A rectangular waveguide, filled with a non$-$magnetic material with $$r$=4,$ has cross$-$sectional

dimensions $2\mathrm{.}5$cm$$b$,$ along the x$-$ and y$-$axes, respectively, and has degenerate mods of TE$20$ and

TE$04$ modes. A mode operating at $10$ GHz has zj

zs eyH $)40$cos$(5\mathrm{.}0$

$$

$$

$$ A$/$m$.$ Determine

a$)$ The dominant mode. Justify your answer.

b$)$ The waveguide dimension along the y$-$axis, i$.$e$.,$ b$.$

c$)$ The mode of operation. Justify your answer.

d$)$ The cut$-$off frequencies of the first six modes.

e$)$ The phase constant and the intrinsic wave impedance of the dominant mode.

f$)$ The phase constant and the intrinsic wave impedance of the mode in part $($c$).$

g$)$ The total average power transmitted across the cross section of the waveguide in part $($c$)$