XIX. The inductance of two parallel wires
James W. Nicholson · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · 1909
W HETS direct and return currents flow in two wires of great length, and the alternation is not rapid, the effective self-induction L per unit length of the system may be calculated readily by the method of geometric mean dis= tancest or by simple intcgration:~.If the wires have radii (a, b) and permeabilities (/~, tt.z), and if c be the distance between their axes, c ~ 1 But this formula ceases ~o be of any practical utility in many cases when the frequency of alternation is several thousands per second.Such frequencies are of constant use in practical work.For example, in the measurement of small inductances by Mr. Albert Campbell's method w it is necessary to employ long leads in order to keep them at some considerable distance from bridge and other circuits.The self-induction of these leads must be small, and a calculation of its value is very desirable.It was therefore suggested to me that I should attack this problem.The general case presents aDparently insuperable mathematical difficulty, but the solutions given below appear to include all cases of practical importance.A short statement of these results was given by the author in ' Nature,' Jan. 30th, 1~08, but the limitations were not emphasized.Let the axis of z be chosen parallel to those of the two wires.Any point in a section defined by a constant value of z may be conveniently specified by means of polar coordinates in two ways.Let these coordinates be (r, 8) and (p, q~), where (r, p) are the distances of the point frolu the two axes respectively, and (0, 6) its orientations measured from a line perpendicular to both axes.In the figure A and B are the projections of the axes of the two wires, and AB = c.A and B will be referred to as the