Test: Plane Waves in Good Conductor & Dielectrics

Answer: c
Explanation: In conductors, the conductivity will be more. Thus the loss tangent σ/ωε will be maximum.

Answer: a
Explanation: The total permittivity is the product of the absolute and the relative permittivity. For metals or conductors, the relative permittivity is unity. Thus the permittivity is simply the absolute permittivity.

Answer: c
Explanation: The total permeability is the product of the absolute and the relative permeability. For metals or conductors, the relative permittivity is not unity. Thus the permittivity is the product of absolute and relative permeability.

Answer: d
Explanation: The phase constant and the attenuation constant are both the same in the case of conductors. Given that the attenuation constant is 0.04, implies that the phase constant is also 0.04.

Answer: a
Explanation: The attenuation constant of a conductor is given by α = √(ωμσ/2). On substituting ω = 10⁶, σ = 200 and μ = 4π x 10^-7, we get α = 11.2 units.

Answer: d
Explanation: The skin depth is the measure of the depth upto which an EM wave can penetrate through the conductor surface. It is the reciprocal of the attenuation constant. On substituting for α = 7, we get δ = 1/α = 1/7 units.

Answer: a
Explanation: The velocity is the ratio of the frequency to the phase constant. In conductors, the phase constant is given by √(ωμσ/2). On substituting for β,ω in v, we get v = √(2ω/μσ) units

Answer: c
Explanation: The electric and magnetic component, E and H respectively have a phase difference of 45 degrees. This is due to the wave propagation in conductors in the air medium.

Answer: a
Explanation: The conductors or metals do not support EM wave propagation onto them due the skin effect. This is the reason why mobile phones cannot be used inside lifts.

Answer: a
Explanation: The propagation constant is the sum of the attenuation constant and the phase constant. In conductors, the attenuation and phase constant both are same and it is given by √(ωμσ/2). Their sum will be √(ωμσ), is the propagation constant.

Answer: c
Explanation: The refrigerator, electric fan and relays are electrical devices. They do not use electromagnetic energy as medium of energy transfer. The mobile transponder is an antenna, which uses the EM waves for communication with the satellites.

Answer: d
Explanation: The intrinsic impedance in a conductor is given by η = √(ωμ/2σ) x (1+j). The phase shift is represented by the 1+j term. In polar form it indicates 45 degree phase shift.

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

Answer: c
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.

Answer: a
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.

Answer: a
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.

Answer: a
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.

Answer: c
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.

Answer: a
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 10^{8 x 20 = 60 x 108 = 6 GHz.}

Answer: a
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.

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

Answer: c
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.

Answer: a
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.

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