# Steady State AC Magnetic: solved equations (vector model 2D)

## Introduction

The vector model is the general model proposed for 2D applications.

## Equation solved with vector model (2D applications)

The Maxwell-Faraday equation implies presence of electric scalar potential **V**, such as:

The equation solved by the finite elements method in a Steady State AC Magnetic application is written:

The complex image of this equation ( is replaced by ) is the following equation:

where:

- [ν
_{r}] is the tensor of the reluctivity of the medium - ν
_{0}is the reluctivity of the vacuum; ν_{0}= 1/μ_{0}= 1/(4 π 10^{-7}) (in m/H) - is the magnetic vector complex potential (in Wb/m)
- [σ] is the tensor of the conductivity of the medium (in S)
- V is the electric scalar potential (in V)

## State variables, vector model (2D)

The state variables are:

- the magnetic vector complex potential
- the electric scalar potential V

The state variables, dependent on the problem type, plane 2D or axisymmetric 2D, are given in the table below.

Type of the problem | State variable |
Notation (in Flux 3D) |
---|---|---|

plane | A_{n} |
AN2* |

axisymmetric | r.A_{n} |
RAN2 |