Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/317

681.] ring is therefore the same, and equal to $$2 n \gamma a$$, where $$a$$ is the linear quantity $$\int_0^{s^\prime} \frac{z^\prime}{ds^\prime} ds^\prime$$. If the closed curve does not embrace the ring, the magnetic induction through it is zero.

Let a second wire be coiled in any manner round the ring, not necessarily in contact with it, so as to embrace it $$n^\prime$$ times. The induction through this wire is $$2n n^\prime \gamma a$$, and therefore $$M$$, the coefficient of induction of the one coil on the other, is $$M = 2 n n^\prime a$$.

Since this is quite independent of the particular form or position of the second wire, the wires, if traversed by electric currents, will experience no mechanical force acting between them. By making the second wire coincide with the first, we obtain for the coefficient of self-induction of the ring-coil