BEE Bachelor of Electrical Engineering Electromagnetic Fields and Waves Questions and Answers — Questions and Answers
Question 1: An electromagnetic plane wave propagates from a lossless medium into a lossy medium. Which of the following effects is expected to occur?
- The wave's frequency will decrease.
- The wave's amplitude will attenuate as it travels through the lossy medium. (Correct answer)
- The wave will speed up significantly.
- The wave's polarization will rotate by 90 degrees.
Correct answer: The wave's amplitude will attenuate as it travels through the lossy medium.
In a lossy medium, which has non-zero conductivity, part of the electromagnetic wave's power is converted into heat, causing the wave's amplitude to decrease or attenuate as it propagates. The frequency of the wave remains constant when moving between media. The speed of the wave is typically lower in a denser, lossy medium, and polarization change is not a guaranteed effect of entering a lossy medium.
Question 2: A transmission line with a characteristic impedance of 50 Ω is terminated with a load impedance of 100 Ω. What is the Voltage Standing Wave Ratio (VSWR) on the line?
- 1.5
- 0.5
- 2.0 (Correct answer)
- 0.333
Correct answer: 2.0
First, calculate the reflection coefficient (Γ) using the formula: Γ = (ZL - Z0) / (ZL + Z0). Here, ZL = 100 Ω and Z0 = 50 Ω. So, Γ = (100 - 50) / (100 + 50) = 50 / 150 = 1/3. Next, calculate the VSWR using the formula: VSWR = (1 + |Γ|) / (1 - |Γ|). VSWR = (1 + 1/3) / (1 - 1/3) = (4/3) / (2/3) = 2.0. A VSWR of 2.0 indicates a mismatch where the maximum voltage on the line is twice the minimum voltage.
Question 3: Which of Maxwell's equations states that magnetic monopoles do not exist and that magnetic field lines must form closed loops?
- Faraday's Law of Induction
- Ampère-Maxwell Law
- Gauss's Law
- Gauss's Law for Magnetism (Correct answer)
Correct answer: Gauss's Law for Magnetism
Gauss's Law for Magnetism, expressed in differential form as ∇ ⋅ B = 0, mathematically states that the divergence of the magnetic field is zero. This implies there are no sources or sinks (i.e., monopoles) for magnetic fields, and consequently, magnetic field lines must always form continuous, closed loops.
Question 4: In a hollow rectangular waveguide, which mode of propagation is characterized by having no electric field component in the direction of wave propagation and is typically the dominant mode?
- Transverse Magnetic (TM)
- Transverse Electric (TE) (Correct answer)
- Transverse Electromagnetic (TEM)
- Longitudinal Mode (LM)
Correct answer: Transverse Electric (TE)
Transverse Electric (TE) modes are characterized by the electric field vector being entirely perpendicular (transverse) to the direction of wave propagation. In standard rectangular waveguides, the TE10 mode has the lowest cutoff frequency and is therefore the dominant mode. TEM modes cannot propagate in a hollow single-conductor waveguide, and TM modes have a magnetic field that is entirely transverse.
Question 5: An engineer is designing a high-frequency circuit on a printed circuit board (PCB). As the frequency of the signals increases, the current tends to flow only near the surface of the copper traces. What is this phenomenon called?
- Hall Effect
- Proximity Effect
- Faraday Effect
- Skin Effect (Correct answer)
Correct answer: Skin Effect
The skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases with greater depths. This effect becomes more pronounced as the frequency increases, reducing the effective cross-section of the conductor and increasing its AC resistance.
Question 6: Which of the following describes the boundary condition for the tangential component of the electric field (E-field) at the surface of a perfect electrical conductor (PEC)?
- It is equal to the surface charge density.
- It is continuous and non-zero across the boundary.
- It must be zero. (Correct answer)
- It is perpendicular to the surface.
Correct answer: It must be zero.
At the surface of a perfect electrical conductor (PEC), the tangential component of the electric field must be zero (E_tan = 0). If a tangential component existed, it would exert a force on the free charges within the conductor, causing an infinite current to flow, which is not physically possible. Therefore, the E-field at the surface of a PEC can only have a normal component.
BEE Bachelor of Electrical Engineering Electromagnetic Fields and Waves Questions and Answers
An electromagnetic plane wave propagates from a lossless medium into a lossy medium.
Which of the following effects is expected to occur?