Aircraft Systems

Appendix ARadiation from Wire Antennas

The analysis of radiation from wire antennas starts with Maxwell’s equations, which describe how electric (E) and magnetic (B) fields behave in space and time. These are:

(A1.1)

(A1.2)

(A1.3)

(A1.4)

where E is the electric field strength, B is the magnetic field strength, ρ is the charge density, and J is the current density. The constants ε₀ (= 8.8542 × 10⁻¹² C² N⁻¹ m⁻²) and μ₀ (= 4π × 10⁻⁷ N A⁻²) are the electric permittivity and magnetic permeability of free space, respectively. Charges that are static or moving with a uniform speed (steady current) do not produce electromagnetic radiation but an accelerating charge or a time‐varying current generate radiation, which the above equations predict will propagate as a wave as shown below.

A. Static Electric Fields Produced by Static Charges

First, we will consider the time‐independent electric and magnetic fields produced by static charges and steady currents.

In this case Faraday’s law reduces to ∇ × E = 0 and since ∇ × (∇Φ) = 0 for any function Φ, the electric field can be written as the gradient ...