18. Two very large, parallel, perfectly conducting plates are separated by a distance b.
One plate coincides with the plane y = 0; the other, with the plane y = b.
(a) Find the electric and magnetic fields for a TEM wave of frequency \omega propagat-
ing in the z direction between the plates. Sketch the fields. What are the wave-
length, phase velocity, and group velocity of the wave?
(b) If the plates are not perfect conductors but have some finite conductivity \sigma, then
the amplitude of the wave will decrease exponentially as the wave travels along.
Estimate what distance in the z direction the wave can travel before it is attenu-
ated by a factor of e. Express your answer in terms of \omega, \sigma, b; assume that the
thickness of the plates is much larger than the skin depth.