In a conducting medium there is an induced current density
in response to the E-field of the wave. The current density
J = σE is linearly proportional
to the electric field (Ohm's law). Maxwell equations are
ε ∂_{t }E = rot H
- σE,
∂_{t }H = - rot E.
1D equations become
(E_{x })_{z}^{t+1} - (E_{x })_{z}^{t} | = – | (H_{y })_{z+½}^{t+½} - (H_{y })_{z-½}^{t+½} | – | σ | (E_{x })_{z}^{t+1} + (E_{x })_{z}^{t} |
———————— | ———————————— | ––– | ———————— | ||
Δt | ε_{z} Δz | ε_{z} | 2 |
(H_{y })_{z+½}^{t+½} - (H_{y })_{z+½}^{t-½} | = | (E_{x })_{z+1}^{t} - (E_{x })_{z}^{t} |
———————————— | – ———————— | |
Δt | Δz |