8.12 a. Refer to Figure 4.1. Arectangular cavity of square cross section (a = b) and height h utilizing the simple TE101mode is to be designed fora millimeter-wave electron device for operation at fr =0.2 THz. Height of the cavity must be kept small (take h =1 mm) to minimize electron transit time. The medium in the cavity is air. The walls are made of copper o = 5.8 x107 s/m. Design the cavity by calculating a, also calculate the quality factor Q of the cavity. b. Suppose the walls of the cavity are made of superconducting material with the following parameters: \text { Normal conductivity } \sigma_{n}=5 \times 106 (S/m); \text { London penetration depth } \lambda_{\mathrm{L}}= 0.5 × 10-7 m. Determine the Q of the cavity. Determine the Q of the cavity.

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