Behavior laws and constitutive equations: definition


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)


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