BEE Electromagnetic Fields and Waves 4 — Questions and Answers
Question 1: An electric dipole antenna of length L << λ radiates power proportional to:
- (L/λ)² (Correct answer)
- (L/λ)⁴
- L/λ
- (λ/L)²
Correct answer: (L/λ)²
Radiated power from a Hertzian dipole is proportional to (L/λ)², making short antennas very inefficient radiators.
Question 2: The continuity equation ∇ · J + ∂ρ/∂t = 0 expresses conservation of:
- Electric charge (Correct answer)
- Energy
- Magnetic flux
- Momentum
Correct answer: Electric charge
The continuity equation is the mathematical statement of charge conservation, linking current density to charge density.
Question 3: In a coaxial transmission line with inner radius a and outer radius b, the characteristic impedance Z₀ is proportional to:
- ln(b/a) (Correct answer)
- b/a
- (b-a)/a
- ln(a/b)
Correct answer: ln(b/a)
Z₀ = (η/2π)ln(b/a) for a coaxial line, where η is the intrinsic impedance of the fill medium.
Question 4: The Biot–Savart Law is used to find:
- Magnetic field produced by a steady current element (Correct answer)
- Electric field produced by a static charge
- Force on a charge in a magnetic field
- Energy stored in an inductor
Correct answer: Magnetic field produced by a steady current element
Biot–Savart gives dH = (I dL × âR)/(4πR²) for the differential H-field from a current element.
Question 5: The directivity of an isotropic radiator is:
- 1 (0 dBi) (Correct answer)
- 1.5 (1.76 dBi)
- 2 (3 dBi)
- 0
Correct answer: 1 (0 dBi)
An isotropic antenna radiates equally in all directions, so its directivity is defined as unity (0 dBi).
Question 6: The phase velocity of a wave in a non-magnetic medium with relative permittivity εr is:
- c/√εr (Correct answer)
- c·√εr
- c/εr
- c·εr
Correct answer: c/√εr
Phase velocity vp = 1/√(με) = c/√(μrεr); for non-magnetic media (μr = 1), vp = c/√εr.
Question 7: Which of these is NOT one of Maxwell's four equations?
- F = q(E + v × B) (Correct answer)
- ∇ × E = -∂B/∂t
- ∇ · D = ρv
- ∇ × H = J + ∂D/∂t
Correct answer: F = q(E + v × B)
F = q(E + v × B) is the Lorentz force law, a separate result, not one of Maxwell's four equations.
BEE Electromagnetic Fields and Waves 4
An electric dipole antenna of length L << λ radiates power proportional to: