Question

A loop of magnetic moment $\overrightarrow{M}$ is placed in the orientation of unstable equilibrium position in uniform magnetic field $\overrightarrow{B}$.The external work done in rotating it through an angle $\theta$ is

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

Answer 1

The correct option is A $-MB(1-cos\theta )$

${\theta }_i={180}^o:{\theta }_f={180}^o-\theta$

$W=U_f-U_i$

$=-MBcos({180}^o-\theta )-(-MBcos{180}^o)$

$=MBcos\theta -MB$

$=-MB(1-cos\theta )$