The ratio of the magnetic field at the centre of a current carrying circular coil to its magnetic moment is $'\alpha '.$ If the current and radius both are doubled then new ratio will become
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$\mathrm{B}=\frac{\mu_{0} \mathrm{NI}}{2 \mathrm{R}}, \mathrm{M}=\mathrm{NI}\left(\mathrm{pR}^{2}\right)$
$\frac{\mathrm{B}}{\mathrm{M}}=\left(\frac{\mu_{0} \mathrm{N} \mathrm{I}}{2 \mathrm{R}}\right)\left(\frac{1}{\mathrm{N} \mathrm{l} \pi \mathrm{R}^{2}}\right)=\frac{\mu_{0}}{2 \pi \mathrm{R}^{3}}$
$\frac{B}{M} \propto \frac{1}{R^{3}} \quad$ (not depend on $I$)
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