
(a)
The time harmonic electric field of an antenna.
(a)

Answer to Problem 8.1P
The time harmonic electric field of an antenna is
Explanation of Solution
Given:
The time harmonic magnetic field
Concept used:
The expression for time harmonic electric field can be written as,
Calculation:
Substitute
Therefore, the electric field is
Conclusion:
Thus, the time harmonic electric field of an antenna is
(b)
The time averaged power density of a wave.
(b)

Answer to Problem 8.1P
The time averaged power density of a wave is
Explanation of Solution
Concept used:
The expression for time averaged power density can be written as,
Calculation:
From part (a), the time harmonic electric field is
The conjugate of time harmonic magnetic field is calculated as,
Substitute
Therefore, the vector for time averaged power density is
Conclusion:
Thus, the time averaged power density of a wave is
(c)
The radiation resistance of the antenna.
(c)

Answer to Problem 8.1P
The radiation resistance of the antenna is
Explanation of Solution
Concept used:
The total power radiated by antenna is,
Calculation:
From part (a), the time averaged power density is
Substitute
The relation between power radiation and radiation resistance is shown below.
Substitute
The value of intrinsic impedance is
So, the radiation resistance can be written as,
Therefore, the value of
Conclusion:
Thus, the radiation resistance of the antenna is
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Chapter 8 Solutions
Fundamentals of Electromagnetics with Engineering Applications
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