A wire of magnetic moment $M$ is moulded according to figure, then magnetic moment becomes
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$\mathrm{M}=\mathrm{m} \ell$
$\mathrm{M}^{\prime}=\mathrm{m} \ell^{\prime}$ [Here $\ell^{\prime}=\sqrt{2} \mathrm{R}$ and $\ell = \frac{{\pi {\text{R}}}}{2}]$
$\Rightarrow \frac{\mathrm{M}}{\mathrm{M}^{\prime}}=\frac{\ell}{\ell^{\prime}}=\frac{\pi \mathrm{R} / 2}{\sqrt{2} \mathrm{R}}$
$\Rightarrow \mathrm{M}^{\prime}=\frac{2 \sqrt{2} \mathrm{M}}{\pi}$
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