A conducting loop of radius r is placed concentric with another loop of much larger radius R, so that both loops are coplanar. The mutual inductance of the system of two loops is proportional to _. Take R r.

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(2) (r²)/R. Idea: pass a current I through the large loop, find the flux it sends through the small loop, then M = Φ/I. Field at the centre of the large loop: B = (μ₀ I)/(2R). Since R r, this field is nearly uniform over the small loop, so Φ = B·π r² = (μ₀ Iπ r²)/(2R). M = Φ/I = (μ₀π r²)/(2R). So M ∝ (r²)/R.

A conducting loop of radius r is placed concentric with another loop of much larger radius R, so that both loops are coplanar. The mutual inductance of the system of two loops is proportional to _____. Take R r.

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Why the other options are wrong