BEE Electromagnetic Fields and Waves 2 — Questions and Answers
Question 1: Which of the following correctly states Faraday's Law of electromagnetic induction in differential form?
- ∇ × E = -∂B/∂t (Correct answer)
- ∇ · E = ρ/ε₀
- ∇ × B = μ₀J
- ∇ · B = 0
Correct answer: ∇ × E = -∂B/∂t
Faraday's Law states that the curl of E equals the negative time rate of change of B.
Question 2: A parallel-plate capacitor with plate area A and separation d is filled with a dielectric of permittivity ε. What is the electric field inside if voltage V is applied?
- V/d (Correct answer)
- Vd/A
- εV/d
- V/(εd)
Correct answer: V/d
The electric field between parallel plates is E = V/d, independent of the dielectric permittivity for a given voltage.
Question 3: What is the skin depth δ for a good conductor with conductivity σ, permeability μ, at frequency f?
- 1/√(πfμσ)
- √(2/ωμσ)
- Both A and B are equivalent (Correct answer)
- 2π/√(μσf)
Correct answer: Both A and B are equivalent
Both 1/√(πfμσ) and √(2/ωμσ) are equivalent expressions for skin depth since ω = 2πf.
Question 4: The Poynting vector S = E × H represents which physical quantity?
- Power density flowing through a surface (Correct answer)
- Energy stored in the electromagnetic field
- Force per unit volume on charges
- Radiation pressure on a conductor
Correct answer: Power density flowing through a surface
The Poynting vector gives the instantaneous power per unit area (W/m²) transported by an EM wave.
Question 5: For a uniform plane wave in free space, the ratio of the magnitudes |E|/|H| equals:
- 377 Ω
- 120π Ω only
- Both A and B since 377 ≈ 120π (Correct answer)
- 1/377 Ω
Correct answer: Both A and B since 377 ≈ 120π
The intrinsic impedance of free space η₀ = √(μ₀/ε₀) ≈ 377 Ω = 120π Ω.
Question 6: Gauss's Law for magnetism (∇ · B = 0) physically implies:
- Magnetic monopoles do not exist (Correct answer)
- Magnetic fields are always uniform
- B field lines have zero circulation
- Permeability of free space is constant
Correct answer: Magnetic monopoles do not exist
Zero divergence of B means magnetic field lines always form closed loops, confirming no isolated magnetic charges (monopoles) exist.
Question 7: Which condition must the tangential components of E satisfy at an interface between two lossless dielectrics?
- E₁t = E₂t (continuous) (Correct answer)
- E₁t = (ε₁/ε₂)E₂t
- E₁t = 0
- E₁t = -E₂t
Correct answer: E₁t = E₂t (continuous)
Tangential electric field components must be continuous across any dielectric–dielectric boundary.
BEE Electromagnetic Fields and Waves 2
Which of the following correctly states Faraday's Law of electromagnetic induction in differential form?