I am currently studying transmission of em waves and skin effect is puzzling me. Let us consider an em wave propogating in z-direction with electric field in x-direction & magnetic field in y-direction. Now, we will find that $\alpha$, attenuation constant is proportional to $\sigma$, conductivity of the medium. Is it not contradictory to common sense that a better conductor should have smaller attenuation constant? Since this leads to skin effect I am asking this question. Also, we observe that this attenuation is along the direction of propogation i.e. along z-axis, so why do standard texts say that the variation is with respect to depth or in other words, there is decrease of electric field as one moves towards the center of the cylindrical line? The wave is propogating along the line(z-axis) so should it not diminish in strength as z increases?
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$\begingroup$ Madhusudana, please ask nicely. Nobody here owes you an answer. Could it be that you misunderstand the textbook? "Conductivity of the medium" usually means the insulating material that fills the empty space of the waveguide or coaxial cable, it's not the conductivity of the metal that the waveguide is made of. Skin effect would be in addition to this effect of the insulator but is usually not the largest source of attenuation of many technically utilized cables. $\endgroup$– CuriousOneCommented May 13, 2015 at 5:15
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$\begingroup$ Note that the wave is mainly propagating outside the conductor and a little bit of it is lost in the metal, so that is a small part of the wave going inward which is then attenuated correctly along its directon of propagation. $\endgroup$– Jos BergervoetCommented Feb 26 at 17:42
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The skin depth becomes smaller as the conductivity increases because the Ohmic dissipation of the wave energy increases.
The current density is given by $\vec{J} =\sigma \vec{E}$ and the work done per unit volume by the fields in moving charges in the conductor is $\vec{J}\cdot \vec{E} = \sigma E^2$.
The attenuation is in the direction of propagation of the wave. There is no discrepancy here. A cylindrical conductor is considered similar to a planar geometry if the skin depth is small compared with radius of the cylinder. So indeed, the fields decrease with depth into the conductor. The "z" axis here refers to depth into the conductor, not a coordinate along the axis of the cylinder.
