Effective reluctivity of an insulated magnetic spherical particle excited by an axisymmetric polar magnetic field

Purpose The purpose of this study is to provide a formula for the homogenized reluctivity of an electrically insulated spherical conductive magnetic particle. The insulated particle is excited by azimuthally symmetric boundary conditions for the magnetic field in the polar direction. Otherwise, the boundary conditions are arbitrary. Design/methodology/approach A magnetodynamic formulation of Maxwell’s equations is considered inside the particle. An electrostatic formulation is considered inside the insulation. The homogenized reluctivity is derived using mathematical methods based on analytical solutions of the formulations. The leading principle in the derivation of the homogenized reluctivity is energy consistency. Findings The most important finding is the formula for the homogenized reluctivity. Furthermore, considering an orthogonal decomposition of the magnetic flux density in terms of spherical harmonics, it turns out that homogenization only distinguishes the first mode of the flux density, regardless of which modes are excited by the boundary conditions. This result is somewhat expected, but it forces us to lump the energy exchange of the higher modes into the homogenized magnetic field strength. The treatment also exposes some of the mathematical structures required for homogenization. Originality/value The formula for the homogenized reluctivity is novel. It admits arbitrary but rotationally symmetric boundary conditions for the magnetic field strength at the outer boundary of the insulation in the polar direction. Industrial applications of the developed methods include powder-like materials such as soft magnetic composites. New perspectives on homogenization are provided.