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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 = a,E, sin () sin(ßz) (V /m) Assume that E, is a known real constant. a) Obtain the H phasor for these solutions. b) Determine all possible values of B in terms of the cavity dimension d by using the boundary condition satisfied by Ē at the perfectly conducting cavity wall placed at z = d.

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 = a,E, sin () sin(ßz) (V /m) Assume that E, is a known real constant. a) Obtain the H phasor for these solutions. b) Determine all possible values of B in terms of the cavity dimension d by using the boundary condition satisfied by Ē at the perfectly conducting cavity wall placed at z = d.

Introductory Circuit Analysis (13th Edition)
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 = ayE, sin sin(ßz) (V/m) Assume that E, 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 Ē at the perfectly conducting cavity wall placed at z = d. Cavity wall at z = d a €o, Ho b Fig. 1 y
Transcribed Image Text: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 = ayE, sin sin(ßz) (V/m) Assume that E, 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 Ē at the perfectly conducting cavity wall placed at z = d. Cavity wall at z = d a €o, Ho b Fig. 1 y
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