Chapter 8, Problem 40P

A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a =5 cm and b = 3 cm. If the x component of its electric field is given by

$\begin{array}{l}{E}_x=-36\cos (40\pi x)\sin (10\pi y)\\ \cdot \sin (2.4\pi \times {10}^{10}t-52.9\pi z),(\text{V/m)}\end{array}$

determine:

1. (a) the mode number,
2. (b) ϵ_r of the material in the guide,
3. (c) the cutoff frequency, and
4. (d) the expression for H_y.