A magnetized wire of magnetic length ‘2l’, pole strength ‘m’ and magnetic moment ‘M’ is bent at angle is ‘ $\mathrm{\theta }$’ radian at the center of the circle, then

When the straight bar magnet is bent into an arc, the pole strength remains unchanged.

As the angle subtended by the arc at the center is '$\mathrm{\theta }$'.

The radius of the arc will be given by $\mathrm{r}=\frac{2\mathrm{l}}{\mathrm{\theta }}$.

So the effective distance between the poles is given by $\left[\frac{4\mathrm{lsin}\left({\displaystyle \frac{\mathrm{\theta }}{2}}\right)}{\mathrm{\theta }}\right]$.

The new magnetic moment is given by $\left[\frac{2\mathrm{Msin}\left({\displaystyle \frac{\mathrm{\theta }}{2}}\right)}{\mathrm{\theta }}\right]$