Computation of the External Magnetic Field, Near-Field or Far-Field, From a Circular Cylindrical Magnetic Source Using Toroidal Functions

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Abstract
A method is developed for computing the magnetic field from a circular or noncircular cylindrical magnetic source. A Fourier series expansion is introduced which yields an alternative to the more familiar spherical harmonic solution, Elliptic integral solution, or Bessel function solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion which is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. Also, one can compute an equivalent multipole distribution of the real magnetic source valid for points close to the circular cylindrical boundary where the more familiar spherical multipole distribution is not valid. This method can also be used to accurately compute the far field where a finite-element formulation is known to be inaccurate