BEE FREE BEE Bachelor of Electrical Engineering Engineering Electromagnetics Fundamentals Questions and Answers 2 — Questions and Answers
Question 1: A parallel-plate capacitor with plate area A and separation d is filled with a dielectric of permittivity ε. What is the capacitance?
- εA/d (Correct answer)
- εd/A
- A/(εd)
- d/(εA)
Correct answer: εA/d
The capacitance of a parallel-plate capacitor is C = εA/d, directly proportional to permittivity and area and inversely proportional to separation.
Question 2: What is the divergence of the electric field in a region containing volume charge density ρ_v according to Gauss's law in differential form?
- ρ_v / ε₀ (Correct answer)
- ε₀ / ρ_v
- ρ_v × ε₀
- Zero
Correct answer: ρ_v / ε₀
Gauss's law in differential form states ∇·E = ρ_v/ε₀, relating the divergence of the electric field to the local charge density.
Question 3: A conducting loop moves through a uniform, time-invariant magnetic field. What is the induced EMF in the loop?
- Zero (Correct answer)
- Maximum
- Equal to the flux
- Dependent on loop resistance
Correct answer: Zero
In a uniform and constant magnetic field, the total magnetic flux through a moving loop does not change, so by Faraday's law the induced EMF is zero.
Question 4: Which boundary condition holds for the tangential component of the electric field at an interface between two perfect dielectrics?
- E_t1 = E_t2 (Correct answer)
- D_t1 = D_t2
- E_t1 = 0
- ε₁E_t1 = ε₂E_t2
Correct answer: E_t1 = E_t2
The tangential component of the electric field is continuous across a boundary between two dielectrics with no surface charge.
Question 5: What is the skin depth in a good conductor proportional to?
- 1/√(πfμσ) (Correct answer)
- √(πfμσ)
- πfμσ
- 1/(πfμσ)
Correct answer: 1/√(πfμσ)
Skin depth δ = 1/√(πfμσ), showing that higher frequency, permeability, or conductivity causes fields to penetrate less deeply.
Question 6: In a lossless transmission line, what is the characteristic impedance Z₀ expressed in terms of distributed inductance L and capacitance C per unit length?
- √(L/C) (Correct answer)
- √(C/L)
- L/C
- LC
Correct answer: √(L/C)
For a lossless transmission line, the characteristic impedance is Z₀ = √(L/C), derived from the telegrapher's equations.
BEE FREE BEE Bachelor of Electrical Engineering Engineering Electromagnetics Fundamentals Questions and Answers 2
A parallel-plate capacitor with plate area A and separation d is filled with a dielectric of permittivity ε.
What is the capacitance?