(a)
Find the total electric field in the air.
(a)
Answer to Problem 57P
The total electric field in the air is
Explanation of Solution
Calculation:
Write the expression for given magnetic field in the air.
Consider the expression to find the total electric field in the air.
Here,
Consider the expression for incident electric field for the given data.
Here,
Find the vector
Consider the expression to find magnitude of incident electric field at
Here,
As the medium-1 is free space (air), the intrinsic impedance is
From Equation (4), substitute
Substitute
Consider the expression for reflected electric field for the given data.
Here,
Consider the expression for reflected electric field at
Here,
Write the expression to find the reflection coefficient.
Here,
Find the intrinsic impedance for medium-2.
Substitute
From Equation (6), substitute
From Equation (4), substitute
Substitute
Substitute
Conclusion:
Thus, the total electric field in the air is
(b)
Find the time-average power density in the plastic region.
(b)
Answer to Problem 57P
The time-average power density in the plastic region is
Explanation of Solution
Calculation:
Consider the expression to find the time-average power density in the plastic region.
Here,
From Equation (1), the
Consider the expression to find the magnitude of transmitted electric field at
Here,
Consider for the expression for transmission coefficient.
Substitute
From Equation (4), substitute
Substitute
Substitute
Conclusion:
Thus, the time-average power density in the plastic region is
(c)
Find the standing wave ratio.
(c)
Answer to Problem 57P
The standing wave ratio is 2.
Explanation of Solution
Calculation:
Consider the expression to find the standing wave ratio.
From Part (a), substitute
Conclusion:
Thus, the standing wave ratio is 2.
Want to see more full solutions like this?
Chapter 10 Solutions
Elements of Electromagnetics
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY