An infinitely long coaxial waveguide is formed in the vacuum volume between two concentric, perfectly conducting cylinders with radii b and a > b.
(a) Find E and B for the TE and TM modes of this guide and find (but do not try to solve) the transcendental equations that determine the mode frequencies.
(b) Approximate expressions for the TE and TM mode frequencies can be found for the case when a − b << p̅ = 1/ 2 (a + b). Replace the variable ρ by p̅ in appropriate places in the radial part of the Helmholtz equation and redo the analysis of part (b), now including a determination of the mode frequencies.