In an electromagnetic plane wave in a conducting medium, the magnetic contribution always dominates over the electric contribution in terms of energy density.
The energy density of an electromagnetic plane wave in a conducting medium can be calculated using Equation 9.138. This equation states that the energy density (u) is given by the sum of the electric field energy density (ue) and the magnetic field energy density (um):
u = ue + um
To show that the magnetic contribution always dominates, we need to compare the magnitudes of ue and um. Let's assume that the wave is propagating in the z-direction.
1. Electric Field Energy Density (ue):
The electric field energy density is given by:
ue = (1/2) * ε * |E|^2
Where ε is the permittivity of the medium and |E| is the magnitude of the electric field.
2. Magnetic Field Energy Density (um):
The magnetic field energy density is given by:
um = (1/2) * (1/μ) * |B|^2
Where μ is the permeability of the medium and |B| is the magnitude of the magnetic field.
Comparing the magnitudes:
We can see that the electric field energy density (ue) depends on the square of the electric field magnitude, while the magnetic field energy density (um) depends on the square of the magnetic field magnitude.
In a conducting medium, the conductivity (σ) is relatively high, which leads to a smaller value of μ compared to ε. As a result, the magnetic field energy density (um) is typically larger than the electric field energy density (ue), and therefore dominates.