On some expressions for the radial and axial components of the magnetic force in the interior of solenoids of circular cross-section

Abstract

In the present paper, certain expressions are arrived at, in terms of zonal spherical harmonics and their first derivatives, by which the values of the two components of the magnetic force may be calculated for any point in the interior of a coil, and hence the total force may be found both in magnitude and direction. The resulting series suffer from the well-known defect in the spherical harmonic method, in that they are not very rapidly converging for points near the boundary of the space for which they apply. A table of the values of the first derivatives of the first seven zonal harmonics is added.