A magnetised wire of magnetic moment M and length $l$ is bent in the form of a semi-circle of radius r. The new magnetic moment is

Magnetic moment M = ml
When the magnet is bent in the form of a semicircle of radius r, the distance between poles becomes 2 r. The new magnetic moment is
$\begin{array}{l}{\mathrm{M}}^{\mathrm{\prime }}=\mathrm{m}\left(2\mathrm{r}\right)\\ \therefore \frac{{\mathrm{M}}^{\mathrm{\prime }}}{\mathrm{M}}=\frac{\mathrm{m}\left(2\mathrm{r}\right)}{\mathrm{ml}}=\frac{2\mathrm{r}}{\mathrm{l}}\\ \mathrm{But} \mathrm{l}=\mathrm{\pi r}\\ \therefore \frac{{\mathrm{M}}^{\mathrm{\prime }}}{\mathrm{M}}=\frac{2}{\mathrm{\pi }}.\end{array}$