Question

A magnetic dipole is placed at right angles to the direction of magnetic induction $B$ . If it is rotated through an angle of $180^\circ $ , then the work done is

• A. $MB$
• B. $2 \, MB$
• C. $-2 \, MB$
• D. zero

Answer 1

Answer: (D)

Work done in rotating a dipole
$W=MB \, \left(cos \left(\theta \right)_{1} - cos ⁡ \left(\theta \right)_{2}\right)$
To rotate it from $90^\circ $ to $0^\circ $
$\theta _{1}=90^\circ $ $\theta _{2}=0^\circ $
$W=MB\left(cos 9 0 ^\circ - cos ⁡ 0 ^\circ \right)$
$W_{1}=MB\left(0 - 1\right)=-MB$
$W_{1}=-MB$ .........(i)
To rotate it from $0^\circ $ to $-90^\circ $ in same manner.
$\theta _{1}=0^\circ $ $\theta _{2}=-90^\circ $
$W_{2}=MB\left(cos 0 ^\circ - cos ⁡ \left(- 90 ^\circ \right)$
$W_{2}=MB$ ........(ii)
Total work done
$W=W_{1}+W_{2}$
$W=-MB+MB$
$W=0$