Intrinsic Wave Impedance for Conductive Medium

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tquiva
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Homework Statement


I know that for air, the intrinsic impedance η is 377 Ω, but it becomes complex in a conductive medium. This fact is sort of hindering me in being able to answer a few problems consisting of electric and magnetic waves in a conductive medium, but I just wanted to clarify one thing.
Say, I am given H(z,t)=0.5cos(ωt-βz)ay+0.7cos(ωt-βz)ax

Homework Equations


I know that the intrinsic impedance for a conductive medium is:
Equation: eta* = sqrt(mu / (epsilon - j sigma/omega)) = sqrt(mu/epsilon) / [1 + (sigma/(omega epsilon))^2]^(1/4) * e^(j(1/2) tan^-1(sigma/(omega epsilon)))


The Attempt at a Solution


When σ=0 for one problem, I was left with:
Equation: eta star equals the square root of mu sub o divided by the quantity epsilon sub o times epsilon sub r.

But I do know that
Equation beta equals omega times the square root of mu sub zero times epsilon sub zero times epsilon sub r, with subscripts as written.


My question is, what in the world is u_o, ε_o, and ε_r ?
Am I supposed to figure this out or is this already provided in a table somewhere?
I have been trying to look in my book and online, but am getting confused easily.
Will someone please clarify this for me?
Any help is greatly appreciated!
 
Attachments
  • Equation: eta star equals the square root of mu over (epsilon minus j sigma over omega), equals the square root of (mu over epsilon) over [1 + (sigma over omega epsilon) squared] to the power 1/4, times e to the power j(1/2) tan inverse of (sigma over omega epsilon).
    Screen Shot 2011-11-06 at 6.12.32 PM.png
    3.7 KB · Views: 1,663
  • Formula for intrinsic impedance: eta star equals the square root of mu sub o divided by the product of epsilon sub o and epsilon sub r.
    Screen Shot 2011-11-06 at 6.15.09 PM.png
    1.2 KB · Views: 1,302
  • Equation beta equals omega times the square root of mu_0 epsilon_0 epsilon_r, written as plain text: β = ω√(μ₀ε₀ε_r).
    Screen Shot 2011-11-06 at 6.17.10 PM.png
    1 KB · Views: 1,297

Discussion

Those are all real constants. mu_0 and epsilon_0 are permeability and permittivity of free space, look them up anywhere, and epsilon_r is the relative permittivity of your medium (= epsilon/epsilon_0).

How you got as far as you did, which is pretty far, without knowing that is a bit of a mysrtery to me, and please believe that I'm nort trying to be condescending or insulting - just wondering!
 

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