BEE FREE BEE Bachelor of Electrical Engineering Engineering Electromagnetics Fundamentals Questions and Answers 3 — Questions and Answers
Question 1: What is the Poynting vector S for an electromagnetic wave with electric field E and magnetic field H?
- E × H (Correct answer)
- H × E
- E · H
- E + H
Correct answer: E × H
The Poynting vector S = E × H represents the directional power flux density of an electromagnetic wave.
Question 2: According to the Biot-Savart law, the magnetic field dB due to a current element Idl at distance r is proportional to which quantity?
- Idl × r̂ / r² (Correct answer)
- Idl · r̂ / r²
- Idl × r̂ / r
- Idl / r³
Correct answer: Idl × r̂ / r²
The Biot-Savart law states dB = (μ₀/4π)(Idl × r̂)/r², showing an inverse-square dependence on distance.
Question 3: A 5 cm radius circular loop carries 2 A of current. What is the approximate magnetic dipole moment magnitude?
- 15.7 × 10⁻³ A·m² (Correct answer)
- 31.4 × 10⁻³ A·m²
- 7.85 × 10⁻³ A·m²
- 50 × 10⁻³ A·m²
Correct answer: 15.7 × 10⁻³ A·m²
The magnetic dipole moment m = IA = 2 × π × (0.05)² ≈ 15.7 × 10⁻³ A·m².
Question 4: What does Ampère's circuital law with Maxwell's correction add to the original formulation?
- Displacement current density ∂D/∂t (Correct answer)
- Magnetic charge density
- Conduction current density
- Electric polarization
Correct answer: Displacement current density ∂D/∂t
Maxwell added the displacement current term ∂D/∂t to Ampère's law, enabling it to account for time-varying electric fields.
Question 5: In a rectangular waveguide operating in the TE₁₀ mode, where does the electric field have its maximum amplitude across the broad wall dimension a?
- At the center (x = a/2) (Correct answer)
- At the edges (x = 0 and x = a)
- At one quarter width (x = a/4)
- Uniformly distributed
Correct answer: At the center (x = a/2)
In the TE₁₀ mode, the electric field follows a half-sine distribution and reaches maximum at the center of the broad wall.
Question 6: A uniform plane wave in free space has an electric field amplitude of 100 V/m. What is the average power density?
- 13.3 W/m² (Correct answer)
- 26.6 W/m²
- 100 W/m²
- 50 W/m²
Correct answer: 13.3 W/m²
Average power density = E²/(2η₀) = (100)²/(2 × 377) ≈ 13.3 W/m².
BEE FREE BEE Bachelor of Electrical Engineering Engineering Electromagnetics Fundamentals Questions and Answers 3
What is the Poynting vector S for an electromagnetic wave with electric field E and magnetic field H?