Question

A bar magnet of length ${}^{\prime }{l}^{\prime }$ 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. $\frac{3}{\pi }M$
• B. $\frac{2}{\pi }M$
• C. $\frac{M}{2}$
• D. $M$

Answer 1

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

Given that,

Length = l

Magnetic dipole moment = M

Now, the magnetic moment is

$M=ml$

According to figure

Now, the length is

$l=\frac{\pi }{3}\times r$

$r=\frac{3l}{\pi }$

Now, the new magnetic moment is

$M^{\prime }=m\times \frac{3l}{\pi }$

$M^{\prime }=\frac{3M}{\pi }$

Hence, the new magnetic dipole moment is $\frac{3M}{\pi }$