BEE Engineering Electromagnetics Fundamentals 2 — Questions and Answers
Question 1: What is the divergence of the magnetic flux density B in free space?
- ∇·B = ρ/ε₀
- ∇·B = μ₀J
- ∇·B = 0 (Correct answer)
- ∇·B = ∂E/∂t
Correct answer: ∇·B = 0
Maxwell's equation states that magnetic monopoles do not exist, so the divergence of B is always zero.
Question 2: The capacitance per unit length of a coaxial cable with inner radius a and outer radius b, filled with dielectric ε, is:
- 2πε / ln(b/a) (Correct answer)
- πε / ln(b/a)
- ε ln(b/a) / 2π
- 2πε(b-a)
Correct answer: 2πε / ln(b/a)
Applying Gauss's law to the coaxial geometry yields C/L = 2πε / ln(b/a).
Question 3: In a good conductor, the skin depth δ is related to frequency f and conductivity σ as:
- δ = √(2/ωμσ) (Correct answer)
- δ = √(ωμσ/2)
- δ = 1/(πfμσ)
- δ = ωμσ
Correct answer: δ = √(2/ωμσ)
Skin depth is defined as δ = √(2/ωμσ), where ω = 2πf, showing fields decay exponentially into the conductor.
Question 4: The Biot-Savart law gives the magnetic field contribution dH from a current element Idl as:
- dH = (Idl × R̂) / (4πR²) (Correct answer)
- dH = (Idl · R̂) / (4πR²)
- dH = μ₀Idl / (2πR)
- dH = Idl / (4πR)
Correct answer: dH = (Idl × R̂) / (4πR²)
The Biot-Savart law states dH = (Idl × R̂)/(4πR²), giving field direction via the cross product.
Question 5: What boundary condition applies to the tangential component of E at the interface between two dielectrics?
- E_t1 = E_t2 (Correct answer)
- ε₁E_t1 = ε₂E_t2
- E_t1 + E_t2 = 0
- E_t1 / E_t2 = ε₂/ε₁
Correct answer: E_t1 = E_t2
The tangential component of E is continuous across any dielectric interface (no surface current).
Question 6: The wave impedance η of a plane wave in a lossless medium with permittivity ε and permeability μ is:
- η = √(ε/μ)
- η = √(μ/ε) (Correct answer)
- η = μ/ε
- η = ωμ/β
Correct answer: η = √(μ/ε)
Intrinsic impedance is η = √(μ/ε); in free space this equals approximately 377 Ω.
Question 7: The continuity equation relating current density J and charge density ρᵥ is:
- ∇·J = ∂ρᵥ/∂t
- ∇·J = -∂ρᵥ/∂t (Correct answer)
- ∇×J = -∂ρᵥ/∂t
- ∇·J = ρᵥ/ε₀
Correct answer: ∇·J = -∂ρᵥ/∂t
The continuity equation ∇·J = -∂ρᵥ/∂t expresses conservation of electric charge.
BEE Engineering Electromagnetics Fundamentals 2
What is the divergence of the magnetic flux density B in free space?