BEE Engineering Electromagnetics Fundamentals 3 — Questions and Answers
Question 1: Stokes' theorem relates a surface integral of the curl of a vector field to:
- A volume integral of the divergence
- A line integral around the bounding contour (Correct answer)
- A surface integral of the field itself
- A volume integral of the field
Correct answer: A line integral around the bounding contour
Stokes' theorem states ∬(∇×A)·dS = ∮A·dl, converting a surface integral to a closed line integral.
Question 2: For a uniform plane wave propagating in the +z direction, if E is in the x̂ direction, then H is in the direction:
- +x̂
- +ẑ
- +ŷ (Correct answer)
- -ẑ
Correct answer: +ŷ
For a +z propagating wave, E × H must point in +z, so H = ŷ (since x̂ × ŷ = ẑ).
Question 3: The inductance per unit length of a two-wire transmission line with wire radius a and separation d (d >> a) is approximately:
- μ ln(d/a) / π (Correct answer)
- πμ / ln(d/a)
- μ / (2π) ln(d/a)
- 2μ ln(d/a) / π
Correct answer: μ ln(d/a) / π
For a two-wire line, L/l = (μ/π) ln(d/a), derived from the magnetic flux linkage per unit length.
Question 4: In electrostatics, Laplace's equation ∇²V = 0 applies in regions where:
- The permittivity is nonuniform
- There is no free charge density (Correct answer)
- The field is time-varying
- The medium is conducting
Correct answer: There is no free charge density
Laplace's equation holds in source-free regions (ρᵥ = 0), while Poisson's equation applies where ρᵥ ≠ 0.
Question 5: The reflection coefficient Γ at a transmission line load is defined as:
- Γ = (Z_L - Z₀) / (Z_L + Z₀) (Correct answer)
- Γ = (Z₀ - Z_L) / (Z_L + Z₀)
- Γ = Z_L / Z₀
- Γ = Z₀ / Z_L
Correct answer: Γ = (Z_L - Z₀) / (Z_L + Z₀)
The voltage reflection coefficient is Γ = (Z_L − Z₀)/(Z_L + Z₀), determining the reflected wave amplitude.
Question 6: The normal component of B across a boundary between two magnetic media satisfies:
- B_n1 = B_n2 (Correct answer)
- μ₁B_n1 = μ₂B_n2
- H_n1 = H_n2
- B_n1 - B_n2 = μ₀K
Correct answer: B_n1 = B_n2
Since ∇·B = 0, the normal component of B is continuous: B_n1 = B_n2.
Question 7: The Poynting vector S represents:
- Stored electromagnetic energy density
- Power flow per unit area (W/m²) (Correct answer)
- Force per unit charge
- Magnetic flux per unit area
Correct answer: Power flow per unit area (W/m²)
The Poynting vector S = E × H gives the instantaneous power flow per unit area in W/m².
BEE Engineering Electromagnetics Fundamentals 3
Stokes' theorem relates a surface integral of the curl of a vector field to: