Magnetic vector potential and magnetic field intensity due to a finite current carrying cylinder considering a variable current density along its axial dimension

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.