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EM Waves in Vacuum

  1. Jan 8, 2014 #1
    1. The problem statement, all variables and given/known data
    EM Waves propagating through vacuum towards the x-direction approaches a conducting surface at x = 0.

    Part (a): Prove the following relations. Find the boundary conditions for [tex]E [/tex] and [tex]B[/tex] if charge density [tex]σ[/tex] and current density [tex]s[/tex] exists on the surface.

    Part (b): Find [tex]B[/tex] in terms of [tex]E_0[/tex]

    Part (c): Show the reflected wave has the following form:

    Part (d) Find magnetic field of reflected wave and [tex]s[/tex]


    2. Relevant equations



    3. The attempt at a solution

    Part(a)
    33xbj9w.png

    Part(b)
    migps3.png

    Part(c)

    This is the part that disturbs me. I assumed the free current s = 0 and σ = 0. Usually [tex]k[/tex] would be perpendicular to the surface, making derivations easier.

    I actually got perpendicular reflected E-field = 0, which is wrong..
    But, I got parallel reflected E-field = - incoming parallel E-field, which is right

    rms6rn.png

    I'm confused - If it's a perfect conductor it should have no free charge or currents, but the question says it does. Then again, in order to derive the reflected e-field, we need to assume they are 0.
     
  2. jcsd
  3. Jan 10, 2014 #2
    Edit: Question here
    29zs96c.png
     
  4. Jan 13, 2014 #3
    bumpp
     
  5. Jan 15, 2014 #4
  6. Jan 16, 2014 #5
    bumppp
     
  7. Jan 17, 2014 #6
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