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

摘要

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.