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EM wave right above and right below the conducting surface.

  1. Jun 30, 2011 #1
    Assume a infinite depth good conductor block with width in y and length in x direction. Boundary is at z=0 and air is at z=-ve and conductor at z=+ve. Let a voltage apply across the length of the block in x direction so a current density established in +ve x direction. We want to look at the EM at the boundary just above and just below the surface.

    1) We know at [itex] z=0^-[/itex](in air):

    [tex]\tilde{E_-}(z) = \hat x E_0 e^{-\alpha z} e^{-j\beta z} \;\hbox { and }\; \tilde B = \frac 1 {\eta_0} \hat z \times \vec E_-(z)\;=\; \hat y \frac {\vec E_-(z)}{\eta_0}[/tex]

    In air, H is perpendicular to E only because [itex]\eta_0[/itex] is real and don't have a phase shift.





    2) We know tangential E continuous cross boundary therefore at [itex] z=0^+[/itex](in conductor):

    [tex]\tilde{E_+}(z) = \hat x E_0 e^{-\alpha z} e^{-j\beta z} \;\hbox { and }\; \tilde B_+ = \frac 1 {\eta_c} \hat z \times \vec E_-(z) [/tex]

    Here [itex]\eta_c[/itex] is complex and therefore has a phase shift, actually the phase angle is [itex]\theta=45^0[/itex]. This mean B is no longer perpendicular to E even though B also propagate in z direction.





    The problem is the book still give:

    [tex] \tilde B_+(z)=\hat y \frac {\tilde E_+(z)}{\eta_c}[/tex]

    This mean B is still perpendicular to E inside the good conductor. I don't understand this. Please help me.

    Thanks
     
    Last edited: Jun 30, 2011
  2. jcsd
  3. Jun 30, 2011 #2
    I think I understand it now. I just want to verify this:

    Even in good conductor, the EM wave is still TEM where E and B are perpendicular to each other and both perpendicular to the direction of propagation. The difference compare to the TEM in lossless free space is the E and B are out of phase in good conductor because [itex]\eta_c[/itex] of metal is complex. In free space that is lossless, [itex]\eta_0[/itex] is 377 ohm and is real, so E and B are in phase.

    Can anyone verify this
     
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