# §19.34 Mutual Inductance of Coaxial Circles

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),

19.34.2

The method of §19.29(ii) uses (19.29.18), (19.29.16), and (19.29.15) to produce

19.34.3

where and

19.34.4

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

19.34.7

References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).