Question

A bar magnet of magnetic moment $M$ is bent in the form of an arc which makes angle ${60}^0$. The $\%$ change in the magnetic moment is

• A. $9\%$ increase
• B. $9\%$ decrease
• C. $4.5\%$ decrease
• D. $4.5\%$ increase

Answer 1

The correct option is C $4.5\%$ decrease

Let the pole strength of the magnet be $m$
Initially, the distance is $2l$
The magnetic moment $M=m.2l$
After bending into an arc of angle $\theta$ as shown in the figure, $l_{new}$ becomes $r\sin \frac{\theta }{2}$ where $r\theta =2l$
Given $\theta =\frac{\pi }{3}$.
$r=\frac{6l}{\pi }$
$l_{new}=r\sin \frac{\pi }{6}=\frac{r}{2}$
So the new distance between the poles is $2l_{new}=r=\frac{6l}{\pi }$
New magnetic moment $M_{new}=m.\frac{6l}{\pi }=\frac{3M}{\pi }$
Therefore, the percentage change in magnetic field is $\frac{M_{new}-M}{M}\times 100=\frac{3-\pi }{\pi }\times 100\approx -4.5$
Therefore this results in a $4.5\%$ decrease in the magnetic moment.