BEE Electromagnetic Fields and Waves 5 — Questions and Answers
Question 1: The voltage standing-wave ratio (VSWR) on a transmission line terminated with a short circuit is:
- Infinity (∞) (Correct answer)
- 0
- 1
- 2
Correct answer: Infinity (∞)
A short circuit creates a reflection coefficient Γ = -1 (|Γ| = 1), so VSWR = (1+1)/(1-1) → ∞.
Question 2: Snell's Law of refraction for electromagnetic waves at a planar interface states:
- n₁ sin θ₁ = n₂ sin θ₂ (Correct answer)
- n₁ cos θ₁ = n₂ cos θ₂
- sin θ₁/sin θ₂ = n₁²/n₂²
- θ₁ + θ₂ = 90°
Correct answer: n₁ sin θ₁ = n₂ sin θ₂
The phase-matching condition at the boundary requires n₁ sin θ₁ = n₂ sin θ₂, identical to optics.
Question 3: Magnetic vector potential A is defined such that:
- B = ∇ × A (Correct answer)
- B = ∇ · A
- B = ∇A
- B = -∇ × A
Correct answer: B = ∇ × A
Since ∇ · B = 0, B can always be written as the curl of a vector potential A.
Question 4: 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:
- Attenuates by 1/e over exactly one wavelength/2π (Correct answer)
- Travels without attenuation
- Has phase velocity greater than c
- Reflects completely at any interface
Correct 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.
Question 5: Image theory in electromagnetics replaces a ground plane conductor with:
- A mirror-image charge of opposite sign at the same depth below the surface (Correct answer)
- A mirror-image charge of the same sign at the same depth below the surface
- No charge; the conductor simply cancels the field
- A surface current sheet of identical magnitude
Correct 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.
Question 6: The wave equation for E in a source-free, lossless medium is:
- ∇²E - με ∂²E/∂t² = 0 (Correct answer)
- ∇²E + με ∂²E/∂t² = 0
- ∇·E - με ∂²E/∂t² = 0
- ∇²E = με ∂E/∂t
Correct 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).
Question 7: The radiation resistance of a half-wave dipole antenna in free space is approximately:
- 73 Ω (Correct answer)
- 50 Ω
- 377 Ω
- 36.5 Ω
Correct 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.
BEE Electromagnetic Fields and Waves 5
The voltage standing-wave ratio (VSWR) on a transmission line terminated with a short circuit is: