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

Let m be strength of each pole of bar magnet of length l.

Then $M=m\times l---\left(i\right)$

When the bar magnet is bent in the form of an arc as shown in figure

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

New magnetic dipole moment

$$\begin{gathered} M^{\text{'}}=m\times 2r\sin {30}^0 \\ =m\times 2\times \frac{3l}{\pi }\times \frac{1}{2}=\frac{3ml}{\pi }=\frac{3M}{\pi } \left(u\sin g\left(i\right)\right) \end{gathered}$$