A large, flat sheet carries a uniformly distributed
the sheet radiates an
(a) Find the wave function for the electric field of the wave to the right of the sheet. (b) Find the Poynting vector as a function of x and t. (c) Find the intensity of the wave. (d) What If? If the sheet is to emit
Figure P33.28
(a)
Answer to Problem 34.46P
Explanation of Solution
Given info: The wave function for the magnetic field of the wave to the right of the sheet is
Explanation:
Write the Maxwell’s third equation,
Here,
Substitute
Integrating the above equation with respect to
Substitute
The direction of electric field must be perpendicular to the direction of propagation
Conclusion:
Therefore, the wave function for the electric field of the wave to the right of the sheet is
(b)
Answer to Problem 34.46P
Explanation of Solution
Given info: The wave function for the magnetic field of the wave to the right of the sheet is
Explanation:
Write the formula to calculate the Poynting vector.
Here,
Substitute
Conclusion:
Therefore, the Poynting vector as a function of
(c)
Answer to Problem 34.46P
Explanation of Solution
Given info: The wave function for the magnetic field of the wave to the right of the sheet is
Explanation:
The wave function for the magnetic field of the wave is.
The maximum value of
The wave function for the electric field of the wave is.
The maximum value of
Write the formula to calculate the intensity of the wave is,
Here,
Substitute
Conclusion:
Therefore, the intensity of the wave is
(d)
Answer to Problem 34.46P
Explanation of Solution
Given info: The intensity of the wave is
Explanation:
The intensity of the wave from part (c) is,
Here,
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the maximum value of sinusoidal current density is
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Chapter 34 Solutions
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