Adapted Amperian Approach for Three-Dimensional Magnetic Quantities Calculations Generated by Particular Permanent Magnet Shapes

In this work, three-dimensional calculations of magnetic flux densities by integral approach were developed from regular polygonal shaped permanent magnets. The principal hypothesis is that their magnetizations vectors are constants and collinearly oriented with the normal vectors of their base surfaces. In these situations, the Amperian calculations were preferred to the Coulombian ones. The reason is that the rectangular forms of side's surfaces are parts of the equivalent thin coil of permanent magnet in which the analytical calculations are possible. The difficulties, concern only the inclinations, which were be resolved in this paper by Euler's transformations matrix. The results were demonstrated for triangular, square, pentagonal and polygonal regular prism permanent magnets. The accuracy and efficiency of the developed analytical model was verified and validated by a comparison with finite element calculation using Flux3D software.