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EM wave with circular polarization interferes with conductor

  1. Feb 21, 2016 #1
    1. The problem statement, all variables and given/known data
    EM wave with circular polarization travels in directon z interferes with perfect conducting surface xy.

    1. find reflected wave
    2. calculate induced charge density and surface current induced on conducting surface

    Can you verify if I started point 1. correctly, and give some idea how to calculate point 2. Because in Griffiths I can only find info that there are volume currents which in limit of perfect coonductor become true surface current.

    2. The attempt at a solution

    I started the first point

    $$
    E_I(z,t) = E_{0I}(\hat{x}+i\hat{y})e^{i(k_1z-\omega t)}
    $$
    $$
    B_I(z,t) = \frac{1}{v_1}E_{0I}(-i\hat{x}+\hat{y})e^{i(k_1z-\omega t)}
    $$

    $$
    E_R(z,t) = E_{0R}(\hat{x}-i\hat{y})e^{i(-k_1z-\omega t)}
    $$
    $$
    B_R(z,t) = -\frac{1}{v_1}E_{0R}(i\hat{x}+\hat{y})e^{i(-k_1z-\omega t)}
    $$

    $$
    E_T(z,t) = E_{0T}(\hat{x}+i\hat{y})e^{i(k_2z-\omega t)}
    $$
    $$
    B_T(z,t) = \frac{k_2}{\omega}E_{0T}(-i\hat{x}+\hat{y})e^{i(k_2z-\omega t)}
    $$

    Then I apply boundary conditions in [itex]z=0[/itex].
    [itex]B^\perp = 0[/itex] and [itex]E^\perp = 0[/itex] so I only parallel conditions left
    $$
    E^\parallel_1 - E^\parallel_2 = 0
    $$
    and
    $$
    \frac{1}{\mu_1}B^\parallel_1 - \frac{1}{\mu_2}B^\parallel_2 = K_{free} \times \hat{n}
    $$

    Griffiths in 9.4.2 says that [itex]K_{free} = 0[/itex], but I'm not sure if its still true with perfect conductor. For [itex]E[/itex] I have
    $$
    (\hat{x}+i\hat{y})E_{0T} + (\hat{x}-i\hat{y})E_{0R} = (\hat{x}+i\hat{y})E_{0T}
    $$
    and for [itex]B[/itex]
    $$
    (-i\hat{x}+\hat{y})\frac{1}{\mu_1v_1}E_{0T} + (-i\hat{x}-\hat{y})\frac{1}{\mu_1v_1}E_{0R} = (-i\hat{x}+\hat{y})\frac{k_2}{\mu_2\omega}E_{0T}
    $$

    which need to be solved, but I'm not sure if I treated polarization right …
     
  2. jcsd
  3. Feb 26, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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