# Electromagnetic Theory Questions and Answers – Plane Waves in Dielectrics

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This set of Electromagnetic Theory Question Bank focuses on “Plane Waves in Dielectrics”.

1. The loss tangent of a perfect dielectric will be
a) Zero
b) Unity
c) Maximum
d) Minimum

Explanation: Dielectrics have poor conductivity. The loss tangent σ/ωε will be low in dielectrics. For perfect dielectrics, the loss tangent will be minimum.

2. In pure dielectrics, the parameter that is zero is
a) Attenuation
b) Propagation
c) Conductivity
d) Resistivity

Explanation: There are no free charge carriers available in a dielectric. In other words, the charge carriers are present in the valence band, which is very difficult to start to conduct. Thus conduction is low in dielectrics. For pure dielectrics, the conductivity is assumed to be zero.

3. The total permittivity of a dielectric transformer oil (relative permittivity is 2.2) will be (in order 10-11)
a) 1.94
b) 19.4
c) 0.194
d) 194

Explanation: The total permittivity is the product of the absolute and the relative permittivity. The absolute permittivity is 8.854 x 10-12 and the relative permittivity(in this case for transformer oil) is 2.2. Thus the total permittivity is 8.854 x 10-12 x 2.2 = 1.94 x 10-11 units.
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4. The permeability of a dielectric material in air medium will be
a) Absolute permeability
b) Relative permeability
c) Product of absolute and relative permeability
d) Unity

Explanation: The total permeability is the product of the absolute and the relative permeability. In air medium, the relative permeability will be unity. Thus the total permeability is equal to the absolute permeability given by 4π x 10-7 units.

5. The attenuation in a good dielectric will be non- zero. State True/False.
a) True
b) False

Explanation: Good dielectrics attenuate the electromagnetic waves than any other material. Thus the attenuation constant of the dielectric will be non-zero, positive and large.

6. Calculate the phase constant of a dielectric with frequency 6 x 106 in air.
a) 2
b) 0.2
c) 0.02
d) 0.002

Explanation: The phase constant of a dielectric is given by β = ω√(με). On substituting for ω = 6 x 106 , μ = 4π x 10-7, ε = 8.854 x 10-12 in air medium, we get the phase constant as 0.02 units.

7. The frequency in rad/sec of a wave with velocity of that of light and phase constant of 20 units is (in GHz)
a) 6
b) 60
c) 600
d) 0.6

Explanation: The velocity of a wave is given by V = ω/β. To get ω, put v = 3 x 108 and β = 20. Thus ω = vβ = 3 x 108 x 20 = 60 x 108 = 6 GHz.

8. The relation between the speed of light, permeability and permittivity is
a) C = 1/√(με)
b) C = με
c) C = μ/ε
d) C = 1/με

Explanation: The standard relation between speed of light, permeability and permittivity is given by c = 1/√(με). The value in air medium is 3 x 108 m/s.

9. The phase constant of a wave with wavelength 2 units is
a) 6.28
b) 3.14
c) 0.5
d) 2

Explanation: The phase constant is given by β = 2π/λ. On substituting λ = 2 units, we get β = 2π/2 = π = 3.14 units.

10.The expression for intrinsic impedance is given by
a) √(με)
b) (με)
c) √(μ/ε)
d) (μ/ε)

Explanation: The intrinsic impedance is given by the ratio of square root of the permittivity to the permeability. Thus η = √(μ/ε) is the intrinsic impedance. In free space or air medium, the intrinsic impedance will be 120π or 377 ohms.

11.The electric and magnetic field components in the electromagnetic wave propagation are in phase. State True/False.
a) True
b) False

Explanation: In dielectrics, the electric and magnetic fields will be in phase or the phase difference between them is zero. This is due to the large attenuation which leads to increase in phase shift.

12. The skin depth of a wave with phase constant of 12 units inside a conductor is
a) 12
b) 1/12
c) 24
d) 1/24

Explanation: The skin depth is the reciprocal of the phase constant. On substituting for β = 12, we get δ = 1/β = 1/12 units.

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