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Given an EM Wave find different values

  1. Nov 11, 2013 #1
    1. The problem statement, all variables and given/known data
    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)


    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. Nov 12, 2013 #2

    rude man

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    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.
     
  4. Nov 12, 2013 #3
    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?
     
  5. Nov 12, 2013 #4
    Would you mind helping with my other question that is the one I struggle with the most
     
  6. Nov 12, 2013 #5

    rude man

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    There is no such thing as a dielectric with er = 0.4.
     
  7. Nov 12, 2013 #6

    rude man

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    Which would that be?
     
  8. Nov 12, 2013 #7
  9. Nov 12, 2013 #8

    rude man

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    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.
     
  10. Nov 12, 2013 #9
    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)
     
  11. Nov 12, 2013 #10

    rude man

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    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.
     
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