A magnetic dipole is placed at right angles to the direction of...

Work done in rotating a dipole

$W = MB$\left(cos {\theta}_{1} - cos {\theta}_{2}\right)

To rotate it from $90 °$ to $0 °$

{\theta}_{1} = 90 °${\theta}_{2} = 0 °$

$W = MB$\left(\cos 90 ° - \cos 0 °\right)

${W}_{1} =$MB\left(0 - 1\right) = - MB

${W}_{1} = - MB$ .........(i)

To rotate it from $0 °$ to $- 90 °$ in same manner.

{\theta}_{1} = 0 °${\theta}_{2} = - 90 °$

${W}_{2} = MB$\left(\cos 0 ° - \cos \left(- 90 °\right)\right)

${W}_{2} = MB$ ........(ii)

Total workdone

$W = {W}_{1} + {W}_{2}$

$W = - MB + MB$

$W = 0$