Plane Waves in Lossy Dielectrics: Multiple Choice Quiz

Question 1

Which of the following is the wave equation for a plane wave propagating in a lossless dielectric?

Accepted Answer

∇²E - μɛω²E = 0

Answer

∇²H - μɛω²H = 0

Answer

∇²E + μɛω²E = 0

Answer

∇²H + μɛω²H = 0

Question 2

What is the transmission coefficient at normal incidence for a plane wave in a lossless dielectric?

Accepted Answer

T = (2η₁)/(η₁ + η₂)

Answer

T = (2η₁)/(η₁ + η₂)*e^(-αd)

Answer

T = (η₁ - η₂)/(η₁ + η₂)

Answer

T = (η₁ - η₂)/(η₁ + η₂)*e^(-αd)

Question 3

What is the Brewster angle for a plane wave at oblique incidence in a lossless dielectric?

Accepted Answer

θB = tan^(-1)(ε₁/ε₂)

Answer

θB = tan^(-1)(ε₁/ε₂)*e^(-αd)

Answer

θB = tan^(-1)(μ₁/μ₂)

Answer

θB = tan^(-1)(μ₁/μ₂)*e^(-αd)

Question 4

What is the skin depth of a plane wave in a lossless dielectric?

Accepted Answer

δ = ∞

Answer

δ = (2/ωμσ)^(1/2)

Answer

δ = (2/ωμσ)^(1/2)*e^(-αd)

Answer

δ = (2/ωεσ)^(1/2)

Question 5

Which of the following statements is NOT true about plane waves in lossy dielectrics?

Accepted Answer

They are always transverse magnetic (TM) waves

Answer

They can exhibit attenuation due to energy dissipation

Answer

Their intrinsic impedance can be complex, indicating both energy storage and dissipation

Answer

They are characterized by the wave equation describing their propagation

Question 6

When a plane wave is incident normally on a lossy dielectric interface, what is the nature of the wave behavior?

Accepted Answer

Partial reflection and partial transmission

Answer

Total reflection

Answer

Total transmission

Answer

Complete absorption

Question 7

What is the significance of the complex permittivity in lossy dielectrics?

Accepted Answer

It incorporates the effects of energy dissipation due to conductivity

Answer

It simplifies the analysis of wave propagation

Answer

It has no physical significance

Answer

It determines the phase velocity of the wave

Question 8

The Brewster angle, a special angle of incidence, is associated with which phenomenon in lossy dielectrics?

Accepted Answer

Zero reflection coefficient

Answer

Total reflection

Answer

Total transmission

Answer

Maximum transmission coefficient

Question 9

The intrinsic impedance of a lossy dielectric medium is given by which expression?

Accepted Answer

(μ/ε)^(1/2)(1 - jδ)^(1/2)

Answer

(μ/ε)^(1/2)(1 + jδ)^(1/2)

Answer

μ/ε

Answer

ε/μ

Question 10

The transmission coefficient for a plane wave incident normally on a lossy dielectric boundary is given by which formula?

Accepted Answer

2Z₀/(Z + Z₀)

Answer

2Z₀/(Z - Z₀)

Answer

(Z + Z₀)/2Z₀

Answer

(Z - Z₀)/2Z₀

Question 11

Which expression represents the power transmitted through a lossy dielectric slab of thickness d?

Accepted Answer

P = P₀e^(-αd)

Answer

P = P₀(1 - e^(-αd))

Answer

P = P₀e^(-βd)

Answer

P = P₀(1 - e^(-βd))

Question 12

For a plane wave incident at an oblique angle on a lossy dielectric boundary, the polarization of the reflected wave is:

Accepted Answer

Elliptical in general

Answer

Linear in general

Answer

Linear only for TM polarization

Answer

Elliptical only for TE polarization

Question 13

For total internal reflection to occur at an interface between two lossy dielectrics, what condition must be satisfied?

Accepted Answer

The angle of incidence must exceed the critical angle.

Answer

The angle of incidence must be below the Brewster angle.

Answer

The angle of incidence must match the critical angle.

Question 14

Consider a plane wave propagating in a lossy dielectric. Which of the following is the correct form of the wave equation?

Accepted Answer

∇²E - μσ∂E/∂t + ∂²E/∂t² = 0

Answer

∇²E - μσ∂E/∂t - ∂²E/∂t² = 0

Answer

∇²E + μσ∂E/∂t + ∂²E/∂t² = 0

Answer

∇²E + μσ∂E/∂t - ∂²E/∂t² = 0

Question 15

The unit of intrinsic impedance is:

Accepted Answer

Ohms per meter

Answer

Farads per meter

Answer

Henrys per meter

Answer

Siemens per meter

Question 16

A characteristic of plane waves in lossy dielectrics is that they:

Accepted Answer

Attenuate as they propagate

Answer

Have a shorter wavelength than in lossless dielectrics

Answer

Have a phase velocity independent of frequency

Answer

Are always polarized

Question 17

Which of the following is the wave equation for a lossy dielectric medium?

Accepted Answer

∇²E - μ₀ε₀εᵣω²E - μ₀σE = 0

Answer

∇²E - μ₀ε₀εᵣω²E = 0

Answer

∇²E - μ₀ε₀εᵣω²E + μ₀σE = 0

Answer

∇²E + μ₀ε₀εᵣω²E - μ₀σE = 0

Question 18

In lossy dielectrics, how do wave propagation characteristics differ from those in lossless dielectrics? Explain the reasons behind these differences.

Accepted Answer

Lossy dielectrics have higher wave attenuation and lower phase velocity than lossless dielectrics.

Answer

Lossy and lossless dielectrics have identical wave propagation characteristics.

Answer

Lossless dielectrics have higher intrinsic impedance than lossy dielectrics.

Answer

Total internal reflection is only possible in lossy dielectrics.

Question 19

What is the intrinsic impedance of a lossy dielectric?

Accepted Answer

√(μ/ϵ)(1 + jσ/ωϵ)

Answer

√(μ/ϵ)(1 - jσ/ωϵ)

Answer

√(μϵ)(1 + jσ/ωϵ)

Answer

√(μϵ)(1 - jσ/ωϵ)

Question 20

The phase velocity of a plane wave in a lossy dielectric is:

Accepted Answer

v = c/(√(1 + (σ/ωϵ)²))

Answer

v = c/(1 + (σ/ωϵ)²)

Answer

v = c√(1 + (σ/ωϵ)²)

Question 21

The group velocity of a plane wave in a lossy dielectric is:

Accepted Answer

u = c/(√(1 + (σ/ωϵ)²)^3)

Answer

u = c√(1 + (σ/ωϵ)²)^3

Answer

u = c/(1 + (σ/ωϵ)²)^3

Question 22

Which of the following materials is NOT a typical lossy dielectric?

Accepted Answer

Glass

Answer

Seawater

Answer

Water

Question 23

Which of the following is a property of plane waves in lossy dielectrics?

Accepted Answer

Exponentially decaying amplitude

Answer

Constant phase velocity

Answer

Unchanged wave number

Question 24

The loss tangent of a lossy dielectric is defined as:

Accepted Answer

tanδ = ε''/ε'

Answer

tanδ = ε'/ε''

Answer

tanδ = (ε' + ε'')/ε''

Answer

tanδ = ε''/(ε' + ε'')

Question 25

Plane waves in a lossy dielectric can be used to model:

Accepted Answer

Propagation of electromagnetic waves in biological tissues

Answer

Propagation of light in vacuum

Answer

Conduction of electricity in metals

Question 26

The propagation constant in a lossy dielectric medium is expressed as:

Accepted Answer

γ = α + jβ

Answer

γ = α - jβ

Answer

γ = jα + β

Answer

γ = αj + β

Question 27

The attenuation constant in a lossy dielectric medium is a measure of:

Accepted Answer

Power loss per unit length

Answer

Wave impedance at a specific frequency

Answer

Phase change per unit length

Answer

Energy stored per unit volume

Question 28

The phase constant in a lossy dielectric medium is a measure of:

Accepted Answer

Phase shift per unit length

Answer

Power loss per unit length

Answer

Energy stored per unit volume

Question 29

A plane wave is incident normally on a lossy dielectric interface. The reflection coefficient is found to be 0.5. What is the transmission coefficient?

Accepted Answer

0.5

Answer

1

Answer

0

Answer

-0.5

Question 30

What is the effect of increasing the conductivity of a dielectric on the attenuation constant of a plane wave?

Accepted Answer

The attenuation constant increases.

Answer

The attenuation constant decreases.

Answer

The attenuation constant remains constant.

Answer

The attenuation constant becomes zero.

Question 31

The skin depth of a plane wave in a lossy dielectric is a measure of:

Accepted Answer

The distance over which the wave amplitude decreases to 1/e of its initial value

Answer

The phase velocity of the wave

Answer

The wavelength of the wave

Question 32

A lossy dielectric can be characterized by which of the following parameters?

Accepted Answer

Permittivity, permeability, and conductivity

Answer

Permittivity and conductivity only

Answer

Permittivity and permeability only

Answer

Permeability and conductivity only

Question 33

A plane wave propagating in a lossy dielectric medium experiences attenuation. What is the primary factor responsible for this attenuation?

Accepted Answer

Conductivity of the dielectric material

Answer

Frequency of the wave

Answer

Permeability of the dielectric material

Answer

Permittivity of the dielectric material

Question 34

A plane wave is incident normally on the boundary between air and a lossy dielectric. How does the reflection coefficient differ from that of a perfect dielectric?

Accepted Answer

The reflection coefficient in the lossy dielectric is complex, indicating a phase shift in the reflected wave.

Answer

The reflection coefficient in the lossy dielectric is always smaller.

Question 35

What is the definition of skin depth in a lossy dielectric?

Accepted Answer

The depth at which the amplitude of a plane wave decays to 1/e of its initial value.

Answer

The distance at which the wave is completely absorbed.

Answer

The distance at which the wave phase shifts by 180 degrees.

Answer

The distance the wave travels in one period.

Question 36

How does the skin depth of a plane wave change as the frequency increases in a lossy dielectric?

Accepted Answer

Skin depth decreases.

Answer

Skin depth oscillates with frequency.

Answer

Skin depth increases.

Answer

Skin depth remains constant.

Question 37

A plane wave is incident on a lossy dielectric with a very high conductivity. What happens to the wave's propagation?

Accepted Answer

The wave is heavily attenuated and cannot penetrate deeply into the dielectric.

Answer

The wave is reflected entirely at the interface.

Answer

The wave speed increases significantly.

Answer

The wave propagates through the dielectric without significant attenuation.

Question 38

In a lossy dielectric, the wave impedance is complex. What does the phase angle of the complex wave impedance represent?

Accepted Answer

The phase difference between the electric and magnetic field components of the wave.

Answer

The wave velocity in the dielectric.

Answer

The attenuation constant of the wave.

Answer

The energy loss per unit length of propagation.

Question 39

Which of the following is NOT a typical application of the study of plane waves in lossy dielectrics?

Accepted Answer

Designing optical fibers for high-speed communication.

Answer

Understanding signal loss in underground cables.

Answer

Analyzing radio wave propagation through the atmosphere.

Answer

Evaluating the performance of antennas in lossy environments.

Question 40

A plane wave propagates in a lossy dielectric medium with conductivity σ, permittivity ε, and permeability μ. What is the correct expression for the intrinsic impedance of the medium?

Accepted Answer

√(μ/ε) * (1 + jσ/ωε)

Answer

√(ε/μ)

Answer

√(ε/μ) * (1 + jσ/ωε)

Answer

√(μ/ε)

Question 41

A uniform plane wave in free space is normally incident on a lossy dielectric slab of thickness d. The wave has an electric field amplitude of E0 at the boundary. If the intrinsic impedance of the dielectric is given by Z = Z0 * (1 + j), where Z0 is the impedance of free space, what is the amplitude of the transmitted electric field at the far side of the slab?

Accepted Answer

E0 * e^(-σd/2)

Answer

E0 * e^(-jσd/2)

Answer

E0

Answer

E0 * e^(-2σd)

Question 42

A plane wave is obliquely incident upon a boundary between two lossless dielectric media with permittivities ε1 and ε2, respectively. If the angle of incidence is θ1 and the angle of transmission is θ2, which of the following equations relates the two angles (Snell's Law)?

Accepted Answer

sin(θ1) / sin(θ2) = √(ε2/ε1)

Answer

cos(θ1) / cos(θ2) = √(ε2/ε1)

Answer

sin(θ1) / sin(θ2) = √(ε1/ε2)

Question 43

A plane wave is normally incident on a lossless dielectric slab of thickness d. The wave has an electric field amplitude of E0. If the reflection coefficient at the boundary is given by Γ = -0.2, what is the standing wave ratio (SWR) inside the slab?

Accepted Answer

1.25

Answer

1.5

Answer

0.75

Question 44

Which of the following boundary conditions must be satisfied at the interface between two lossy dielectric media?

Accepted Answer

The tangential components of E and H are continuous.

Answer

The normal components of E and H are continuous.

Answer

The divergence of E and H is continuous.

Question 45

A plane wave propagates in a lossy dielectric medium with loss tangent tan(δ). If the wavelength in the medium is λ, which of the following expressions represents the distance over which the wave amplitude decays to 1/e of its original value?

Accepted Answer

λ / (4π tan(δ))

Answer

λ tan(δ) / (2π)

Answer

λ / (8π tan(δ))

Answer

λ tan(δ) / (8π)

Question 46

A uniform plane wave is normally incident on a lossless dielectric slab of thickness d. If the wave has a power density of P0 in free space, what is the power density inside the slab?

Accepted Answer

P0

Answer

P0 * e^(-2σd)

Answer

2P0

Answer

P0 / 2

Question 47

Which of the following parameters is a unique property of lossy dielectric materials?

Accepted Answer

Loss tangent

Answer

Permittivity

Answer

Conductivity

Answer

Permeability

Question 48

A plane wave is obliquely incident on a boundary between a lossy dielectric and a perfect conductor. If the angle of incidence is θi, what is the angle of reflection?

Accepted Answer

- θi

Answer

90° - θi

Answer

180° - θi

Answer

θi

Question 49

Which of the following factors does NOT affect the intrinsic impedance of a lossy dielectric medium?

Accepted Answer

Frequency

Answer

Permeability

Answer

Permittivity

Answer

Conductivity

Question 50

The wave equation for a plane wave propagating in a lossy dielectric medium is given by:

Accepted Answer

∇²E - μω²(ε - jσ/ω)E = 0

Answer

∇²E - μω²(ε + jσ/ω)E = 0

Answer

∇²E + μω²(ε + jσ/ω)E = 0

Answer

∇²E + μω²(ε - jσ/ω)E = 0

Question 51

The intrinsic impedance of a lossy dielectric medium is given by:

Accepted Answer

η = √(μ/ε) * (1 - j(σ/ωε))

Answer

η = √(μ/ε) * (1 + j(σ/ωε))

Answer

η = (μ/ε) * (1 + j(σ/ωε))

Answer

η = (μ/ε) * (1 - j(σ/ωε))

Question 52

Which of the following is the characteristic attenuation constant in a lossy dielectric medium?

Accepted Answer

α = ω√(μ/ε) * √(ε'/2) * (1/2)

Answer

α = ω√(μ/ε) * √(ε'/4) * (1/4)

Answer

α = ω√(μ/ε) * √(ε'/4) * (1/2)

Answer

α = ω√(μ/ε) * √(ε'/2) * (1/4)

Question 53

For normal incidence of a plane wave on a lossy dielectric interface, the reflection coefficient is given by:

Accepted Answer

Γ = (η₁ - η₂)/(η₁ + η₂)

Answer

Γ = (2η₁)/(η₁ + η₂)

Answer

Γ = (2η₁)/(η₁ - η₂)

Answer

Γ = (η₁ + η₂)/(η₁ - η₂)

Question 54

For oblique incidence of a plane wave on a lossy dielectric interface, the transmission coefficient is given by:

Accepted Answer

T = 2η₁cos(θ₁)/(η₁cos(θ₁) + η₂cos(θ₂))

Answer

T = (η₁cos(θ₁) + η₂cos(θ₂))/(2η₁cos(θ₁))

Answer

T = 2η₁cos(θ₁)/(η₁cos(θ₁) - η₂cos(θ₂))

Answer

T = (η₁cos(θ₁) - η₂cos(θ₂))/(2η₁cos(θ₁))

Question 55

Which of the following is true about the Poynting vector in a lossy dielectric medium?

Accepted Answer

The average power flow is less than the incident power flow.

Answer

The average power flow is equal to the incident power flow.

Answer

The average power flow is greater than the incident power flow.

Question 56

What is the skin depth in a lossy dielectric medium?

Accepted Answer

δ = 1/α

Answer

δ = α/ω

Answer

δ = ω/α

Answer

δ = α

Question 57

Which of the following materials is an example of a lossy dielectric?

Accepted Answer

Seawater

Answer

Vacuum

Answer

Air

Answer

Teflon

Question 58

What is the effect of losses on the phase velocity of a plane wave in a lossy dielectric medium?

Accepted Answer

Phase velocity is reduced.

Answer

Phase velocity is increased.

Answer

Phase velocity is unaffected.

Answer

Phase velocity becomes complex.

Question 59

Which of the following applications utilizes plane waves in lossy dielectrics?

Accepted Answer

Microwave heating

Answer

Radar

Answer

Optical fibers

Answer

Antennas