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yungman

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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,

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

The problem is the book still give:

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

This mean

Thanks

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

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