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Electromagnetics: Plane Wave Propagation, Unknown Medium

  • #1

Homework Statement


Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is
gif.latex?28.1%5Cangle%2045%5E%5Ccirc%20%5C%20%28%5COmega%29.gif
, and the skin depth is 2m.
Determine:
a) The conductivity of the medium
b) The wavelength in the medium
c) The phase velocity.

Answer to a) 2.52x10^-2 S/m

Homework Equations


N/A

The Attempt at a Solution


I need to know what type of medium this wave is traveling through. We learned five types in class: Perfect Dielectric, Low-Loss Dielectric, Quasi-Conductor, Good Conductor, Perfect Conductor. The way I learned to determine the type of medium was by using a ratio of
gif.latex?%5Cfrac%7B%5Cepsilon%27%27%7D%7B%5Cepsilon%27%7D.gif
. Where
gif.latex?%5Cepsilon%27%27%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Comega%7D.gif
, and
gif.latex?%5Cepsilon%27%20%3D%20%5Cepsilon.gif
. How can I determine this ratio if one of the terms in the ratio is unknown (namely, the conductivity ##\sigma##)? The angle ##45^\circ## was mentioned in class when we were talking about good conductors. And, the phase angle of the intrinsic impedance is ##45^\circ##. But, is there a method for determining medium type using phase angle of the intrinsic impedance?

-Captain1024
 
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Answers and Replies

  • #2
18,050
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
rude man
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Homework Statement


Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is
gif.latex?28.1%5Cangle%2045%5E%5Ccirc%20%5C%20%28%5COmega%29.gif
, and the skin depth is 2m.
Determine:
a) The conductivity of the medium
b) The wavelength in the medium
c) The phase velocity.

Answer to a) 2.52x10^-2 S/m

Homework Equations


N/A

The Attempt at a Solution


I need to know what type of medium this wave is traveling through. We learned five types in class: Perfect Dielectric, Low-Loss Dielectric, Quasi-Conductor, Good Conductor, Perfect Conductor. The way I learned to determine the type of medium was by using a ratio of
gif.latex?%5Cfrac%7B%5Cepsilon%27%27%7D%7B%5Cepsilon%27%7D.gif
. Where
gif.latex?%5Cepsilon%27%27%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Comega%7D.gif
, and
gif.latex?%5Cepsilon%27%20%3D%20%5Cepsilon.gif
. How can I determine this ratio if one of the terms in the ratio is unknown (namely, the conductivity ##\sigma##)? The angle ##45^\circ## was mentioned in class when we were talking about good conductors. And, the phase angle of the intrinsic impedance is ##45^\circ##. But, is there a method for determining medium type using phase angle of the intrinsic impedance?

-Captain1024
If and only if conductivity is zero, the intrinsic impedance η is real. There is a formula relating η to μ, ε, ω and conductivity γ. Here η has real and imaginary parts.
There is another formula relating skin depth δ to ω, μ and γ. δ also has real and imaginary parts here.
From the given data (ω and the real and imaginary parts of η) you can answer the question.
 
Last edited:

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