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I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Lets say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the line and the signal wavefront propagates at the speed of light from the start to the line to infinite. My physical understanding is that conventional current moves on average at drift velocity (a few mm/second) even though the signal propagates at the speed of light. This is due to the fact that the lines are electrically neutral and the electric field associated with the wavefront travelling at the speed of light is terminated by mobile charges moving slightly toward or away from the conductor surface, bearing in mind that the lattice is fixed positive charge. This effectively supplies the surface charges terminating the transverse electric field.

Now, my thoughts were confirmed by the book 'The Power and Beauty of Electromagnetic Fields', by Frederic R. Morgenthaler. (Chapter 18 - TEM Transmission Lines - pg. 189-191)

However, as my knowledge of relativity is rather limited, I am struggling to understand one of his equations;

j(x,y)=ρ

_{0}(x,y)c

which he calls the relativistic current-density as c is the speed of light. He says this equation "arises from imposition of the Lorentz-gauge and conservation of charge", without any derivation.

I do not know where this comes from and physically its distinction from my classical understanding of convection current density j=ρu where u is the drift velocity. It appears that his equation is a fictional current density relating to the relativistic signal propagating at the speed of light?

Can anyone shed any light on this equation or provide a derivation?

Thanks in advance, apologies for any ignorance on my behalf...

Regards,

Chris