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Formulations in Magnetostatics

QuickField can solve both linear and nonlinear magnetic problems. Magnetic field may be induced by the concentrated or distributed currents, permanent magnets or external magnetic fields.

The magnetic problem is formulated as the Poisson's equation for vector magnetic potential A (B = curl A, B - magnetic flux density vector). The flux density is assumed to lie in the plane of model (xy or zr), while the vector of electric current density j and the vector potential A are orthogonal to it. Only jz and Az in planar or jθ and Aθ in axisymmetric case are not equal to zero. We will denote them simply j and A. The equation for planar case is

and for axisymmetric case is

where components of magnetic permeability tensor μx and μy (μz and μr), components of coercive force vector Hcx and Hcy (Hcz and Hcr), and current density j are constants within each block of the model.

Note. Isotropic (μx = μy or μz = μr) but field dependent permeability is assumed in nonlinear case. Magnetization characteristic of material is described by the B-H curve.