Two single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. The mutual inductance of the pair is (approximately)

A current i in the large loop of radius .R produces a magnetic field of magnitude B=μ0i2R at its center. Since the radius 2R of the small loop r <.< R, we may treat the flux through the small loop as being approximately ΦB=BAcos⁡0∘=μ0i2RA=μ0πr2i2R. The mutual inductance of the loops is thenM=ΦBi=μ0πr22R