B1. The energy flow rate (power per unit area) in an electromagnetic wave in vacuum is given by the Poynting vector S=EX B . The magnitude of the time-averaged value of S is called the intensity I=Sy. Calculate the intensity of a sinusoidal plane electromagnetic wave traveling in vacuum in the +x -direction, described by
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- A perfectly reflecting surface of area 46.7 cm2 experiences a momentum transfer per second of magnitude 1.85 x 10-10 N when a plane electromagnetic wave strikes it. Determine the intensity of the wave. W/m2At a certain geographic location, light intensity from the Sun is 900 J/(m² .s). This means that sunlight delivers 900 joules of energy to each square meter of ground in each second. Suppose solar panels are installed on the roof of a house to generate electricity from sunlight. The total area of the solar panels is 25 m². Calculate the maximum electric energy that can be generated per second: Unfortunately, solar panels are not 100% efficient at converting electromagnetic energy to electricity. Suppose the solar panels have an efficiency of 15%. This means that only 15% of the electromagnetic energy incident on the solar panels is converted to electricity, while the rest is reflected or converted to thermal energy. Given this efficiency, calculate the electric energy that can be generated per second:4. An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is 1.20 x 10° W/m2. What is the rms value of the electric field in the electromagnetic wave emitted by the laser? N/C
- A certain electromagnetic wave has an average intensity of 6 x 104 W/m2. What is the average energy density of the wave? High O3x10-8 J/m³ 2x 10-4J/m³ O6x 104 J/m³An electromagnetic wave of frequency 3.2×1014 Hz falls on a medium of refractive index 4.1. The speed of E-M waves in vacuum is 3×108 m/s. The wavelength of the E-M wave in vacuum, λ0 = Unit . The speed of the E-M wave in the medium, v = Unit . The wavelength of the E-M wave in the medium, λ = Unit . If the incident wave falls from air and the angle of incidence is 17.5°, what is the angle of refraction? The angle of refraction, θr = UnitFrom a local TV station transmitter, a sinusoidal, plane electromagnetic wave is normally incident on an open window that has an area of 0.510m2. The wave travels to the right in the positive x-direction at the speed of light c and the window is thus perpendicular to the x-axis. See the schematic. Suppose the three electric field components have wave functions: EX = 0 EY = Emsin(kx-ωt) EZ = 0 See the axes below. At the moment shown the electric field - indicated by the vertically upward arrow - points in the positive y direction. Assume the field magnitude Em = 0.01000 V/m. The Erms (root mean square) of the electric field would thus be Erms = 0.00707 V/m. (a) At the moment shown above, in what direction does the magnetic field point? Indicate this direction by drawing a symbol near the z-axis. (b) Compute the numerical value of amplitude Bm of the magnetic field component pointing in the direction you found.
- 2. A sinusoidal electromagnetic wave with frequency 5.0x10“Hz travels in vacuum in the +x direction. The amplitude of electric field is 1.2x10³V/m. Find angular frequency w, wave number k, and amplitude of magnetic field. Write the wave function for the magnetic field in the form B = BmaxSin (wt –- kx).There is a vector defined by John Henry Poynting in 1884 whose direction gives the direction that an electromagnetic wave transmits its field energy and whose magnitude is the rate at which energy is being transmitted per square meter of the wavefront. For mutually perpendicular E- and B-fields in the wave, the magnitude of the Poynting vector is S =EB/mu0 and the direction is given by a right-hand rule, curling fingers from E vector and B vector. a) Carefully analyze the units of the Poynting vector and show that they are indeed watts per square meter. b) Find the intensity of the light in a beam of light whose electric field strength is 360 N/C and whose magnetic field is 1.2 muT.From a local TV station transmitter, a sinusoidal, plane electromagnetic wave is normally incident on an open window that has an area of 0.510 m2. The wave travels to the right in the positive x-direction at the speed of light c and the window is thus perpendicular to the x-axis. See the schematic. Suppose the three electric field components have wave functions: EX = 0 EY = Emsin(kx-ωt) EZ = 0 See the axes below. At the moment shown the electric field - indicated by the vertically upward arrow - points in the positive y direction. Assume the field magnitude Em = 0.01000 V/m. The Erms (root mean square) of the electric field would thus be Erms = 0.00707 V/m. (a) At the moment shown above, in what direction does the magnetic field point? Indicate this direction by drawing a symbol near the z-axis. Compute the numerical value of amplitude Bm of the magnetic field component pointing in the direction you found. (b) Write the wave function for the magnetic field component you referenced in…