Magneto Static: solved equations (vector model 2D)
Introduction
The vector model is the general model proposed for 2D applications.
This model is used by default (automatically) by:
 the 2D solver of Flux 2D
 the 3D solver of Flux 3D for solving a 2D application
Equation solved with vector model (2D applications)
The Gauss law for magnetism, , allows the introduction of a magnetic vector potential , such as:
The equation solved by the finite elements method in a Magneto Static application is written:
where:
 [ν_{r}] is the tensor of the relative reluctivity of the medium

ν_{0} is the magnetic reluctivity of the vacuum, ν_{0} = 1/μ_{0} = 1/(4 π 10^{7})
(in m/H)
 is the vector potential (in Wb/m)
 is coercive magnetic field (permanent magnets) (in A/m)
 is the density of current source (in A/m^{2})
State variable, vector model (2D applications)
The state variable in 2D applications is the magnetic vector potential .
The magnetic field B is written :
and :
; ;
In 2D problems, the vector has a non null component, the normal component to the plane of figure; let A_{n} (or A_{z})
The magnetic field B is written:
; ;
The state variable, dependent on the problem type, plane 2D or axisymmetric 2D, is given in the table below.
Type of the problem  State variable 
Notation (in Flux 3D) 

plane  A_{n}  AN1* 
axisymmetric  rA_{n}  RAN1* 