Electromagnetics: Plane Wave Propagation, Unknown Medium

[Captain1024]

Homework Statement

Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is

, 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

. Where

, and

. 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

 

[rude man]

Homework Statement

Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is

, 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

. Where

, and

. 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.