Question

A bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

• A. $\frac{2}{\pi }M$
• B. $\frac{M}{\pi }$
• C. $M$
• D. $\frac{3}{\pi }M$

Answer 1

The correct option is D $\frac{3}{\pi }M$

Let $m$ be strength of each pole of bar magnet of lenght $l$. Then
$M=m\times l$
When the bar magnet is bent in the form of an arc as shown in figure.
Then,
$l=\frac{\pi }{3}\times r\left(or\right)r=\frac{3l}{\pi }$
New magnetic dipole moment
$M\text{'}=m\times 2r\sin \left({30}^0\right)=m\times 2\times \frac{3l}{\pi }\times \frac{1}{2}=\frac{3M}{\pi }$