Propagation of electromagnetic waves
Before seeing the characteristics of the antennas, we will first present the equations that translate the propagation of electromagnetic waves, the relations between the vectors of the electric field (E ⃗ and D ⃗), the magnetic field vectors (B ⃗ and H ⃗), and the density of charges and currents (ρ and J ⃗):
D ⃗ = εE ⃗
B ⃗ = μH ⃗
Maxwell's equations:
(rot) ⃗ E ⃗ = - (∂B ⃗) / ∂t
(rot) ⃗ H ⃗ = J ⃗ + (∂D ⃗) / ∂t
div D ⃗ = ρ
div B ⃗ = 0
And div J ⃗ + ∂ρ / ∂t = 0
By then combining Maxwell's equations we obtain the two differential equations called propagation equations:
ΔE ⃗-εμ (∂²E ⃗) / ∂t² = 0
ΔH ⃗-εμ (∂²H ⃗) / ∂t² = 0
With ε and μ the electrical permittivity and the magnetic permeability which are characteristics of the propagation medium.
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