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. $2MB$
• C. $\frac{MB}{\sqrt{2}}$
• D. Zero
• E. $\sqrt{MB}$

Answer 1

The correct option is B $2MB$

If the magnet be rotated from an initial orientation ${\theta }_1=0^o$ to final orientation ${\theta }_o={180}^o$,
The total work done
$W={\int }_{{\theta }_1}^{{\theta }_0}MBsind\theta$
$W=MB[-cos\theta {]}_{{\theta }_1}^{{\theta }_0}$
where $B$ is magnetic field induction and $M$ is magnetic moment.
$W=MB(-cos{180}^o+cos{0}^o)$
$W=MB(1+1)=2MB$