Magnetic Field Analysis of Coplanar Coils and Linear Magnetic Materials Using the Equivalent Permanent Magnetization and Magnetic Scalar Potential

For coplanar coils characterized by homogeneous current density, magnetic field analysis by total magnetic scalar potential formulation was made possible for all regions by transforming the current density into equivalent permanent magnetization. Such total scalar potential formulation significantly reduces the computational cost. The equation for equivalent permanent magnetization and its magnetic scalar potential formulation were suggested in previous research. However, the modeling method, which includes materials with permeability or permanent magnetization, was not introduced. This article proposes a generalized method for analyzing coplanar coils in the presence of magnetic materials. This method utilizes a total magnetic scalar potential formulation, its variational formulation, and its application to the finite element method (FEM). The magnetic scalar potential formulation of permanent magnets with high permeability is also provided for contrast to fully generalize the method and prevent possible confusion between the two formulations. To demonstrate the feasibility and usefulness of the proposed method, the results of the magnetic field analysis using the scalar potential formulation are compared with the analytical solution of a spherical coil and the results obtained from the conventional vector potential formulation.