Affiliations: [a] Electrical Engineering Faculty, Universidad de La Salle, Bogotá, Colombia | [b] CONICET-Universidad Nacional de San Juan, San Juan, Argentina
Correspondence:
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Corresponding author: Guillermo A. Díaz, Electrical Engineering Faculty, Universidad de La Salle, Cra 2 # 10-70, 7th floor, section C, Bogotá, Colombia. Tel.: +571 3535360; ext.: 2528; E-mail:guandiaz@unisalle.edu.co
Abstract: This paper presents new compact analytical expressions for the magnetic
field calculation produced by a finite cylindrical sheet. A linearly varying
surface current density between the ends of the cylindrical sheet has been
assumed as current source. The expressions presented in this work are
substantially more compact if compared with the ones currently available in
the literature. Since the solutions are given in terms of complete elliptic
integrals of the first, second and third kind, and the last two ones diverge
at certain arguments, the field expressions also diverge at these critical
points, even though the field solution is finite. These singular points are
located at the ends of the current sheet cylinder. New analytical
expressions are also presented for these critical points avoiding the
singularities in an elegant way. The radial component of the magnetic field
strength is separately discussed, and it has been proven that its solution
at singular points diverges. To improve the computational performance on the
evaluation of magnetic field at critical points, an alternative formulation
is presented, where complete elliptic integrals of the second and third kind
are replaced with alternative functions. Numerical algorithms for the
computation of these functions are also presented.
Keywords: Current carrying cylinder, elliptic integrals, magnetic field, singularity
