On the calculation of the coefficient of mutual induction a circle and a coaxial helix, and of the electromagnet force between a helical current and a uniform coaxial circular cylindrical current sheet

Abstract

1. In measuring electrical resistance by the method of Lorenz have to determine the coefficient of mutual induction of a helix wire and the circumference of a rotating circular disc placed coaxially with it, the mean planes of the helix and the disc being coincident. In a paper presented to the Physical Society November, 1888, I gave a method of calculating this coefficient; by subsequent consideration of the problem in connection with the Lorenz apparatus recently made for the McGill University, Montrea has led me both to a simplification of the method previously described, and also to a more general solution. 2. If M is the coefficient of mutual induction of any two curve we have M = ∫∫cos ϵ / r dsds' , where r = the distance between two elements ds, ds' ; and ϵ = the angle between these elements.