Suppose η₂ = 2η₁ at normal incidence; what is the electric reflection coefficient?
A −1
B −1/3
C +1/2
D +1/3
Answer: D. +1/3. Γ = (η₂−η₁)/(η₂+η₁), which gives +1/3.
Given εr = 4 and μr = 1, phase velocity is?
A 3×10⁸ m/s
B 1.5×10⁸ m/s
C 0.75×10⁸ m/s
D 6×10⁸ m/s
Answer: B. 1.5×10⁸ m/s. In a lossless medium v = c/√(εrμr), giving 1.5×10⁸ m/s.
When peak E is 6 V/m in free space, peak H is about?
A 0.016 A/m
B 0.060 A/m
C 2.0 A/m
D 0.002 A/m
Answer: A. 0.016 A/m. H₀ = E₀/η₀; 6/377 is about 0.016 A/m.
Normal incidence on a perfect conductor produces what electric reflection coefficient?
A +1/2
B +1
C −1
D 0
Answer: C. −1. The reflected electric field reverses phase at a perfect electric conductor.
If σ/(ωε) is much less than one, the dielectric is?
A Low-loss dielectric
B Good conductor
C Perfect conductor
D High-loss plasma
Answer: A. Low-loss dielectric. A small loss tangent indicates conduction loss is small relative to displacement current.
Under good-conductor conditions, which inequality holds?
A σ = 0
B ω = 0
C σ ≪ ωε
D σ ≫ ωε
Answer: D. σ ≫ ωε. A good conductor has conduction current much larger than displacement current.
Across a dielectric interface without changing magnetic flux, tangential E is?
A Normal to interface
B Discontinuous always
C Continuous
D Zero everywhere
Answer: C. Continuous. Faraday’s law requires tangential E to be continuous across an ordinary interface.
With no surface current, tangential H across an interface is?
A Always zero
B Continuous
C Discontinuous
D Infinite
Answer: B. Continuous. The tangential-H jump is set by surface current density.
For E along +x and H along +y, wave propagation is along?
A +x
B −y
C −z
D +z
Answer: D. +z. E×H points in the propagation direction; x cross y is +z.
For β = 20 rad/m, the wavelength is approximately?
A 0.314 m
B 1.257 m
C 0.100 m
D 0.628 m
Answer: A. 0.314 m. λ = 2π/β = 0.314 m.
Given εr = 9 and μr = 1, intrinsic impedance is near?
A 42 Ω
B 377 Ω
C 126 Ω
D 1131 Ω
Answer: C. 126 Ω. η = η₀√(μr/εr), so 377/3 is about 126 Ω.
In a lossless medium, E and H phasors have what phase relation?
A 180° apart
B In phase
C Random phase
D 90° apart
Answer: B. In phase. For a lossless medium, intrinsic impedance is real and E and H are in phase.
Lossless dielectric interface at Brewster angle: parallel-polarized reflection becomes?
A Infinite
B Unity
C Negative one
D Zero
Answer: D. Zero. The parallel-polarized reflected wave vanishes at Brewster angle.
When a wave travels from a higher-index to a lower-index medium at critical incidence, what is the refracted angle?
A 90°
B 0°
C 45°
D 180°
Answer: A. 90°. At the critical angle, the transmitted ray travels along the interface.
Using angles measured from the normal, which law relates refraction angles?
A Lenz’s law
B Snell’s law
C Biot–Savart law
D Ampère’s law
Answer: B. Snell’s law. Snell’s law relates refractive indices and sines of the two angles.
With normal incidence and η₂ < η₁, the electric reflection coefficient has what sign?
A Imaginary only
B Positive
C Negative
D Zero always
Answer: C. Negative. For normal incidence, η₂−η₁ is negative when η₂<η₁.
For a lossless interface, power reflectance plus transmittance equals?
A One
B Zero
C Two
D The impedance
Answer: A. One. Energy conservation gives R+T=1 when there is no absorption.
In a lossless medium, attenuation constant α equals?
A ω
B ε
C β
D Zero
Answer: D. Zero. A lossless medium has no exponential amplitude decay.
How does B₀ relate to E₀ for a uniform plane wave?
A B₀ = E₀
B B₀/E₀ = v
C B₀/E₀ = 1/v
D B₀E₀ = v
Answer: C. B₀/E₀ = 1/v. For a plane wave, E₀/B₀ equals phase velocity.
Moving from lower to higher refractive index, a ray bends where?
A Away from normal
B Toward normal
C Along interface
D Back to source
Answer: B. Toward normal. Snell’s law makes the refracted angle smaller in the higher-index medium.
With fixed εr, how does η vary as μr rises?
A Square-root increase
B No change
C Inverse-square increase
D Linear decrease
Answer: A. Square-root increase. Intrinsic impedance varies as √(μr/εr).
As εr rises with μr fixed, phase velocity generally?
A Becomes infinite
B Increases
C Decreases
D Stays fixed
Answer: C. Decreases. Phase velocity varies inversely with √(εrμr).
What does the propagation constant γ combine?
A Charge and current
B Permittivity and charge
C Power and energy
D Attenuation and phase
Answer: D. Attenuation and phase. The complex propagation constant contains attenuation α and phase constant β.
When a wave enters a good conductor, its field amplitude generally?
A Remains constant
B Decays rapidly
C Becomes static
D Grows without limit
Answer: B. Decays rapidly. Good conductors have strong attenuation and small skin depth.
Which theorem states electromagnetic-field energy balance?
A Poynting theorem
B Green’s theorem
C Gauss’s theorem
D Stokes’ theorem
Answer: A. Poynting theorem. Poynting’s theorem balances field-energy change, power flow, and work on charges.