How it works
The uniform plane wave in a lossless medium has E and H fields perpendicular to each other and to the direction of propagation, with phase velocity v_p = 1/√(µε) = c/√(µr·εr). The intrinsic impedance η = √(µ/ε); for free space η₀ = 377 Ω. In a lossy medium with conductivity σ, the propagation constant γ = α + jβ where attenuation α = ω√(µε/2)·√(√(1+(σ/ωε)²)−1) and phase constant β = ω√(µε/2)·√(√(1+(σ/ωε)²)+1). For a good conductor (σ >> ωε): α ≈ β ≈ √(ωµσ/2) = 1/δ.
Key points to remember
Skin depth δ = 1/α = √(2/ωµσ) for a good conductor. Power density is given by the time-averaged Poynting vector S_avg = (1/2)|E₀|²/η in the direction of propagation. Linear, circular, and elliptical polarisation describe the locus of the E-field tip as the wave propagates — circular polarisation results when two equal-amplitude orthogonal E components are 90° out of phase. The reflection coefficient at a normal-incidence interface is Γ = (η₂−η₁)/(η₂+η₁); transmission coefficient τ = 2η₂/(η₂+η₁). At a perfect conductor (η₂ = 0), Γ = −1, total reflection with phase reversal.
Exam tip
The examiner always asks you to calculate skin depth and surface resistance for a given conductor at a specified frequency — show the full substitution into δ = √(2/ωµσ) with all values in SI units before computing.