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Wave in a conductor

  1. Jan 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Wangsness exercise 24-12
    A plane wave travels in the postiive z direction in a conductor with real conductivity.

    a) Find the instantaeous and time average power loss per unit volume due to resisitive heating for any z

    b) Find the total power loss per unit area between z= 0- and z approaching infinity

    c) Find the time average Poynting vector at any z

    2. Relevant equations
    Poynting vector is given by
    [tex] \vec{S} = \frac{1}{2} \Re (\vec{E} \times \vec{H*}) [/tex]
    For a conducting medium

    [tex] E = E_{0a} e^{-\beta z} e^{i(az-\omega t+ \upsilon} [/tex]
    [tex] B= \frac{|k|}{\omega} \hat{z} \times E_{0a} e^{-\beta z} \cos (\alpha z-\omega t + \upsilon + \Omega) [/tex]

    3. The attempt at a solution
    Im a little stumped here

    per unit area it would be the [tex] <S> \bullet \vec{n} [/tex]

    but per unit volume??

    The instantaneous would simply the derivative of the prveious quantity with respect to time.. right/

    FOr total power loss we need to integrate the power oss per unit volume over hte whole volume. What is the shape of the condutor though??
     
  2. jcsd
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