Answered: A rectangular waveguide cavity in Fig.1…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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A rectangular waveguide cavity in Fig.1 is essentially a hollow (filled by air) metallic box in the shape of a rectangular prism with side lengths a,b and d along x,y and z axes, respectively, as shown in the figure below. Assume that the closed walls of this cavity are made of perfect conductors. A set of possible electromagnetic field solutions (which can exist within this cavity)
has the E phasor in the following form

E=ayE₀ sin(πx/a) sin(ßz) (V/m)

Assume that E₀ is a known real constant.
a) Obtain the H phasor for these solutions.
b) Determine all possible values of ß in terms of the cavity dimension d by using the boundary condition satisfied by E at the perfectly conducting cavity wall placed at z=d.

Cavity wall at z = d
a
Eo, Ho
d.
Fig. 1
y

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