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 =\int\limits_{\theta_{1}}^{\theta_{2}} M B \sin d \theta $
$=M B[-\cos \theta]_{\theta_{1}}^{\theta_{2}} $
$=M B\left(\cos \theta_{1}-\cos \theta_{2}\right)$
where $B=$ magnetic field induction
$M =$ magnetic moment
$=M B\left(+\cos 0^{\circ}-\cos 180^{\circ}\right) $
$=M B[1+1]=2 \,M B$