Concept explainers
A uniform plane wave has electric field E8 = (Ey0ay - Eza3)e -axe -jBx V/m. The intrinsic impedance of the medium is given as
=
where ^ is a constant phase, (a) Describe the wave polarization and state the direction of propagation, (b) Find Hs. (c) Find s(x, t) and H(x, f). (d) Find < S > in W/m2. (e) Find the time-average power in watts that is intercepted by an antenna of rectangular cross-section, having width -w and height h, suspended parallel to the yz plane, and at a distance d from the wave source.
(a)
The wave polarization and the direction of propagation.
Explanation of Solution
Given:
Electric Field,
Intrinsic Impedance of the medium is
Wave polarization describes the direction as well as magnitude of EM field of wave. When the plane is vibrating, it is said to be wave polarization. The electromagnetic wave vibrates at right angles. Mostly, wave vibrates in one plane like vibrating up and down or vibrating sideways. This polarization is called linear polarization.
If the wave is linearly polarised in the y - z plane, then it propagates in the forward x direction (as seen from the
(b)
The value of
Answer to Problem 11.6P
The value of
Explanation of Solution
Given:
Electric Field
Intrinsic Impedance of the medium is
Calculation:
When ES is crossed with Hs, the resultant vector will be in positive x -direction.
The value of Hs is found by changing the y -component to z -component and z -component to negative y -component.
Conclusion:
The value of
(c)
The value of
Answer to Problem 11.6P
The value of
Explanation of Solution
Given:
Electric Field is
Intrinsic impedance of the medium is
Calculation:
Conclusion:
Therefore, the value of
(d)
The value of
Answer to Problem 11.6P
The value of
Explanation of Solution
Given:
Electric field is
Intrinsic Impedance of the medium is
Calculation:
The value of
Conclusion:
The value of
(e)
Time average power in watts.
Answer to Problem 11.6P
Time average power is
Explanation of Solution
Given:
Electric field is
Intrinsic impedance of the medium is
The width of antenna is w and height of antenna is h. It is located at distance of d from the wave source.
Calculation:
Time average power is calculated as
Conclusion:
Time average power is
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Chapter 11 Solutions
Engineering Electromagnetics
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