Magnetic vector potential and magnetic field intensity due to a
finite current carrying cylinder considering a variable current density along
its axial dimension
Affiliations: [a] Instituto de Energía Eléctrica-Universidad
Nacional de San Juan, San Juan, Argentina | [b] Siemens Aktiengesellschaft, Transformers, Nuremberg, Germany
Correspondence:
[*]
Corresponding author: Guillermo A. Díaz, PhD. Candidate,
Instituto de Energía Eléctrica-Universidad Nacional de San Juan
(IEE-UNSJ), Av. Libertador San Martín 1109 (Oeste) San Juan P.C.
J5400ARL, Argentina. Tel.: +54 644 226 444-Int. 245; E-mail:
gdiaz@iee.unsj.edu.ar, guillermo.diaz_f@siemens.com
Abstract: With the aim of introducing a computationally efficient solution for
problems such as the fast computation of magnetic field magnitudes and forces
in coils and windings, this paper presents analytical expressions for the
magnetic vector potential and magnetic field intensity in radial and axial
directions due to a finite cylinder with infinitesimal wall thickness carrying
a linearly varying current density between the values at the lower and upper
ends. All expressions have been derived in terms of complete elliptic integrals
of first, second and third kind, whose evaluation is achieved by means of very
fast algorithms. The formulas presented make possible the fast computation of
magnetic field at any point in space at reduced computational cost. The
formulation is not only specially suited for modeling the current distribution
in foil windings of power transformers but also for representing the
magnetization of transformer core legs. The present method is also useful for
efficient modeling of cylinders with constant current density since it is a
generalization of this especial case. Finally, an example is presented where
the results achieved using the proposed method are compared with those obtained
using the finite element method showing a very good agreement between them.
Keywords: Azimuthal current density, Biot-Savart law, elliptic integral, magnetic field
