Electromagnetic Fields and Waves Flashcards

The voltage standing-wave ratio (VSWR) on a transmission line terminated with a short circuit is:

Answer: Infinity (∞)

A short circuit creates a reflection coefficient Γ = -1 (|Γ| = 1), so VSWR = (1+1)/(1-1) → ∞.

Snell's Law of refraction for electromagnetic waves at a planar interface states:

Answer: n₁ sin θ₁ = n₂ sin θ₂

The phase-matching condition at the boundary requires n₁ sin θ₁ = n₂ sin θ₂, identical to optics.

Magnetic vector potential A is defined such that:

Answer: B = ∇ × A

Since ∇ · B = 0, B can always be written as the curl of a vector potential A.

For a lossy transmission line, the propagation constant γ = α + jβ. At very high frequencies in a good conductor, α ≈ β. This means the wave:

Answer: Attenuates by 1/e over exactly one wavelength/2π

When α = β = 1/δ (skin depth formula), the wave decays by e⁻¹ over a distance equal to 1/α = δ ≈ λ/2π inside the conductor.

Image theory in electromagnetics replaces a ground plane conductor with:

Answer: A mirror-image charge of opposite sign at the same depth below the surface

Image theory removes the conductor by placing an opposite charge at the mirror-image position, reproducing the correct boundary conditions above the surface.

The wave equation for E in a source-free, lossless medium is:

Answer: ∇²E - με ∂²E/∂t² = 0

Combining Faraday's and Ampere's laws yields the vector wave equation ∇²E = με ∂²E/∂t² (zero on one side).

The radiation resistance of a half-wave dipole antenna in free space is approximately:

Answer: 73 Ω

The half-wave dipole has a radiation resistance of ≈ 73 Ω, which is why it is commonly fed with 75 Ω coaxial cable.