The magnetic field due to a permanent magnet of a tube-side segment as shape and of radial-oriented magnetization is considered. Such a sheet modelling a single pole of the magnet is used to express the suitable contribution to magnetic quantities. A boundary-integral approach is applied that is based on a virtual scalar quantity attributed to the magnet pole. Such an approach leads to express analytically the scalar magnetic potential and the magnetic flux density by means of the elliptic integrals. Numerical examples of the computed fields are given. The general idea of the presented approach is mainly directed towards designing the magnetic field within the air gap of electric machines with permanent magnets as an excitation source. Other technical structures with permanent magnets may be a subject of this approach as well.

In this paper the application of so called wedge functions is presented to solve two-dimensional simple geometries of magnetostatic and electrostatic problems, e.g. rectangles of varying aspect ratio and with different values of the magnetic permeability μ. Such problems require the use of surface charge density, or segment source, functions of the form ρs = σa-1, where the power parameters, a, have special fractional values. A methodology is presented to determine these special values of a and use them in segment sources on simple geometries, i.e. rectangles of varying aspect ratio, and with different values of the magnetic permeability μ. Wedge solutions are obtained by coupling the strength coefficients of source segments of the same power around an edge. These surface source functions have been used in the analysis of conducting and infinite permeability structures. Here we apply such functions in a boundary integral analysis method to problems having regions of finite permeability.