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A small single-turn square loop of side 'a' lies inside a much larger single-turn square loop of side 'b' (with b >> a). The two loops are coplanar and share a common centre. When a current I flows through the larger loop of side 'b', what is the mutual inductance between the two loops?

1. (1) (mu0/4pi) * 8*sqrt(2) * a²/b
2. (2) (mu0/4pi) * 8*sqrt(2)/b * a
3. (3) (mu0/4pi) * 8*sqrt(2) * b²/a
4. (4) (mu0/4pi) * 8*sqrt(2)/b

Correct answer: (1) (mu0/4pi) * 8*sqrt(2) * a²/b

Solution

The large loop produces a nearly uniform field over the region of the small loop. The flux linking the small loop divided by I gives M. Each side of the square contributes a finite-wire field; summing all four sides gives the standard square-loop centre field, and the small area a² then yields M proportional to a²/b.

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