A uniform plane wave is defined as: E(x,t)=120(2π×107 t-2πx) ax (V/m) and H(x,t)=1.5(2π×107 t-2πx) az (A/m). Select the correct answer:Select the correct answer:a.Polarisation x, wave impedance η=100 Ω, phase velocity up=5×106 (m/s)b.Polarisation y, wave impedance η=377 Ω, phase velocity up=3×108 (m/s)c.Polarisation x, wave impedance η=100 Ω, phase velocity up=314×107 (m/s)d.Direction of propagation z, Polarisation x, wave impedance η=100 Ωe.Polarisation x, wave impedance η= 80 Ω, phase velocity up=1×107 (m/s)
Question
A uniform plane wave is defined as: E(x,t)=120(2π×107 t-2πx) ax (V/m) and H(x,t)=1.5(2π×107 t-2πx) az (A/m). Select the correct answer:Select the correct answer:a.Polarisation x, wave impedance η=100 Ω, phase velocity up=5×106 (m/s)b.Polarisation y, wave impedance η=377 Ω, phase velocity up=3×108 (m/s)c.Polarisation x, wave impedance η=100 Ω, phase velocity up=314×107 (m/s)d.Direction of propagation z, Polarisation x, wave impedance η=100 Ωe.Polarisation x, wave impedance η= 80 Ω, phase velocity up=1×107 (m/s)
Solution
To answer this question, we need to understand the properties of a uniform plane wave.
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Polarization: The polarization of a wave is determined by the direction of the electric field vector E. In this case, the electric field E is in the x direction (as indicated by ax), so the polarization is x.
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Wave impedance (η): The wave impedance is the ratio of the electric field strength E to the magnetic field strength H. In this case, E = 120 V/m and H = 1.5 A/m, so η = E/H = 120/1.5 = 80 Ω.
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Phase velocity (up): The phase velocity of a wave is the speed at which the phase of the wave propagates in space. This is given by the ratio of the frequency to the wave number. In this case, the frequency is 2π×107 Hz and the wave number is 2π m^-1, so up = frequency/wave number = (2π×107)/(2π) = 1×107 m/s.
Therefore, the correct answer is e. Polarisation x, wave impedance η= 80 Ω, phase velocity up=1×107 (m/s).
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