BEE Engineering Electromagnetics Fundamentals 4 — Questions and Answers
Question 1: The electric flux density D and electric field E in a linear isotropic dielectric are related by:
- D = ε₀E
- D = εᵣE
- D = ε₀εᵣE (Correct answer)
- D = E/εᵣ
Correct answer: D = ε₀εᵣE
In a linear isotropic medium, D = ε₀εᵣE = εE, where εᵣ is the relative permittivity.
Question 2: The magnetic vector potential A is defined such that:
- B = ∇×A (Correct answer)
- B = ∇·A
- E = ∇×A
- H = ∇²A
Correct answer: B = ∇×A
The magnetic flux density is defined as B = ∇×A, automatically satisfying ∇·B = 0.
Question 3: Standing waves on a transmission line occur when:
- The line is matched (Z_L = Z₀)
- The source is DC
- The load is mismatched (Γ ≠ 0) (Correct answer)
- Attenuation is very high
Correct answer: The load is mismatched (Γ ≠ 0)
A mismatched load causes a reflected wave; the incident and reflected waves superpose to form standing waves.
Question 4: The electric field intensity E is related to the scalar potential V and vector potential A by:
- E = -∇V
- E = -∇V - ∂A/∂t (Correct answer)
- E = ∇V + ∂A/∂t
- E = -∂A/∂t
Correct answer: E = -∇V - ∂A/∂t
In the general time-varying case, E = -∇V - ∂A/∂t, reducing to E = -∇V in electrostatics.
Question 5: The condition for total internal reflection at a dielectric interface is that the angle of incidence θᵢ satisfies:
- θᵢ < θ_c where sin θ_c = n₂/n₁ (n₁ > n₂)
- θᵢ > θ_c where sin θ_c = n₂/n₁ (n₁ > n₂) (Correct answer)
- θᵢ = 90°
- θᵢ < Brewster's angle
Correct answer: θᵢ > θ_c where sin θ_c = n₂/n₁ (n₁ > n₂)
Total internal reflection occurs when θᵢ exceeds the critical angle θ_c = arcsin(n₂/n₁) for n₁ > n₂.
Question 6: Which of the following correctly states Faraday's law in integral form?
- ∮E·dl = -d/dt ∬B·dS (Correct answer)
- ∮E·dl = ∬J·dS
- ∮E·dl = d/dt ∬D·dS
- ∮E·dl = Q_enc/ε₀
Correct answer: ∮E·dl = -d/dt ∬B·dS
Faraday's law states that the EMF around a closed path equals the negative rate of change of magnetic flux through the surface.
Question 7: The phase velocity of a wave in a medium with relative permittivity εᵣ and relative permeability μᵣ is:
- v_p = c√(εᵣμᵣ)
- v_p = c / √(εᵣμᵣ) (Correct answer)
- v_p = c·εᵣ·μᵣ
- v_p = c / (εᵣ + μᵣ)
Correct answer: v_p = c / √(εᵣμᵣ)
Phase velocity is v_p = 1/√(με) = c/√(εᵣμᵣ), always less than or equal to c in passive media.
BEE Engineering Electromagnetics Fundamentals 4
The electric flux density D and electric field E in a linear isotropic dielectric are related by: