Concept explainers
A uniform plane wave at frequency f= 100 MHz propagates in a material having conductivity c = 3.0 S/m and dielectric constant đ�œ–r' = 8.00. The wave carries electric field amplitude E0 = 100 V/m. (a) Calculate the loss tangent and determine whether the medium would qualify as a good dielectric or a good conductor, (b) Calculate a, đ�›½, and
(a)
The loss tangent and whether the material is good dielectric or good conductor.
Answer to Problem 11.11P
The value of loss tangent is
Explanation of Solution
Calculation:
The line loss tangent is given by
Here,
The permeability
Here,
Substitute equation (2) in equation (1).
The conversion from
The conversion of
Hence, the frequency is,
Radial frequency
Here,
Substitute
Substitute
Since, the value is greater than 10; the material is a good conductor.
Conclusion:
Therefore, the value of loss tangent is
(b)
The attenuation coefficient
Answer to Problem 11.11P
The attenuation coefficient
Explanation of Solution
Calculation:
The value of
Here,
The value of
Here,
Substitute
For a good conductor, the value of
Hence, the phase constant
The value of wave impedance is given by
Substitute
For a good conductor, the value of impedance angle is
The wave impedance
Conclusion:
Thus, attenuation coefficient
(c)
The electric field in phasor form.
Answer to Problem 11.11P
The phasor expression of electric field is
Explanation of Solution
Calculation:
The electric field in phasor form is given by
Here,
Substitute
Conclusion:
The phasor expression of electric field is
(d)
The magnetic field strength in phasor form.
Answer to Problem 11.11P
The magnetic field strength in phasor form is
Explanation of Solution
Calculation:
The magnetic field strength in phasor form is given by,
Substitute
Conclusion:
Thus, the magnetic field strength in phasor form is
(e)
The time averaging Poynting vector.
Answer to Problem 11.11P
The time averaging Poynting vector is
Explanation of Solution
Calculation:
The time averaging Poynting vector is given by
Here,
Substitute
Conclusion:
The time averaging Poynting vector is
(f)
The6 dB material thickness at which the wave power drops to 25 % of its value on entry.
Answer to Problem 11.11P
The
Explanation of Solution
Calculation:
The power loss in dB can be given by
Here,
Substitute
The intensity of the wave is represented by the Poynting vector. In this case, the Poynting vector changes in the direction of wave propagation, with the factor of
Taking intensity in the term of Poynting vector,
Conclusion:
Thus, the 6-dB material thickness is
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Chapter 11 Solutions
Engineering Electromagnetics
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