Question

Consider our standard coax cable as an “infinite” length wire of radius a surrounded by a thin conducting cylinder, coaxial with the wire, with inner radius b and outer radius c. Again, assume
a < b
ab and cbb (thin shell and wire), as show in the figure.

We now want to investigate energy flow in the same cylindrical coax cable defined above. However, for now, let’s just look at fields constant in time, not varying in time. Assume that constant current I flows in the +z direction on the inner wire and that total current I flows in the opposite direction in the shell. Also assume that there is a constant voltage difference V between the wire and the shell.
a) For this steady current and voltage case: Find E and B everywhere in space. You may assume that the coax cable (wire plus shell) is neutral.
b) Calculate the Poynting vector S everywhere. The magnitude of S gives the energy flux density and represents the power per area moving through space. Does its direction make sense for the coax? Integrate this flux through the cross sectional area of the coax to find the power transported down the coax line. Does your answer make sense relative to the circuit maintaining the current and voltage? Briefly, comment!

Answer 1

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