A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L(L >> l)$. The loops are coplaner and their centres coincide. The mutual inductance of the system is propotional to
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Magnetic field induction at $\mathrm{O}$ due to current carrying straight conductor $\mathrm{BC}$
$\mathrm{B}_{1}=\frac{\mu_{0} \mathrm{i}}{4 \pi\left(\frac{\mathrm{L}}{2}\right)}(\sin \alpha+\sin \beta)$
or $\quad \mathrm{B}_{1}=\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{L}}\left(\sin 45^{\circ}+\sin 45^{\circ}\right)=\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{L}}$
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