Résumé
The aim of this paper is to present an analytical calculation of permanent magnet rings whose magnetic polarization is either radial or axial. The calculation of magnetic field created by permanent magnet rings is generally based on either a 2D analytical approach or a 3D semi-analytical approach. However, when the inner radius of the permanent magnet ring becomes small, the 2D analytical calculation is not appropriate. Moreover, the semi-analytical approach is less useful than an analytical approach. We propose in this paper to compare the 2D analytical calculation and the 3D analytical calculation. In particular, we show when the use of 3D analytical calculation is necessary and when the ring curvature effect is important.