Question

If a magnetic dipole of moment $M$ situated in the direction of a magnetic field $B$ is rotated by $180^{\circ }$, then the amount of work done is

• A. MB
• B. 2 MB
• C. $\frac{MB}{\sqrt{2}}$
• D. 0
• E. $\sqrt{MB}$

Answer 1

Answer: (B)

If the magnet be rotated from an initial orientation ${\theta }_1=0^{\circ }$ to final orientation ${\theta }_2=180^{\circ }$ the total work done
$W=\underset{{\theta }_1}{\overset{{\theta }_2}{\int }}MB\sin d\theta$
$=MB[-\cos \theta {]}_{{\theta }_1}^{{\theta }_2}$
$=MB\left(\cos {\theta }_1-\cos {\theta }_2\right)$
where $B=$ magnetic field induction
$M=$ magnetic moment
$=MB\left(+\cos 0^{\circ }-\cos 180^{\circ }\right)$
$=MB[1+1]=2MB$