(a)
Find the wave frequency and magnetic field intensity for the given EM wave.
(a)
Answer to Problem 47P
The wave frequency and magnetic field intensity for the given EM wave are
Explanation of Solution
Calculation:
Write the expression for electric field component of given EM wave.
Rewrite the expression.
Write the general form of the electric field component of EM wave.
Compare Equation (1) with Equation (2) and write the values of
Consider the expression for phase constant in lossless dielectric medium.
Rewrite the expression for the given data.
Rearrange the expression for wave frequency.
Substitute
Find the direction of wave propagation of magnetic field for the given EM wave.
Write the expression to find the magnetic field
As
Consider the expression to find the magnitude of the intrinsic impedance in the lossless dielectric medium.
Rewrite the expression for the given data.
Substitute
Substitute
Conclusion:
Thus, the wave frequency and magnetic field intensity for the given EM wave are
(b)
Find the Poynting
(b)
Answer to Problem 47P
The Poynting vector for the given EM wave is
Explanation of Solution
Calculation:
Consider the expression for pointing vector.
Use electric field intensity
Conclusion:
Thus, the Poynting vector for the given EM wave is
(c)
Find the total time-average power crossing the given surface.
(c)
Answer to Problem 47P
The total time-average power crossing the given surface is
Explanation of Solution
Calculation:
Write the expression for total time-average Poynting vector.
From Part (a) and Part (b), substitute
Simplify the expression.
Consider the expression to find the average power crossing the surface
Here,
Substitute
Apply the limits and rewrite the expression.
Conclusion:
Thus, the total time-average power crossing the given surface is
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Chapter 10 Solutions
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