

Answer: (C)

The amount of work done by the external torque will be given by
$W=\underset{{\theta }_0}{\overset{{\theta }_1}{\int }}{\tau }_{\text{ext }}(\theta )d\theta =\underset{{\theta }_0}{\overset{{\theta }_1}{\int }}pE\sin \theta d\theta =pE\left(\cos {\theta }_0-\cos {\theta }_1\right)$