(b) In a simple and nonconducting source-free medium, please derive the homogenous vector Helmholtz's equation for H. (8%)

(a) For a uniform waveguide with arbitrary cross section as shown in Fig. 3(a), please derive the two- dimensional (2-D) vector phasor expression of transverse magnetic field components in terms of are 2-D vector phasors for Ez and Hz. (10%)