question_answer

A bar magnet of length \['\ell '\] and magnetic dipole moment ?M? is bent in the form of an are 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

Correct Answer: A

Solution :

[a] Magnetic dipole moment \[M=m\times \ell \]           \[M'=m\times r\] From figure                    \[\ell =\frac{\pi r}{3}\]  or   \[r=\frac{3\ell }{\pi }\] so,   \[M'=m\times r\] \[=\frac{m\times 3\ell }{\pi }=\frac{3}{\pi }M\]