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
• ν₀ is the reluctivity of the vacuum; ν₀ = 1/μ₀ = 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.