BEE Electromagnetic Fields and Waves 3 — Questions and Answers
Question 1: A TEM wave travels in the +z direction with E in the x-direction. The magnetic field H points in which direction?
- +y direction (Correct answer)
- -y direction
- +x direction
- +z direction
Correct answer: +y direction
For a +z-propagating wave with E in x̂, H = (1/η)(ẑ × E) points in the +ŷ direction.
Question 2: The displacement current density introduced by Maxwell is given by:
- ∂D/∂t (Correct answer)
- ∂B/∂t
- J/ε
- σE
Correct answer: ∂D/∂t
Maxwell added the displacement current density Jd = ∂D/∂t to Ampere's law to make it consistent with charge conservation.
Question 3: For a rectangular waveguide, the cutoff frequency of the TE₁₀ mode with broad-wall dimension a is:
- c/(2a) (Correct answer)
- c/a
- c/(4a)
- 2c/a
Correct answer: c/(2a)
The cutoff frequency for TE₁₀ is fc = c/(2a), making it the dominant (lowest cutoff) mode.
Question 4: The electric potential V due to a point charge Q at distance r in free space is:
- Q/(4πε₀r) (Correct answer)
- Q/(4πε₀r²)
- Qr/(4πε₀)
- Q²/(4πε₀r)
Correct answer: Q/(4πε₀r)
The scalar electric potential falls off as 1/r while the electric field falls off as 1/r².
Question 5: Standing waves are formed in a transmission line when:
- The load is mismatched, causing reflections (Correct answer)
- The source impedance equals the load impedance
- The line length equals one wavelength
- The wave travels only in one direction
Correct answer: The load is mismatched, causing reflections
A mismatched load causes partial or total reflection; the incident and reflected waves superpose to form standing waves.
Question 6: The attenuation constant α for a lossy dielectric medium is primarily associated with:
- Power absorption (heat loss) per unit length (Correct answer)
- Phase shift per unit length of propagation
- Reflection at the medium boundary
- The wavelength inside the medium
Correct answer: Power absorption (heat loss) per unit length
α (Np/m) describes the exponential decay of wave amplitude due to energy absorption in the medium.
Question 7: Brewster's angle is defined as the angle of incidence at which:
- No reflected wave exists for parallel (p) polarization (Correct answer)
- Total internal reflection occurs
- The transmitted wave is 90° from the reflected wave
- No transmitted wave exists
Correct answer: No reflected wave exists for parallel (p) polarization
At Brewster's angle, the reflection coefficient for p-polarization (TM) is zero, so only s-polarization reflects.
BEE Electromagnetic Fields and Waves 3
A TEM wave travels in the +z direction with E in the x-direction.
The magnetic field H points in which direction?