Given an EM Wave find different values

[DODGEVIPER13]

Homework Statement

The magnetic field intensity of an electromagnetic wave that propagates in vacuum is described with the following phasor notation: (H_{z} = H_{0}e^{+jkx}u_{z}) if the previous equation is hard to read maybe this will be easier: Hz=H0e^(+jkx)Uz. Assuming that the frequency of oscillation of the wave is omega, determine:

1) Electric Field Intensity
2) Average Power (use poynting theorem)
3) How would the wavelength change if the wave propagates in a dielectric with
epsilon_{r}=0.4
4)If the wave propagates in a lossy medium with gamma=2.3+j3.4, describe its electric field.
P=(Ez x Hz)/(2)

Homework Equations

The Attempt at a Solution

I honestly have looked at this problem long and hard and still do not understand. Can anyone give me a push maybe some equations to start with or a pointer in the right direction of where to look. The book has no example problem like this and I have seen nothing of the sort on homework any help is appreciated?

 

[rude man]

1) what is the relationship between H and E for a plane wave such as yours?
2) poynting vector
3) think of light. what happens to velocity in an medium with insdex of refraction > 1? what stays constant, what changes?
4) for this you have to delve into your textbook.

 

[DODGEVIPER13]

Heh ended up figuring it out took me a while but I got it done I get
part (a) -120∏H0e^(jkx)Uy
part (b) Pavg=(120∏H^2)/2
part (c) it would increase if εr=0.4 however this is impossible as εr≥1
part (d) E=E0e^-(2.3x)e^j(ωt-βx)Uy

are these ok?

 

[DODGEVIPER13]

Would you mind helping with my other question that is the one I struggle with the most

 

[rude man]

part (c) it would increase if εr=0.4 however this is impossible as εr≥1

There is no such thing as a dielectric with e_r = 0.4.

 

[rude man]

Would you mind helping with my other question that is the one I struggle with the most

Which would that be?

 

[DODGEVIPER13]

https://www.physicsforums.com/showthread.php?t=722144 this one and yes I agree with epsilon r = 0.4 is impossible

 

[rude man]

Heh ended up figuring it out took me a while but I got it done I get
part (d) E=E0e^-(2.3x)e^j(ωt-βx)Uy

What happened to the imaginary part of gamma? Hint: β is larger in a conducting medium than in a non-conducting one. If goes up, what happens to λ for a given w?

Let gamma = alpha + j beta
and put gamma in the exponent of your wave: E₀exp(jwt - gamma*x)

You should then be able to describe in words what happens to an incident plane wave when it goes from a vacuum to a dielectric with finite conductivity.

 

[DODGEVIPER13]

Well k=beta=2∏/λ so for beta to increase I would think lamda would get smaller right? I thought I did have the imaginary part I just plugged into an equation using gamma=σ+jβ and then E(z,t)=Eye^(-αx)e^(jωt-jβz)

 

[rude man]

Well k=beta=2∏/λ so for beta to increase I would think lamda would get smaller right? I thought I did have the imaginary part I just plugged into an equation using gamma=σ+jβ and then E(z,t)=Eye^(-αx)e^(jωt-jβz)

Right. λ gets smaller (for a given ω).

I should not have mentioned that β gets larger in a conductor since you're already given β in the conductor.

Anyway, all your expressions look right now.

I'll try to get to your other problem sometime.