A transmission line consisting of two concentric circular cylinders of metal with conductivity a and skin depth ?, as shown, is filled with a uniform lossless dielectric (?, ?). ? ??? mode is propagated along this line. Section 8.1 applies.

(a) Show that the time-averaged power flow along the line is

where H₀ is the peak value of the azimuthal magnetic field at the surface of the inner conductor.

(b) Show that the transmitted power is attenuated along the line as P(z) = P₀e ^?2?z where

(c) The characteristic impedance Z₀ of the line is defined as the ratio of the voltage between the cylinders to the axial current flowing in one of them at any position z. Show that for this line

(d) Show that the series resistance and inductance per unit length of the line are

where ?_? is the permeability of the conductor. The correction to the inductance comes from the penetration of the flux into the conductors by a distance of order ?.

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