A linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx – ωt), give values for (a) Bmax, (b) k, and (c) ω. (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what
(a)
The value for
Answer to Problem 73P
The value for
Explanation of Solution
Write the expression to calculate the peak value of magnetic field.
Here,
Conclusion:
Substitute
Thus, the value for
(b)
The magnitude of k.
Answer to Problem 73P
The magnitude of k is
Explanation of Solution
Write the expression to calculate the wavenumber of k.
Here,
Conclusion:
Substitute
Thus, the magnitude of k is
(c)
The magnitude of
Answer to Problem 73P
The magnitude of
Explanation of Solution
Write the expression to calculate the angular frequency or
Conclusion:
Substitute
Thus, the magnitude of
(c)
The magnitude of
Answer to Problem 73P
The magnitude of
Explanation of Solution
Write the expression to calculate the angular frequency or
Conclusion:
Substitute
Thus, the magnitude of
(d)
The plane at which magnetic field vector vibrates.
Answer to Problem 73P
The plane of vibration of magnetic field vector is z direction.
Explanation of Solution
Here, both the electric and magnetic field vectors are vibrates in xy-plane. The direction of pointing vector is same as that of the direction of the wave since the wave carries the energy along the direction of propagation.
From the expression of the magnetic field given, the electric field vibrates along y direction. Therefore, the magnetic field must vibrate in z direction since the wave travels along the x direction which is mutually normal to both the electric and magnetic vibrations.
Conclusion:
Substitute
Thus, the plane of vibration of magnetic field vector is z direction.
(e)
The average value of pointing vector in the wave.
Answer to Problem 73P
The average value of pointing vector is
Explanation of Solution
Write the expression to calculate the average value of pointing vector.
Here,
Conclusion:
Substitute
Thus, the average value of pointing vector is
(f)
The radiation pressure exerted by the wave.
Answer to Problem 73P
The radiation pressure exerted by the wave is
Explanation of Solution
Write the expression to calculate the radiation pressure.
Here,
Conclusion:
Substitute
Thus, the radiation pressure exerted by the wave is
(g)
The acceleration imparted to the given sheet.
Answer to Problem 73P
The acceleration is
Explanation of Solution
The area of the sheet is
Write the expression to calculate the acceleration.
Here, a is the acceleration, A is the area and m is the mass.
Conclusion:
Substitute
Thus, the acceleration is
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Chapter 24 Solutions
Principles of Physics: A Calculus-Based Text
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