Magnetic flux density and vector potential of linear polyhedral sources

Purpose – The purpose of this paper is to evaluate analytically the magnetic flux density and the magnetic vector potential produced by a linear current density or a linear magnetization inside an arbitrary polyhedron. Design/methodology/approach – In order to obtain expressions of the field and potential integrals in an intrinsic vector form, independently of any reference frame, the approach is to avoid the use of a local coordinate system to perform the integrations. Findings – The expressions obtained contain only the same functions just needed for the uniform sources case, do not introduce any new singularity or discontinuity, and computed results illustrate their effectiveness. Research limitations/implications – Being in intrinsic vector form the expressions obtained are well suited to cope with the data structures, i.e. faces-edges and edges-vertices incidence matrices, provided by unstructured polygonal meshes generators. Their use, especially when dealing with a generic mixed unstructured polygonal mesh, avoids the need of different routines, thus decreasing the complexity of the numerical code. Practical implications – Besides, avoiding numerical integration, the results do not require usage of any function other than those already defined for the uniform sources case, and do not introduce any new singularity or discontinuity. Thus, the calculation of the magnetic flux density and the magnetic vector potential produced by linear sources needs nearly the same effort as the uniform sources one. Originality/value – The closed-form expressions obtained are in intrinsic vector form and can be implemented in a unique routine suitable for the calculation of the magnetic flux density and vector potential produced by any linear or uniform polyhedral source.