Steady State AC Magnetic: solved equations (introduction)
Introduction
The equations used for the solving are:
 Maxwell's equations (for a magnetic system)
 the constitutive equations of the matter
The computation conditions for a Steady state AC Magnetic application are the following:
 the state variables are time dependent: d/dt ≠ 0 (steady state sinusoidal: sinusoidal time dependence of the current sources)

the computation concerns only the B, H and E fields (the D field is not computed).
The equations of the electric fields E and D and of the magnetic fields B, H cannot be decoupled.
Equations and conditions
In the previously defined conditions of computation, the equations are summarized as follows:
E: electric
field strength (in V/m) B: magnetic flux density (in T) H: magnetic field strength (in A/m) J: current density (in A/m^{2}) 

σ : conductivity (in S) μ : permeability (in H/m) 
The main equation for magnetic materials, can be put in form B(H) or H(B) as presented below.
⇒ 
μ_{r} : relative permeability μ_{0} : vacuum permeability 
⇒ 
ν_{r} : reluctivity ν_{r} =1/μ_{r} ν_{0} : vacuum reluctivity ν_{0} =1/μ_{0} 
Models
To solve these equations, two models are used:

the vector model, which uses: the magnetic vector potential (written )

the scalar model, which uses: magnetic scalar potentials (written ϕ_{tot} or ϕ_{red})
Model and 2D or 3D application
The two models (vector and scalar) are proposed: the vector model for the 2D applications
 the scalar model for the 3D applications