Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/337

701.]

In the case of the coil, let the outer and inner radii be $$A + \frac{1}{2}\xi$$, and $$A-\frac{1}{2}\xi$$ respectively, and let the distance of the planes of the windings from the origin lie between $$B + \frac{1}{2}\eta$$ and $$B -\frac{1}{2}\eta$$, then the breadth of the coil is $$\eta$$, and its depth $$\xi$$, these quantities being small compared with $$A$$ or $$C$$.

In order to calculate the magnetic effect of such a coil we may write the successive terms of the series as follows:—

&c., &c.;

The quantities $$G_0$$, $$G_1$$, $$G_2$$, &c. belong to the large coil. The value of $$\omega$$ at points for which $$r$$ is less than $$C$$ is

The quantities $$g_1$$, $$g_2$$, &c. belong to the small coil. The value of $$\omega^\prime$$ at points for which $$r$$ is greater than $$c$$ is

The potential of the one coil with respect to the other when the total current through the section of each coil is unity is

701.] When the distance of the circumferences of the two circles