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A small square loop of side l is placed at the centre of and coplanar with a large square loop of side L, where L >> l, with their centres coinciding. The mutual inductance of the pair is proportional to which quantity?

1. l² / L
2. l / L
3. L / l
4. L² / l

Correct answer: l² / L

Solution

Current I in the large loop produces a central field B proportional to I/L. The flux through the small loop is B*l² proportional to I*l²/L. Thus M = flux/I proportional to l²/L.

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