Analytic Solution for Variations of Magnetic Fields in Closed Circuits: Examination of Deviations From the “Standard” Ampere's Law Equation

The calculation of magnetic fields in devices with a nonuniform distribution of magnetomotive force (MMF) and with nonlinear magnetic components has proven problematic within electromagnetic systems. This is caused by insufficiently precise determination of the dependence of magnetic induction B, on magnetic field H. This paper develops a method for analytically calculating the variation of magnetic fields H, in magnetic circuits by introducing a specific expression into to the Ampere's circuital law formula to take into account nonuniform MMF. The new formula uses a conformal mapping procedure which allows calculation of the magnetic field at different displacements from the field generating coil. The analytic approximation proposed is developed for the specific problem of a closed circuit magnetic core. This analytic model gives accurate results faster than can be achieved in FEM software.