Question

A bar magnet of length $L$ and magnetic moment $M$ is bent into the form of a semicircle. Now, its magnetic moment will be -

• A. $M$
• B. $\frac{2M}{\pi }$
• C. $\frac{M}{\pi }$
• D. $M\pi$

Answer 1

The correct option is B $\frac{2M}{\pi }$


Magnetic moment of bar magnet, $M=mL$

Now, when the bar magnet is bent into the form of a semicircle,


So, $L=\pi r\Rightarrow r=\frac{L}{\pi }$

$\therefore$ New magnetic moment will be,

$M^{\prime }=m\times \left(2r\right)$
$=m\times 2\times \frac{L}{\pi }=\frac{2mL}{\pi }=\frac{2M}{\pi }$

Hence, option $\left(B\right)$ is the correct answer.