BEE Engineering Electromagnetics Fundamentals 5 — Questions and Answers
Question 1: The magnetization M of a magnetic material is related to the magnetic susceptibility χ_m and H by:
- M = χ_m H (Correct answer)
- M = H / χ_m
- M = μ₀χ_m H
- M = B / χ_m
Correct answer: M = χ_m H
By definition, M = χ_m H, where χ_m is dimensionless and positive for paramagnetic materials.
Question 2: In the method of images, a point charge +Q placed at height h above an infinite grounded conducting plane is equivalent to:
- +Q at height -h (below the plane)
- -Q at height -h (below the plane) (Correct answer)
- +2Q at height h
- -Q at the plane surface
Correct answer: -Q at height -h (below the plane)
The image charge is -Q placed at distance h on the opposite side of the grounded plane to enforce V = 0 on the surface.
Question 3: Ampere's law with Maxwell's displacement current correction in integral form is:
- ∮H·dl = I_enc + ∬(∂D/∂t)·dS (Correct answer)
- ∮H·dl = I_enc - ∬(∂D/∂t)·dS
- ∮H·dl = I_enc + ε₀(∂Φ_E/∂t)
- ∮H·dl = ∬J·dS
Correct answer: ∮H·dl = I_enc + ∬(∂D/∂t)·dS
Maxwell added the displacement current ∂D/∂t to Ampere's law: ∮H·dl = I_enc + ∬(∂D/∂t)·dS.
Question 4: The critical angle for total internal reflection when light passes from glass (n=1.5) to air (n=1.0) is approximately:
- 41.8° (Correct answer)
- 48.2°
- 33.6°
- 56.4°
Correct answer: 41.8°
θ_c = arcsin(1.0/1.5) = arcsin(0.667) ≈ 41.8°, the minimum angle for total internal reflection.
Question 5: The torque T experienced by a magnetic dipole m in a uniform magnetic field B is:
- T = m × B (Correct answer)
- T = m · B
- T = B × m
- T = m / B
Correct answer: T = m × B
The torque is T = m × B, tending to align the magnetic moment with the applied field.
Question 6: The power dissipated per unit volume in a conducting medium with conductivity σ and electric field E is:
- P = σE
- P = σE² (Correct answer)
- P = E²/σ
- P = σ²E
Correct answer: P = σE²
Ohmic power loss per unit volume is P = J·E = σE·E = σE², known as Joule heating.
Question 7: Which parameter determines the ratio of conduction current to displacement current in a material at angular frequency ω?
- Loss tangent tan δ = σ/(ωε) (Correct answer)
- Skin depth δ = √(2/ωμσ)
- Phase constant β = ω√(με)
- Reflection coefficient Γ
Correct answer: Loss tangent tan δ = σ/(ωε)
The loss tangent tan δ = σ/(ωε) = J_c/J_d is the ratio of conduction to displacement current density magnitude.
BEE Engineering Electromagnetics Fundamentals 5
The magnetization M of a magnetic material is related to the magnetic susceptibility χ_m and H by: