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  4. Magnetic moment of bar magnet is M. The work done to turn the magnet by 90° of magnet in direction of magnetic field B will be

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Q. Magnetic moment of bar magnet is $M$. The work done to turn the magnet by $90^{\circ}$ of magnet in direction of magnetic field $B$ will be

BITSATBITSAT 2012

Solution:

Potential energy of a magnetic moment at an angle $\theta$ with the magnetic field $=- MB \cos \theta$
Thus work done in rotating from angle $\theta_{1}$ to $\theta_{2}$
$= MB \left(\cos \theta_{1}-\cos \theta_{2}\right)$
$= MB \left(\cos 0^{\circ}-\cos 90^{\circ}\right) $
$= MB (1-0) $
$= MB$