* Electric conductivity (σ) having units of S/m
* Magnetic conductivity (σ<sub>m</sub>) having units of Ω/m
Â
The permittivity and permeability of a material are typically related to the permittivity and permeability of the free space as follows:
Â
:<math> \epsilon = \epsilon_r \epsilon_0 </math>
Â
:<math> \mu = \mu_r \mu_0, \quad \quad </math>
Â
where ε<sub>0</sub> = 8.854e-12 F/m, μ<sub>r</sub> = 1.257e-6 H/m, and ε<sub>r</sub> and μ<sub>r</sub> are called relative permittivity and permeability of the material, respectively.
Â
The constitutive parameters relate the field quantities in the material medium:
Â
:<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math>
Â
:<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math>
Â
where '''E''' and '''H''' are the electric and magnetic fields, respectively, '''D''' is the electric flux density, also known as the electric displacement vector, '''B''' is the magnetic flux density, also known as the magnetic induction vector, and '''J '''and '''M '''are the electric and magnetic current densities, respectively.
Â
The electric conductivity and magnetic conductivity parameters represent the material losses. In frequency-domain simulations under a time-harmonic (e<sup>jωt</sup>) field assumption, it is often convenient to define a complex relative permittivity and a complex relative permeability in the following manner:
Â
:<math> \epsilon_r = \epsilon^{\prime}_r -j\epsilon^{\prime\prime}_r = \epsilon^{\prime}_r -j\frac{\sigma}{\omega \epsilon_0} = \epsilon^{\prime}_r (1 - j \tan \delta ) </math>
Â
:<math> \mu_r = \mu^{\prime}_r -j\mu^{\prime\prime}_r = \mu^{\prime}_r - j\frac{\sigma_m}{\omega \mu_0} = \mu^{\prime}_r (1 - j \tan \delta_m)</math>
Â
where ω = 2πf, and f is the operational frequency, and the electric and magnetic loss tangents are defined as follows:
Â
:<math> \tan \delta = \epsilon^{\prime\prime}_r / \epsilon^{\prime}_r </math>
Â
:<math> \tan \delta_m = \mu^{\prime\prime}_r / \mu^{\prime}_r </math>
Â
Three special media are frequently encountered in electromagnetic problems:
{| class="wikitable"
|-
! scope="col"| Medium
! scope="col"| ε<sub>r</sub>
! scope="col"| μ<sub>r</sub>
! scope="col"| σ
! scope="col"| σ<sub>m</sub>
|-
| Free Space
| 1.0
| 1.0
| 0.0
| 0.0
|-
| Perfect Electric Conductor (PEC)
| 1.0
| 1.0
| ∞
| 0.0
|-
| Perfect Magnetic Conductor (PMC)
| 1.0
| 1.0
| 0.0
| ∞
|}
Â
[[EM.Cube]] offers a large variety of material types listed in the table below: