Question

If a bar magnet in magnetic moment $m$ is deflected from an angle $\theta$ in a uniform magnetic field of induction $B$, the work done in reversing the direction is

• A. $MB\sin \theta$
• B. $MB$
• C. $MB(1-\cos \theta )$
• D. $MB\cos \theta$

Answer 1

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

Now lets assume that the bar magnetic is initially placed parallel to the field the initial potential energy will be $U_i=-\overrightarrow{M}.\overrightarrow{B}=-MB\cos 0=-MB$
Now when it is deflected by an angle $\theta$ then $U_f=-\overrightarrow{M}.\overrightarrow{B}=-MB\cos \theta$
Now we know that the work done = $-\Delta U$
$\Delta U=U_i-U_f$
$\Delta U=-MB(1-\cos \theta )$

therefore, work done $=MB(1-\cos \theta )$.