A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a= 5 cm and

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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


Ex = -36 cos(40x) sin(100ty) • sin(2.47 x 1010t – 52.9tz), %3D (V/m)
Determine:
(a) The mode number,
(b) r of the material in the guide,
(c) The cutoff frequency, and
(d) The expression for Hy.
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