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Behavior laws and constitutive equations: definition
Introduction
The solving of an electromagnetic problem consists of solving a set of equations:
- the Maxwell equations, which represent the backbone of the theory
- the constitutive equations of the matter, which model the material properties.
Reading advice
The Maxwell equations are presented in the chapters pertaining to magnetic and electric applications: Magnetic applications: principles and Electric applications: principes.
This chapter will cover the constitutive equations of the matter.
Constitutive equations
The constitutive equations of the matter characterize the different materials: conductive, magnetic, dielectric or thermal (by thermal conductivity or volumetric heat capacity) .
They are presented in the table below.
| Material | Constitutive equation | Material property |
|---|---|---|
| magnetic |
 (1) |
μ: permeability H/m |
| dielectric |
 (2) |
ε: permittivity F/m |
| conductive |
 (3) |
σ: conductivity Ω-1.m-1 |
| thermal (thermal conductivity) |
 (4) |
k: tensor of the thermal conductivity W/m/degree |
| thermal (volumetric heat capacity) |
 (5) |
ρCp (T): volumetric heat capacity (J/m3/degree) |
Denomination
These constitutive equations express:
- (1) law of magnetic behavior
- (2) law of dielectric behavior
- (3) law of electric behavior or local formulation of Ohm's law
- (4) law of thermal behavior by conductivity
- (5) law of thermal behavior by volumetric heat capacity