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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 coplanar and their centre coincide. The mutual inductance of the system is proportional to

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\frac{L^{2}}{l}

\frac{l}{L}

\frac{l^{2}}{L}

\frac{L}{l}

answer is B.

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Detailed Solution

Magnetic field produced due to large loop

$B = \frac{μ_{0}}{4 π} \frac{8 \sqrt{2} i}{L}$

Flux linked with smaller loop

$φ = B (l^{2}) = \frac{μ_{0}}{4 π} \frac{8 \sqrt{2} i l^{2}}{L}$

$∴ φ = M i \Rightarrow M = \frac{φ}{i} = \frac{μ_{0}}{4 π} \cdot \frac{8 \sqrt{2} l^{2}}{L} \Rightarrow M \propto \frac{l^{2}}{L}$

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