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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