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 maximum value of magnetic field.
Answer to Problem 34.77CP
The maximum value of magnetic field is
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
Formula to calculate the maximum value of magnetic field is,
Here,
Substitute
Conclusion:
Therefore, the maximum value of magnetic field is
(b)
The value of propogation vector
Answer to Problem 34.77CP
The value of propogation vector
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
Formula to calculate the propagation vector is,
Here,
Substitute
Conclusion:
Therefore, the value of propogation vector
(c)
The value of angular frequency
Answer to Problem 34.77CP
The value of angular frequency
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
Formula to calculate the angular frequency is,
Here,
Substitute
Conclusion:
Therefore, the value of angular frequency
(d)
The plane in which the magnetic field vector vibrates.
Answer to Problem 34.77CP
The plane in which the magnetic field vector vibrates is
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
The electromagnetic waves comprises of sinusoidally varying magnetic and electric fields which travel with a speed of light in vacuum. Both electric and magnetic field vectors oscillate perpendicular to each other as well as perpendicular to the direction of propagation of waves.
The wave is propagating along the positive
Conclusion:
Therefore, the plane in which the magnetic field vector vibrates is
(e)
The average value of Poynting vector for the microwave.
Answer to Problem 34.77CP
The average value of Poynting vector for the microwave is
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
Formula to calculate the magnitude of average value of poynting vector for the microwave is,
Here,
Substitute
The vector notation of Poynting vector is,
Conclusion:
Therefore, the average value of Poynting vector for the microwave is
(f)
The radiation pressure exerted on the perfectly reflecting sheet.
Answer to Problem 34.77CP
The radiation pressure exerted on the perfectly reflecting sheet is
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
Here,
Formula to calculate the radiation pressure on a perfectly reflecting sheet is,
Here,
Substitute
Conclusion:
Therefore, the radiation pressure exerted on the perfectly reflecting sheet is
(g)
The acceleration imparted to a
Answer to Problem 34.77CP
The acceleration imparted to a
Explanation of Solution
Given Info: The wavelength of polarized microwave directed along positive
The magnetic field component of wave is,
Here,
Formula to calculate the area of sheet is,
Here,
Substitute
Formula to calculate the acceleration imparted to sheet is,
Here,
Substitute
The vector notation of acceleration is,
Conclusion:
Therefore, the acceleration imparted to a
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Chapter 34 Solutions
PHYSICS:F/SCI.+.,V.2-STUD.S.M.+STD.GDE.
- 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 t), give values for (a) Bmax, (b) k, and (c) . (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 radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?arrow_forwardSuppose the magnetic field of an electromagnetic wave is given by B = (1.5 1010) sin (kx t) T. a. What is the maximum energy density of the magnetic field of this wave? b. What is maximum energy density of the electric field?arrow_forwardThe electric field of an electromagnetic wave traveling in vacuum is described by the following wave function: E =(5.00V/m)cos[kx(6.00109s1)t+0.40] j where k is the wavenumber in rad/m, x is in m, t s in Find the following quantities: (a) amplitude (b) frequency (c) wavelength (d) the direction of the travel of the wave (e) the associated magnetic field wavearrow_forward
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- At one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.80 μT. From this value, calculate (a) the rms electric field due to solar radiation, (b) the average energy density of the solar component of electromagnetic radiation at this location, and (c) the average magnitude of the Poynting vector for the Sun’s radiation.arrow_forwardA plane electromagnetic wave varies sinusoidally at 90.0 MHz as it travels through vacuum along the positive x direction. The peak value of the electric field is 2.00 mV/m, and it is directed along the positive y direction. Find (a) the wavelength, (b) the period, and (c) the maximum value of the magnetic field. (d) Write expressions in SI units for the space and time variations of the electric field and of the magnetic field. Include both numerical values and unit vectors to indicate directions. (e) Find the average power per unit area this wave carries through space. (f) Find theaverage energy density in the radiation (in joules per cubic meter). (g) What radiation pressure would this wave exert upon a perfectly reflecting surface at normal incidence?arrow_forwardIf the wave vector k of the plane wave moving in the xz plane is k = 2i+j ; According to this, a)The electric field (E) and the wave vector k satisfy the orthogonality condition. b)Determine the orthogonality condition of the magnetic field (B) and the wave vector k. c)Show that E and B satisfy the orthogonality condition.arrow_forward
- A uniform beam of laser light has a circular cross section of diameter d = 7.5 mm. The beam’s power is P = 4.9 mW. (a) Calculate the intensity, I, of the beam in units of W / m2. (b) The laser beam is incident on a material that completely absorbs the radiation. How much energy, ΔU, in joules, is delivered to the material during a time interval of Δt = 0.89 s? (c) Use the intensity of the beam, I, to calculate the amplitude of the electric field, E0, in volts per meter. (d) Calculate the amplitude of the magnetic field, B0, in teslas.arrow_forwardAt one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.90 µT. (a) Calculate the rms electric field due to solar radiation. V/m(b) Calculate the average energy density of the solar component of electromagnetic radiation at this location. µJ/m3(c) Calculate the average magnitude of the Poynting vector for the Sun's radiation. W/m2(d) Assuming that the average magnitude of the Poynting vector for solar radiation at the surface of the Earth is Sav = 1000 W/m2, compare your result in part (c) with this value. %arrow_forward
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