(a)
Find the total electric field component of the wave in region 1.
(a)
Answer to Problem 58P
The total electric field component of the wave in region 1 is
Explanation of Solution
Calculation:
Write the expression for given incident electric field in region 1.
Consider the expression to find the total electric field in region 1.
Here,
Consider the expression for phase constant in lossless medium (region).
Rewrite the expression for the given data.
Substitute
Consider the expression for reflected electric field in region 1.
Here,
Consider the expression for reflected electric field at
Here,
Write the expression to find the reflection coefficient.
Here,
As region 2 is free space, the intrinsic impedance is
Find the intrinsic impedance for region 1.
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the total electric field component of the wave in region 1 is
(b)
Find the time-average Poynting
(b)
Answer to Problem 58P
The time-average Poynting vector in region 1 is
Explanation of Solution
Calculation:
Consider the expression to find the time-average Poynting vector in region 1.
From Equation (1), the vector
Substitute
Conclusion:
Thus, the time-average Poynting vector in region 1 is
(c)
Find the time-average Poynting vector in region 2.
(c)
Answer to Problem 58P
The time-average Poynting vector in region 2 is
Explanation of Solution
Calculation:
Consider the expression to find the time-average Poynting vector in region 2.
Here,
Consider the expression to find the magnitude of transmitted electric field at
Here,
Consider for the expression for transmission coefficient.
Substitute
Substitute
Substitute
Conclusion:
Thus, the time-average Poynting vector in region 2 is
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