The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is

Question

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x . When both the current and radius is doubled the ratio will be\

Professor PC Thomas Classes · Answer

magnetic field at the center of a circular loop $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \mathrm{R}}$\ Magnetic moment $\mathrm{M}=\mathrm{IA}=\mathrm{I} \pi \mathrm{R}^{2}$\ When both current and radius doubled $\frac{B}{M} \alpha \frac{1}{(2 R)^{3}}=\frac{1}{8 R^{3}}$\ $=\frac{\mathrm{x}}{8}$\