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A small coil of radius r is placed at the centre of, and coplanar with, a large coil of radius R (with R >> r). Find the coefficient of mutual inductance between the two coils.

1. mu0*pi*r / (2*R)
2. mu0*pi*r² / (2*R)
3. mu0*pi*r² / (2*R²)
4. mu0*pi*r / (2*R²)

Correct answer: mu0*pi*r² / (2*R)

Solution

Pass current I through the large coil; its field at the centre is B = mu0*I/(2R), essentially uniform over the small coil (since R >> r). The flux through the small coil is Phi = B*(pi*r²) = mu0*I*pi*r²/(2R). The mutual inductance is M = Phi/I = mu0*pi*r²/(2R).

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