Exact solutions for the magnetic fields of axisymmetric solenoids and current distributions

An analytical method originally developed for fluid mechanics has been applied to the analogous problem of calculating the magnetic field induced by axisymmetric current sheets, disks, and solenoids. The magnetic fields of a generalized axisymmetric current distribution are given either in closed form as elliptic integral expressions or as integrals of elementary functions over a finite range. The paper concentrates on the analysis of the fields generated by specified current distributions, though the method can also be applied to solve boundary value problems.