# 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/m^{3}/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