Comparison of the coulombian and amperian current models for calculating the magnetic field produced by radially magnetized arc shaped permanent magnets

Abstract—This paper presents some improved analytical expressions of the magnetic field produced by arc-shaped permanent magnets whose polarization is radial with the amperian current model. First, we show that the radial component of the magnetic field produced by a ring permanent magnet whose polarization is radial can be expressed entirely in terms of elliptic integrals. Such an expression is useful for optimization purposes. We also present a semi-analytical expression of the axial component produced by the same configuration. For this component, we discuss the terms that are difficult to integrate analytically and compare our expression with the one established by Furlani [1]. In the second part of this paper, we use the amperian current model for calculating the magnetic field produced by a tile permanent magnet radially magnetized. This method was in fact still employed by Furlani for calculating the magnetic field produced by radially polarized cylinders. We show that it is possible to obtain a fully analytical expression of the radial component based on elliptic integrals. In addition, we show that the amperian current model allows us to obtain a fully analytical expression of the azimuthal component. All the expressions determined in this paper are compared with the ones established by Furlani [1] or in previous works carried out by the authors. 1