A perfectly conducting waveguide has a cross section in the shape of a semicircle with radius R.

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A perfectly conducting waveguide has a cross section in the shape of a semicircle with radius R.
(a) Find the longitudinal fields Eand Bfor the TM and TE modes, respectively. Find also the cut-off frequency for these modes.
(b) Write explicit formulae for the transverse fields for the lowest cutoff frequency found in part (a).

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