Question

Potential energy of a bar magnet, of magnetic moment M is placed in a magnetic filed of induction B such that it makes an angle $\theta$ with the direction of B is?

• A. $MBsin\theta$
• B. $-MBcos\theta$
• C. $MB(1-cos\theta )$
• D. $MB(1+cos\theta )$

Answer 1

The correct option is B $-MBcos\theta$

$dw=-\tau .d\theta =-MB\sin \theta .d\theta$ where $\theta$ is angle between $\overrightarrow{M}$ and $\overrightarrow{B}$.

Since work done $=$ potential energy lost

$=>du=-dw=MB\sin \theta .d\theta$

$=>u=\int MB\sin \theta .d\theta =-MB\cos \theta$