Magnetic Field Analysis of Electric Current in Coplanar Coils Using Equivalent Permanent Magnetization and Magnetic Scalar Potential

Use of magnetic scalar potential instead of magnetic vector potential can dramatically reduce the computational cost for 3D magnetic field analysis, but for most methods, the use of scalar potential was limited to current-free conditions. However, for coplanar coils characterized by homogeneous current density, the current density can be transformed into an equivalent permanent magnetization to satisfy the current-free condition. By utilizing this equivalent permanent magnetization as a source, a variational formulation for the magnetic scalar potential can be derived, and finite element analysis becomes feasible for complex systems that analytical method cannot be used. However, the equation for the equivalent permanent magnetization was previously presented only for rectangular coils, and its detailed derivation process, variational scalar potential formulation, and application method for finite element analysis were not introduced, limiting the practicality of the method. To generalize the method to practical applications, this study introduces a generalized equation for equivalent permanent magnetization applicable to arbitrary cross-sectional coplanar coils, its variational formulation using the magnetic scalar potential, and a method for its application in finite element analysis. The results of the magnetic field analysis using the scalar potential formulation were compared with those of the traditional vector potential formulation to demonstrate the feasibility and usefulness of the formulation.