EM Wave Propagation Homework.Incident/Transmitted Power Density

[derek l]

Homework Statement

An E field with f = 2.45*10^9 Hz passes through a material with the following properties

e_r = 10
u_r = 1
sigma = 1 (S/m)

The Incident E field has peak magnitude of 300 V/m at the air to surface boundary.

(a) *solved* Find the incident power density at the material surface

p_avg = 1/2*Real[E×H]

because η_o = 120π in free space

p_avg = (0.5)(300)(0.795) ≅ 120 W/m^2 similarly 300^2/2*η_o *correct*(b) Calculate transmitted power into the material at the surface boundary

Homework Equations

loss tangent of material = 0.6329 rad^-1 = 18°

The Attempt at a Solution

η = 106e^(j*18°)

H = 0.795e^(-αz)
E = H*η = 84.25

E = 84.25e^(-αz)

p_avg = 1/2*Real[E×H] = 33.48 *incorrect*

 

[TSny]

I'm not up on all the relationships between the E and H field amplitudes for the incident, transmitted and reflected waves. But I will point out a couple of things.

The Attempt at a Solution

η = 106e^(j*18°)

H = 0.795e^(-αz)

You didn't state what $\eta$ represents (maybe impedence?) nor how you arrived at η = 106e^(j*18°). So, it's hard to check your work here.

You are taking H for the transmitted wave at z = 0 to have the same value (0.795 units) as H for the incident wave. But, isn't there also a reflected wave? Shouldn't the amplitude of H for the transmitted wave at the interface be less than the amplitude for H for the incident wave?

 

[derek l]

I'm not up on all the relationships between the E and H field amplitudes for the incident, transmitted and reflected waves. But I will point out a couple of things.

You didn't state what $\eta$ represents (maybe impedence?) nor how you arrived at η = 106e^(j*18°). So, it's hard to check your work here.

You are taking H for the transmitted wave at z = 0 to have the same value (0.795 units) as H for the incident wave. But, isn't there also a reflected wave? Shouldn't the amplitude of H for the transmitted wave at the interface be less than the amplitude for H for the incident wave?

Oh yes I'm sorry. η is impedance. I calculated η for the material given the material properties. I agree with your point I will try to find the amplitude for H of the transmitted wave