Concept explainers
A plane wave in air with an electric field amplitude of 20 V/m is incident normally upon the surface of a lossless, nonmagnetic medium with ϵr = 25. Determine the following:
- (a) The reflection and transmission coefficients.
- (b) The standing-wave ratio in the air medium.
- (c) The average power densities of the incident, reflected, and transmitted waves.
(a)
The reflection coefficient
Answer to Problem 1P
The reflection coefficient
Explanation of Solution
Given data:
The electric field amplitude
The permittivity
Calculation:
The reflection coefficient
Here,
Write formula to find intrinsic impedance.
Here,
So, find intrinsic impedance of the medium
Hence,
Here,
Substitute
Now, find intrinsic impedance of medium 2.
Here,
Substitute
Substitute
The transmission coefficient
Here,
Substitute
Conclusion:
Therefore, the reflection coefficient
(b)
The standing-wave ratio
Answer to Problem 1P
The value of standing-wave ratio
Explanation of Solution
The calculated value of reflection coefficient
Calculation:
The standing-wave ratio is given by,
Here,
Substitute
Conclusion:
Therefore, the value of standing-wave ratio
(c)
The average power density of the incident
Answer to Problem 1P
The value of average power density of the incident wave
Explanation of Solution
Given data:
The electric field amplitude
The calculated value of intrinsic impedance of air
The calculated value of reflection coefficient
Calculation:
The average power density of the incident
Here,
Substitute
The average power density of the reflected
Substitute
The average power density of the transmitted
Substitute
Conclusion:
Therefore, the value of average power density of the incident wave
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Chapter 8 Solutions
Fundamentals Of Applied Electromagnetics
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