The mutual inductance of two coaxial circles of radius and with centers at a distance apart is given in cgs units by
where is the speed of light, and in (19.29.11),
The method of §19.29(ii) uses (19.29.18), (19.29.16), and (19.29.15) to produce
is the square of the maximum (upper signs) or minimum (lower signs) distance between the circles. Application of (19.29.4) and (19.29.7) with , , , and yields
or, by (19.21.3),
A simpler form of the result is
References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).