Consider a hollow conducting tube with a circular cross section of radius R and infinite length. (a)

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Consider a hollow conducting tube with a circular cross section of radius R and infinite length.

(a) Find monochromatic TE (Ez = 0) and TM (Hz = 0) solutions of the Maxwell equations inside the tube which propagate around the tube circumference and thus do not depend on the longitudinal
coordinate z.

(b) Identify the subset of waves where the electric field has no nodes inside the tube and almost all of the field energy is concentrated in a very small annular volume near the wall of the tube.

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