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

• ν₀ is the magnetic reluctivity of the vacuum, ν₀ = 1/μ₀ = 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/m²)

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.