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A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is:
- (μ0)/(4π) 8√2 a²/b
- (μ0)/(4π) 8√2 b²/a
- (μ0)/(4π) 8√2 b²/a
- (μ0)/(4π) 8√2/b
Correct answer: (μ0)/(4π) 8√2 a²/b
Solution
Field at the centre of the outer square loop of side b is B = (mu0 I/4pi)*(8*sqrt(2)/b). Mutual inductance M = B*a^2/I = (mu0/4pi)*8*sqrt(2)*a^2/b, which is option 1.
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