An electromagnetic wave, propagating in a wave guide, is given as follows: E = E, cos (@t + ßx) ax + Eo sin (@t + ßx) (a,)V/m H=H, cos(@t + Bx) (a: ) A/m a. The medium in the waveguide is filled with a lossless material having (&, =4 and µ=1), the frequency is f= 3 GHz, and its phase constant is ß = 37 (rad/m). Determine the mode of wave. b. Find the cutoff frequency, wave impedance, and phase velocity of the wave. c. Calculate the time-averaged power density in the structure. d. Calculate the magnitude of the electric and magnetic field intensities Eo and Ho if the time- averaged power density is uniform in the structure and equals 80 W/m².
An electromagnetic wave, propagating in a wave guide, is given as follows: E = E, cos (@t + ßx) ax + Eo sin (@t + ßx) (a,)V/m H=H, cos(@t + Bx) (a: ) A/m a. The medium in the waveguide is filled with a lossless material having (&, =4 and µ=1), the frequency is f= 3 GHz, and its phase constant is ß = 37 (rad/m). Determine the mode of wave. b. Find the cutoff frequency, wave impedance, and phase velocity of the wave. c. Calculate the time-averaged power density in the structure. d. Calculate the magnitude of the electric and magnetic field intensities Eo and Ho if the time- averaged power density is uniform in the structure and equals 80 W/m².
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter34: Maxwell’s Equations And Electromagnetic Waves
Section: Chapter Questions
Problem 32PQ
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![Problem 4:
An electromagnetic wave, propagating in a wave guide, is given as follows:
E = E, cos (ot + Bx) ax + Eo sin (@t + Bx) (a,)V/m
H= H, cos(@t + ßx) (a: ) A/m
a. The medium in the waveguide is filled with a lossless material having (&, =4 and u=1), the
frequency is f= 3 GHz, and its phase constant is ß = 37 (rad/m). Determine the mode of wave.
b. Find the cutoff frequency, wave impedance, and phase velocity of the wave.
c. Calculate the time-averaged power density in the structure.
d. Calculate the magnitude of the electric and magnetic field intensities Eo and Ho if the time-
averaged power density is uniform in the structure and equals 80 W/m².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30b7d54a-d9a9-4ed7-be36-d361c6f2d5db%2F69e28a22-24b7-4472-b7b4-e67e9d23302a%2Fugm3ctg_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4:
An electromagnetic wave, propagating in a wave guide, is given as follows:
E = E, cos (ot + Bx) ax + Eo sin (@t + Bx) (a,)V/m
H= H, cos(@t + ßx) (a: ) A/m
a. The medium in the waveguide is filled with a lossless material having (&, =4 and u=1), the
frequency is f= 3 GHz, and its phase constant is ß = 37 (rad/m). Determine the mode of wave.
b. Find the cutoff frequency, wave impedance, and phase velocity of the wave.
c. Calculate the time-averaged power density in the structure.
d. Calculate the magnitude of the electric and magnetic field intensities Eo and Ho if the time-
averaged power density is uniform in the structure and equals 80 W/m².
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