An accurate knowledge of the magnetic as well as other field distributions is of great importance in design optimization. In two dimensional problems with the current flow in only one direction, the magnetic field can be solved by computing a scalar potential or one component of the vector potential, The general formulation for three-dimensional solutions, including nonlinearities, is more complex and requires all three components of the vector potential as well as a scalar potential for the description of the fields. It is the purpose of this paper to present a general systematic, novel formulation at low frequencies feasible for the computer-aided design or analysis in terms of potential functions for three-dimensional numerical solutions of the nonlinear electromagnetic field problems that include either nonlinear magnetic materials or nonlinear electric materials. Special cases of the magnetostatic as well as eddy-current problems are discussed.


Author's manuscript; originally published in Proc. of the International Electrical Machines Conference, London, Sept 1974.


CAD, eddy currents, magnetostatic problems, electrical machinery, design optimization, scalar potential, vector potential, electric materials

Subject Categories

Electromagnetic fields, Computer-aided design, Magnetic materials


Electromagnetics and photonics



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