A rectangular waveguide with dimensions a = 1.5 cm, b = 0.8 cm is filled with a dielectric with µ = µ0 and ε = 4ε0. The magnetic field inside the guide is characterized by Hx = 2 sin πx a  cos  3πy...

A rectangular waveguide with dimensions a = 1.5 cm, b = 0.8 cm is filled with a dielectric with
µ = µ0 and ε = 4ε0. The magnetic field inside the guide is characterized by
Hx = 2 sin πx
a

cos 
3πy
b

sin(π × 1011t − βz) (A/m)
Determine:
(a) The mode that is propagating inside the guide.
(b) The cutoff frequency.
(c) The propagation constant.
(d) The wave impedance.