1cc. The displacement current, id, for the charging circular
capacitor with radius R shown in the figure is equal to the conduction
current, i, in the wires. Points 1 and 3 are located a perpendicular
distance r from the wires, and point 2 is located the same perpendicular
distance r from the center of the capacitor, such that r > R. Rank
the magnetic fields at points 1, 2, and 3, from largest magnitude to
smallest....a) B1 > B2 > B3b) B3 > B2 > B1c) B1 = B3 >
B2d) B2 > B1 = B3e) B1 = B2 = B3 Get solution
1mcq. Which of the following phenomena can be observed for electromagnetic waves but not for sound waves?a) interferenceb) diffractionc) polarizationd) absorptione) scattering Get solution
2cc. The displacement current, id, for the charging circular capacitor with radius R shown in the figure is equal to the conduction current, i, in the wires. Points 1 and 3 are located a perpendicular distance r from the wires, and point 2 is located the same perpendicular distance r from the center of the capacitor, such that r R. Rank the magnetic fields at points 1, 2, and 3, from largest magnitude to smallest....a) B1 > B2 > B3b) B3 > B2 > B1c) B1 = B3 > B2d) B2 > B1 = B3e) B1 = B2 = B3 Get solution
3cc. An electromagnetic plane wave is traveling through vacuum. The electric field of the wave is given by ...Which of the following equations describes the magnetic field of the wave?a) ...b) ...c) ...d) ...e) ... Get solution
4cc. What is the time required for laser light to travel from the Earth to the Moon and back again? The distance between the Earth and the Moon is 3.84 ·108 m.a) 0.640 sb) 1.28 sc) 2.56 sd) 15.2 se) 85.0 s Get solution
4mcq. Which of the following exerts the largest amount of radiation pressure?a) a 1-mW laser pointer on a 2-mm-diameter spot 1 m awayb) a 200-W light bulb on a 4-mm-diameter spot 10 m awayc) a 100-W light bulb on a 2-mm-diameter spot 4 m awayd) a 200-W light bulb on a 2-mm-diameter spot 5 m awaye) All of the above exert the same pressure. Get solution
5cc. What is the radiation pressure due to sunlight incident on a perfectly absorbing surface, whose surface normal vector is at an angle of 70° relative to the incident light?...a) (4.67 μPa)(cos 70°)b) (4.67 μPa)(sin 70°)c) (4.67 μPa)(tan 70°)d) (4.67 μPa)(cot 70°) Get solution
6cc. What is the maximum radiation pressure due to sunlight incident on a perfectly reflecting surface?a) 0b) 2.34 μPac) 4.67 μPad) 9.34 μPa Get solution
6mcq. A proton moves perpendicularly to crossed electric and magnetic fields as shown in the figure. What is the direction of the net force on the proton?a) toward the leftb) toward the rightc) into the paged) out of the page... Get solution
8mcq. According to Gauss’s Law for Magnetic Fields, all magnetic field lines form a complete loop. Therefore, the direction of the magnetic field ... points from _____ pole to _____ pole outside of an ordinary bar magnet and from _____ pole to _____ pole inside the magnet.a) north, south, north, southb) north, south, south, northc) south, north, south, northd) south, north, north, south Get solution
9mcq. Unpolarized light with intensity Iin = 1.87 W/m2 passes through two polarizers. The emerging polarized light has intensity Iout = 0.383 W/m2. What is the angle between the two polarizers?a) 23.9°b) 34.6°c) 50.2°d) 72.7°e) 88.9° Get solution
11cq. In a polarized light experiment, a setup similar to the one in Figure 31.23 is used. Unpolarized light with intensity I0 is incident on polarizer 1. Polarizers 1 and 3 are crossed (at a 90° angle), and their orientations are fixed during the experiment. Initially, polarizer 2 has its polarizing angle at 45°. Then, at time t = 0, polarizer 2 starts to rotate with angular velocity ω about the direction of propagation of light in a clockwise direction as viewed by an observer looking toward the light source. A photodiode is used to monitor the intensity of the light emerging from polarizer 3.a) Determine an expression for this intensity as a function of time.b) How would the expression from part (a) change if polarizer 2 were rotated about an axis parallel to the direction of propagation of the light but displaced by a distance d R, where R is the radius of the polarizer?Figure 31.23 Unpolarized light passing through three polarizers.... Get solution
12cq. A dipole antenna is located at the origin with its axis along the z-axis. As electric current oscillates up and down the antenna, polarized electromagnetic radiation travels away from the antenna along the positive y-axis. What are the possible directions of electric and magnetic fields at point A on the y-axis? Explain.... Get solution
15cq. If two communication signals were sent at the same time to the Moon, one via radio waves and one via visible light, which one would arrive at the Moon first? Get solution
16cq. Show that Ampere’s Law is not necessarily consistent if the surface through which the flux is to be calculated is a closed surface, but that the Maxwell-Ampere Law always is. (Hence, Maxwell’s introduction of his law of induction and the displacement current are not optional; they are logically necessary.) Show also that Faraday’s Law of Induction does not suffer from this consistency problem. Get solution
18cq. Practically everyone who has studied the electromagnetic spectrum has wondered how the world would appear if we could see over a range of frequencies comparable to the ten octaves over which we can hear rather than the less than one octave over which we can see. (An octave refers to a factor of 2 in frequency.) But this is practically impossible. Why? Get solution
20cq. A pair of sunglasses is held in front of a flat-panel computer monitor (which is on) so that the lenses are always parallel to the display. As the lenses are rotated, it is noticed that the intensity of light coming from the display and passing through the lenses is varying. Why? Get solution
21cq. Two polarizing filters are crossed at 90°, so when light is shined from behind the pair of filters, no light passes through. A third filter is inserted between the two, initially aligned with one of them. Describe what happens as the intermediate filter is rotated through an angle of 360°. Get solution
25. A parallel plate capacitor has air between disk-shaped plates of radius 4.00 mm that are coaxial and 1.00 mm apart. Charge is being accumulated on the plates of the capacitor. What is the displacement current between the plates at an instant when the rate of charge accumulation on the plates is 10.0 µC/s? Get solution
24. The current flowing in a solenoid that is 20.0 cm long and has a radius of 2.00 cm and 500. turns decreases from 3.00 A to 1.00 A in 0.100 s. Determine the magnitude of the induced electric field inside the solenoid 1.00 cm from its center. Get solution
27. The voltage across a cylindrical conductor of radius r, length L, and resistance R varies with time. The time-varying voltage causes a time-varying current, i, to flow in the cylinder. Show that the displacement current equals ε0ρdi/dt, where ρ is the resistivity of the conductor Get solution
28. The amplitude of the electric field of an electromagnetic wave is 250. V/m. What is the amplitude of the magnetic field of the electromagnetic wave? Get solution
30. How long does it take light to travel from the Moon to the Earth? From the Sun to the Earth? From Jupiter to the Earth? Get solution
33. The wavelength range for visible light is 400 nm to 700 nm (see Figure 31.10) in air. What is the frequency range of visible light?Figure 31.10 The electromagnetic spectrum.... Get solution
34. The antenna of a cell phone is a straight rod 8.0 cm long. Calculate the operating frequency of the signal from this phone, assuming that the antenna length is ¼ of the wavelength of the signal. Get solution
36. Three FM radio stations covering the same geographical area broadcast at frequencies 91.1, 91.3, and 91.5 MHz, respectively. What is the maximum allowable wavelength width of the band-pass filter in a radio receiver such that the FM station 91.3 can be played free of interference from FM 91.1 or FM 91.5? Use c = 3.00 · 108 m/s, and calculate the wavelength to an uncertainty of 1 mm. Get solution
37. A monochromatic point source of light emits 1.5 W of electromagnetic power uniformly in all directions. Find the Poynting vector at a point situated at each of the following locations:a) 0.30 m from the sourceb) 0.32 m from the sourcec) 1.00 m from the source Get solution
39. A 3.00-kW carbon dioxide laser is used in laser welding. If the beam is 1.00 mm in diameter, what is the amplitude of the electric field in the beam? Get solution
42. The most intense beam of light that can propagate through dry air must have an electric field whose maximum amplitude is no greater than the breakdown value for air: ... = 3.0 106 V/m, assuming that this value is unaffected by the frequency of the wave.a) Calculate the maximum amplitude the magnetic field of this wave can have.b) Calculate the intensity of this wave.c) What happens to a wave more intense than this? Get solution
43. A continuous-wave (cw) argon-ion laser beam has an average power of 10.0 W and a beam diameter of 1.00 mm. Assume that the intensity of the beam is the same throughout the cross section of the beam (which is not true, as the actual distribution of intensity is a Gaussian function).a) Calculate the intensity of the laser beam. Compare this with the average intensity of sunlight at Earth’s surface (1400. W/m2).b) Find the root-mean-square electric field in the laser beam.c) Find the average value of the Poynting vector over time.d) If the wavelength of the laser beam is 514.5 nm in vacuum, write an expression for the instantaneous Poynting vector, where the instantaneous Poynting vector is zero at t = 0 and x = 0.e) Calculate the root-mean-square value of the magnetic field in the laser beam. Get solution
45. Radiation from the Sun reaches the Earth at a rate of 1.40 kW/m2 above the atmosphere and at a rate of 1.00 kW/m2 on an ocean beach.a) Calculate the maximum values of E and B above the atmosphere.b) Find the pressure and the force exerted by the radiation on a person lying flat on the beach who has an area of 0.750 m2 exposed to the Sun. Get solution
47. A solar sail is a giant circle (with a radius R = 10.0 km) made of a material that is perfectly reflecting on one side and totally absorbing on the other side. In deep space, away from other sources of light, the cosmic microwave background will provide the primary source of radiation incident on the sail. Assuming that this radiation is that of an ideal black body at T = 2.725 K, calculate the net force on the sail due to its reflection and absorption. Also assume that any heat transferred to the sail will be conducted away, and that the photons are incident perpendicular to the surface of the sail. Get solution
48. Two astronauts are at rest in outer space, one 20.0 m from the Space Shuttle and the other 40.0 m from the shuttle. Using a 100.0-W laser, the astronaut located 40.0 m away from the shuttle decides to propel the other astronaut toward the Space Shuttle. He focuses the laser on a piece of totally reflecting fabric on her space suit. If her total mass with equipment is 100.0 kg, how long will it take her to reach the Space Shuttle? Get solution
49. A laser that produces a spot of light that is 1.00 mm in diameter is shone perpendicularly on the center of a thin, perfectly reflecting circular (2.00 mm in diameter) aluminum plate mounted vertically on a flat piece of cork that floats on the surface of the water in a large beaker. The mass of this “sailboat” is 0.100 g, and it travels 2.00 mm in 63.0 s. Assuming that the laser power is constant in the region where the sailboat is located during its motion, what is the power of the laser? (Neglect air resistance and the viscosity of water.) Get solution
50. A tiny particle of density 2000. kg/m3 is at the same distance from the Sun as the Earth is (1.50 · 1011 m). Assume that the particle is spherical and perfectly reflecting. What would its radius have to be for the outward radiation pressure on it to be 1.00% of the inward gravitational attraction of the Sun? (Take the Sun’s mass to be 2.00 · 1030 kg.) Get solution
51. Silica aerogel, an extremely porous, thermally insulating material made of silica, has a density of 1.00 mg/cm3. A thin circular slice of aerogel has a diameter of 2.00 mm and a thickness of 0.10 mm.a) What is the weight of the aerogel slice (in newtons)?b) What are the intensity and the radiation pressure of a 5.00-mW laser beam of diameter 2.00 mm on the sample?c) How many 5.00-mW lasers with a beam diameter of 2.00 mm would be needed to make the slice float in the Earth’s gravitational field? Use g = 9.81 m/s2. Get solution
53. A 10.0-mW vertically polarized laser beam passes through a polarizer whose polarizing angle is 30.0° from the horizontal. What is the power of the laser beam when it emerges from the polarizer? Get solution
54. Unpolarized light of intensity I0 is incident on a series of five polarizers, with the polarization direction of each rotated 10.0° from that of the preceding one. What fraction of the incident light will pass through the series? Get solution
56. A laser beam takes 50.0 ms to be reflected back from a totally reflecting sail on a spacecraft. How far away is the sail? Get solution
57. A house with a south-facing roof has photovoltaic panels on the roof. The photovoltaic panels have an efficiency of 10.0% and occupy an area with dimensions 3.00 m by 8.00 m. The average solar radiation incident on the panels is 300. W/m2, averaged over all conditions for a year. How many kilowatt-hours of electricity will the solar panels generate in a 30-day month? Get solution
59. A 200.-W laser produces a beam with a cross-sectional area of 1.00 mm2 and a wavelength of 628 m. What is the amplitude of the electric field in the beam? Get solution
60. What is the wavelength of the electromagnetic waves used for cell phone communications at 848.97 MHz? Get solution
62. A 14.9-µF capacitor, a 24.3-kΩ resistor, a switch, and a 25.0-V battery are connected in series. What is the rate of change of the electric field between the plates of the capacitor at t = 0.3621 s after the switch is closed? The area of the plates is 1.00 cm2 Get solution
63. A focused 300-W spotlight delivers 40% of its light within a circular area with a diameter of 2 m. What is the root-mean-square electric field in this illuminated area? Get solution
65. What is the distance between successive heating antinodes in a microwave oven’s cavity? A microwave oven typically operates at a frequency of 2.4 GHz. Get solution
66. The solar constant measured by Earth satellites is roughly 1400 W/m2.a) Find the maximum electric field of the electromagnetic radiation from the Sun.b) Find the maximum magnetic field of these electromagnetic waves. Get solution
67. The peak electric field at a distance of 2.25 m from a light bulb is 21.2 V/m.a) What is the peak magnetic field there?b) What is the power output of the bulb? Get solution
68. If the peak electric field due to a star whose radius is twice that of the Sun is 44.0 V/m at a distance of 15 AU, what is its temperature? Treat the star as a blackbody. Get solution
69. A 5.00-mW laser pointer has a beam diameter of 2.00 mm.a) What is the root-mean-square value of the electric field in this laser beam?b) Calculate the total electromagnetic energy in 1.00 m of this laser beam. Get solution
70. At the surface of the Earth, the Sun delivers an estimated 1.00 kW/m2 of energy. Suppose sunlight hits a 10.0 m by 30.0 m roof at an angle of 90.0°.a) Estimate the total power incident on the roof.b) Find the radiation pressure on the roof. Get solution
71. The National Ignition Facility has the most powerful laser in the world; it uses 192 beams to aim 500. TW of power at a spherical pellet of diameter 2.00 mm. How fast would a pellet of density 2.00 g/cm3 accelerate if only one of the laser beams hits it for 1.00 ns and 2.00% of the light is absorbed? Get solution
72. A resistor consists of a solid cylinder of radius r and length L. The resistor has resistance R and is carrying current i. Use the Poynting vector to calculate the power radiated out of the surface of the resistor. Get solution
73. A radio tower is transmitting 30.0 kW of power equally in all directions. Assume that the radio waves that hit the Earth are reflected.a) What is the magnitude of the Poynting vector at a distance of 12.0 km from the tower?b) What is the root-mean-square value of the electric force on an electron at this location? Get solution
74. Quantum theory says that electromagnetic waves actually consist of discrete packets—photons—each with energy E = ħω, where ħ =1.054572·10–34 J s is Planck’s reduced constant and ω is the angular frequency of the wave.a) Find the momentum of a photon.b) Find the magnitude of angular momentum of a photon. Photons are circularly polarized; that is, they are described by a superposition of two plane-polarized waves with equal field amplitudes, equal frequencies, and perpendicular polarizations, one-quarter of a cycle (90° or π/2 rad) out of phase, so the electric and magnetic field vectors at any fixed point rotate in a circle with the angular frequency of the waves. It can be shown that a circularly polarized wave of energy U and angular frequency ω has an angular momentum of magnitude L = U/ω. (The direction of the angular momentum is given by the thumb of the right hand, when the fingers are curled in the direction in which the field vectors circulate.)c) The ratio of the angular momentum of a particle to ħ is its spin quantum number. Determine the spin quantum number of the photon. Get solution
79. During the testing of a new light bulb, a sensor is placed 52.5 cm from the bulb. It records a root-mean-square value of 9.142 · 10–7 T for the magnetic field of the radiation emitted by the bulb. What is the intensity of that radiation at the sensor’s location? Get solution
77. During the testing of a new light bulb, a sensor is placed 31.9 cm from the bulb. It records an intensity of 182.9 W/m2 for the radiation emitted by the bulb. What is the root-mean-square value of the electric field at the sensor’s location? Get solution
78. During the testing of a new light bulb, a sensor is placed 42.1 cm from the bulb. It records an intensity of 191.4 W/m2 for the radiation emitted by the bulb. What is the root-mean-square value of the magnetic field at the sensor’s location? Get solution
80. During the testing of a new light bulb, a sensor is placed 17.7 cm from the bulb. It records a root-mean-square value of 279.9 V/m for the electric field of the radiation emitted from the bulb. What is the intensity of that radiation at the sensor’s location? Get solution
81. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two polarizers on the telescope. Th e first polarizer has a polarizing angle of 28.1° relative to the horizontal, and the second has a polarizing angle of 88.6°. By what fraction is the intensity of the incident sunlight reduced by the polarizers? Get solution
82. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two polarizers on the telescope. The first polarizer has a polarizing angle of 38.3° relative to the horizontal. If the astronomers want to reduce the intensity of the sunlight by a factor of 0.7584, what polarizing angle should the second polarizer have with the horizontal? Assume that this angle is greater than that of the first polarizer. Get solution
83. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two linear polarizers on the telescope. The second polarizer has a polarizing angle of 110.6° relative to the horizontal. If the astronomers want to reduce the intensity of the sunlight by a factor of 0.7645, what polarizing angle should the first polarizer have with the horizontal? Assume that this angle is smaller than that of the second polarizer. Get solution
1mcq. Which of the following phenomena can be observed for electromagnetic waves but not for sound waves?a) interferenceb) diffractionc) polarizationd) absorptione) scattering Get solution
2cc. The displacement current, id, for the charging circular capacitor with radius R shown in the figure is equal to the conduction current, i, in the wires. Points 1 and 3 are located a perpendicular distance r from the wires, and point 2 is located the same perpendicular distance r from the center of the capacitor, such that r R. Rank the magnetic fields at points 1, 2, and 3, from largest magnitude to smallest....a) B1 > B2 > B3b) B3 > B2 > B1c) B1 = B3 > B2d) B2 > B1 = B3e) B1 = B2 = B3 Get solution
3cc. An electromagnetic plane wave is traveling through vacuum. The electric field of the wave is given by ...Which of the following equations describes the magnetic field of the wave?a) ...b) ...c) ...d) ...e) ... Get solution
4cc. What is the time required for laser light to travel from the Earth to the Moon and back again? The distance between the Earth and the Moon is 3.84 ·108 m.a) 0.640 sb) 1.28 sc) 2.56 sd) 15.2 se) 85.0 s Get solution
4mcq. Which of the following exerts the largest amount of radiation pressure?a) a 1-mW laser pointer on a 2-mm-diameter spot 1 m awayb) a 200-W light bulb on a 4-mm-diameter spot 10 m awayc) a 100-W light bulb on a 2-mm-diameter spot 4 m awayd) a 200-W light bulb on a 2-mm-diameter spot 5 m awaye) All of the above exert the same pressure. Get solution
5cc. What is the radiation pressure due to sunlight incident on a perfectly absorbing surface, whose surface normal vector is at an angle of 70° relative to the incident light?...a) (4.67 μPa)(cos 70°)b) (4.67 μPa)(sin 70°)c) (4.67 μPa)(tan 70°)d) (4.67 μPa)(cot 70°) Get solution
6cc. What is the maximum radiation pressure due to sunlight incident on a perfectly reflecting surface?a) 0b) 2.34 μPac) 4.67 μPad) 9.34 μPa Get solution
6mcq. A proton moves perpendicularly to crossed electric and magnetic fields as shown in the figure. What is the direction of the net force on the proton?a) toward the leftb) toward the rightc) into the paged) out of the page... Get solution
8mcq. According to Gauss’s Law for Magnetic Fields, all magnetic field lines form a complete loop. Therefore, the direction of the magnetic field ... points from _____ pole to _____ pole outside of an ordinary bar magnet and from _____ pole to _____ pole inside the magnet.a) north, south, north, southb) north, south, south, northc) south, north, south, northd) south, north, north, south Get solution
9mcq. Unpolarized light with intensity Iin = 1.87 W/m2 passes through two polarizers. The emerging polarized light has intensity Iout = 0.383 W/m2. What is the angle between the two polarizers?a) 23.9°b) 34.6°c) 50.2°d) 72.7°e) 88.9° Get solution
11cq. In a polarized light experiment, a setup similar to the one in Figure 31.23 is used. Unpolarized light with intensity I0 is incident on polarizer 1. Polarizers 1 and 3 are crossed (at a 90° angle), and their orientations are fixed during the experiment. Initially, polarizer 2 has its polarizing angle at 45°. Then, at time t = 0, polarizer 2 starts to rotate with angular velocity ω about the direction of propagation of light in a clockwise direction as viewed by an observer looking toward the light source. A photodiode is used to monitor the intensity of the light emerging from polarizer 3.a) Determine an expression for this intensity as a function of time.b) How would the expression from part (a) change if polarizer 2 were rotated about an axis parallel to the direction of propagation of the light but displaced by a distance d R, where R is the radius of the polarizer?Figure 31.23 Unpolarized light passing through three polarizers.... Get solution
12cq. A dipole antenna is located at the origin with its axis along the z-axis. As electric current oscillates up and down the antenna, polarized electromagnetic radiation travels away from the antenna along the positive y-axis. What are the possible directions of electric and magnetic fields at point A on the y-axis? Explain.... Get solution
15cq. If two communication signals were sent at the same time to the Moon, one via radio waves and one via visible light, which one would arrive at the Moon first? Get solution
16cq. Show that Ampere’s Law is not necessarily consistent if the surface through which the flux is to be calculated is a closed surface, but that the Maxwell-Ampere Law always is. (Hence, Maxwell’s introduction of his law of induction and the displacement current are not optional; they are logically necessary.) Show also that Faraday’s Law of Induction does not suffer from this consistency problem. Get solution
18cq. Practically everyone who has studied the electromagnetic spectrum has wondered how the world would appear if we could see over a range of frequencies comparable to the ten octaves over which we can hear rather than the less than one octave over which we can see. (An octave refers to a factor of 2 in frequency.) But this is practically impossible. Why? Get solution
20cq. A pair of sunglasses is held in front of a flat-panel computer monitor (which is on) so that the lenses are always parallel to the display. As the lenses are rotated, it is noticed that the intensity of light coming from the display and passing through the lenses is varying. Why? Get solution
21cq. Two polarizing filters are crossed at 90°, so when light is shined from behind the pair of filters, no light passes through. A third filter is inserted between the two, initially aligned with one of them. Describe what happens as the intermediate filter is rotated through an angle of 360°. Get solution
25. A parallel plate capacitor has air between disk-shaped plates of radius 4.00 mm that are coaxial and 1.00 mm apart. Charge is being accumulated on the plates of the capacitor. What is the displacement current between the plates at an instant when the rate of charge accumulation on the plates is 10.0 µC/s? Get solution
24. The current flowing in a solenoid that is 20.0 cm long and has a radius of 2.00 cm and 500. turns decreases from 3.00 A to 1.00 A in 0.100 s. Determine the magnitude of the induced electric field inside the solenoid 1.00 cm from its center. Get solution
27. The voltage across a cylindrical conductor of radius r, length L, and resistance R varies with time. The time-varying voltage causes a time-varying current, i, to flow in the cylinder. Show that the displacement current equals ε0ρdi/dt, where ρ is the resistivity of the conductor Get solution
28. The amplitude of the electric field of an electromagnetic wave is 250. V/m. What is the amplitude of the magnetic field of the electromagnetic wave? Get solution
30. How long does it take light to travel from the Moon to the Earth? From the Sun to the Earth? From Jupiter to the Earth? Get solution
33. The wavelength range for visible light is 400 nm to 700 nm (see Figure 31.10) in air. What is the frequency range of visible light?Figure 31.10 The electromagnetic spectrum.... Get solution
34. The antenna of a cell phone is a straight rod 8.0 cm long. Calculate the operating frequency of the signal from this phone, assuming that the antenna length is ¼ of the wavelength of the signal. Get solution
36. Three FM radio stations covering the same geographical area broadcast at frequencies 91.1, 91.3, and 91.5 MHz, respectively. What is the maximum allowable wavelength width of the band-pass filter in a radio receiver such that the FM station 91.3 can be played free of interference from FM 91.1 or FM 91.5? Use c = 3.00 · 108 m/s, and calculate the wavelength to an uncertainty of 1 mm. Get solution
37. A monochromatic point source of light emits 1.5 W of electromagnetic power uniformly in all directions. Find the Poynting vector at a point situated at each of the following locations:a) 0.30 m from the sourceb) 0.32 m from the sourcec) 1.00 m from the source Get solution
39. A 3.00-kW carbon dioxide laser is used in laser welding. If the beam is 1.00 mm in diameter, what is the amplitude of the electric field in the beam? Get solution
42. The most intense beam of light that can propagate through dry air must have an electric field whose maximum amplitude is no greater than the breakdown value for air: ... = 3.0 106 V/m, assuming that this value is unaffected by the frequency of the wave.a) Calculate the maximum amplitude the magnetic field of this wave can have.b) Calculate the intensity of this wave.c) What happens to a wave more intense than this? Get solution
43. A continuous-wave (cw) argon-ion laser beam has an average power of 10.0 W and a beam diameter of 1.00 mm. Assume that the intensity of the beam is the same throughout the cross section of the beam (which is not true, as the actual distribution of intensity is a Gaussian function).a) Calculate the intensity of the laser beam. Compare this with the average intensity of sunlight at Earth’s surface (1400. W/m2).b) Find the root-mean-square electric field in the laser beam.c) Find the average value of the Poynting vector over time.d) If the wavelength of the laser beam is 514.5 nm in vacuum, write an expression for the instantaneous Poynting vector, where the instantaneous Poynting vector is zero at t = 0 and x = 0.e) Calculate the root-mean-square value of the magnetic field in the laser beam. Get solution
45. Radiation from the Sun reaches the Earth at a rate of 1.40 kW/m2 above the atmosphere and at a rate of 1.00 kW/m2 on an ocean beach.a) Calculate the maximum values of E and B above the atmosphere.b) Find the pressure and the force exerted by the radiation on a person lying flat on the beach who has an area of 0.750 m2 exposed to the Sun. Get solution
47. A solar sail is a giant circle (with a radius R = 10.0 km) made of a material that is perfectly reflecting on one side and totally absorbing on the other side. In deep space, away from other sources of light, the cosmic microwave background will provide the primary source of radiation incident on the sail. Assuming that this radiation is that of an ideal black body at T = 2.725 K, calculate the net force on the sail due to its reflection and absorption. Also assume that any heat transferred to the sail will be conducted away, and that the photons are incident perpendicular to the surface of the sail. Get solution
48. Two astronauts are at rest in outer space, one 20.0 m from the Space Shuttle and the other 40.0 m from the shuttle. Using a 100.0-W laser, the astronaut located 40.0 m away from the shuttle decides to propel the other astronaut toward the Space Shuttle. He focuses the laser on a piece of totally reflecting fabric on her space suit. If her total mass with equipment is 100.0 kg, how long will it take her to reach the Space Shuttle? Get solution
49. A laser that produces a spot of light that is 1.00 mm in diameter is shone perpendicularly on the center of a thin, perfectly reflecting circular (2.00 mm in diameter) aluminum plate mounted vertically on a flat piece of cork that floats on the surface of the water in a large beaker. The mass of this “sailboat” is 0.100 g, and it travels 2.00 mm in 63.0 s. Assuming that the laser power is constant in the region where the sailboat is located during its motion, what is the power of the laser? (Neglect air resistance and the viscosity of water.) Get solution
50. A tiny particle of density 2000. kg/m3 is at the same distance from the Sun as the Earth is (1.50 · 1011 m). Assume that the particle is spherical and perfectly reflecting. What would its radius have to be for the outward radiation pressure on it to be 1.00% of the inward gravitational attraction of the Sun? (Take the Sun’s mass to be 2.00 · 1030 kg.) Get solution
51. Silica aerogel, an extremely porous, thermally insulating material made of silica, has a density of 1.00 mg/cm3. A thin circular slice of aerogel has a diameter of 2.00 mm and a thickness of 0.10 mm.a) What is the weight of the aerogel slice (in newtons)?b) What are the intensity and the radiation pressure of a 5.00-mW laser beam of diameter 2.00 mm on the sample?c) How many 5.00-mW lasers with a beam diameter of 2.00 mm would be needed to make the slice float in the Earth’s gravitational field? Use g = 9.81 m/s2. Get solution
53. A 10.0-mW vertically polarized laser beam passes through a polarizer whose polarizing angle is 30.0° from the horizontal. What is the power of the laser beam when it emerges from the polarizer? Get solution
54. Unpolarized light of intensity I0 is incident on a series of five polarizers, with the polarization direction of each rotated 10.0° from that of the preceding one. What fraction of the incident light will pass through the series? Get solution
56. A laser beam takes 50.0 ms to be reflected back from a totally reflecting sail on a spacecraft. How far away is the sail? Get solution
57. A house with a south-facing roof has photovoltaic panels on the roof. The photovoltaic panels have an efficiency of 10.0% and occupy an area with dimensions 3.00 m by 8.00 m. The average solar radiation incident on the panels is 300. W/m2, averaged over all conditions for a year. How many kilowatt-hours of electricity will the solar panels generate in a 30-day month? Get solution
59. A 200.-W laser produces a beam with a cross-sectional area of 1.00 mm2 and a wavelength of 628 m. What is the amplitude of the electric field in the beam? Get solution
60. What is the wavelength of the electromagnetic waves used for cell phone communications at 848.97 MHz? Get solution
62. A 14.9-µF capacitor, a 24.3-kΩ resistor, a switch, and a 25.0-V battery are connected in series. What is the rate of change of the electric field between the plates of the capacitor at t = 0.3621 s after the switch is closed? The area of the plates is 1.00 cm2 Get solution
63. A focused 300-W spotlight delivers 40% of its light within a circular area with a diameter of 2 m. What is the root-mean-square electric field in this illuminated area? Get solution
65. What is the distance between successive heating antinodes in a microwave oven’s cavity? A microwave oven typically operates at a frequency of 2.4 GHz. Get solution
66. The solar constant measured by Earth satellites is roughly 1400 W/m2.a) Find the maximum electric field of the electromagnetic radiation from the Sun.b) Find the maximum magnetic field of these electromagnetic waves. Get solution
67. The peak electric field at a distance of 2.25 m from a light bulb is 21.2 V/m.a) What is the peak magnetic field there?b) What is the power output of the bulb? Get solution
68. If the peak electric field due to a star whose radius is twice that of the Sun is 44.0 V/m at a distance of 15 AU, what is its temperature? Treat the star as a blackbody. Get solution
69. A 5.00-mW laser pointer has a beam diameter of 2.00 mm.a) What is the root-mean-square value of the electric field in this laser beam?b) Calculate the total electromagnetic energy in 1.00 m of this laser beam. Get solution
70. At the surface of the Earth, the Sun delivers an estimated 1.00 kW/m2 of energy. Suppose sunlight hits a 10.0 m by 30.0 m roof at an angle of 90.0°.a) Estimate the total power incident on the roof.b) Find the radiation pressure on the roof. Get solution
71. The National Ignition Facility has the most powerful laser in the world; it uses 192 beams to aim 500. TW of power at a spherical pellet of diameter 2.00 mm. How fast would a pellet of density 2.00 g/cm3 accelerate if only one of the laser beams hits it for 1.00 ns and 2.00% of the light is absorbed? Get solution
72. A resistor consists of a solid cylinder of radius r and length L. The resistor has resistance R and is carrying current i. Use the Poynting vector to calculate the power radiated out of the surface of the resistor. Get solution
73. A radio tower is transmitting 30.0 kW of power equally in all directions. Assume that the radio waves that hit the Earth are reflected.a) What is the magnitude of the Poynting vector at a distance of 12.0 km from the tower?b) What is the root-mean-square value of the electric force on an electron at this location? Get solution
74. Quantum theory says that electromagnetic waves actually consist of discrete packets—photons—each with energy E = ħω, where ħ =1.054572·10–34 J s is Planck’s reduced constant and ω is the angular frequency of the wave.a) Find the momentum of a photon.b) Find the magnitude of angular momentum of a photon. Photons are circularly polarized; that is, they are described by a superposition of two plane-polarized waves with equal field amplitudes, equal frequencies, and perpendicular polarizations, one-quarter of a cycle (90° or π/2 rad) out of phase, so the electric and magnetic field vectors at any fixed point rotate in a circle with the angular frequency of the waves. It can be shown that a circularly polarized wave of energy U and angular frequency ω has an angular momentum of magnitude L = U/ω. (The direction of the angular momentum is given by the thumb of the right hand, when the fingers are curled in the direction in which the field vectors circulate.)c) The ratio of the angular momentum of a particle to ħ is its spin quantum number. Determine the spin quantum number of the photon. Get solution
79. During the testing of a new light bulb, a sensor is placed 52.5 cm from the bulb. It records a root-mean-square value of 9.142 · 10–7 T for the magnetic field of the radiation emitted by the bulb. What is the intensity of that radiation at the sensor’s location? Get solution
77. During the testing of a new light bulb, a sensor is placed 31.9 cm from the bulb. It records an intensity of 182.9 W/m2 for the radiation emitted by the bulb. What is the root-mean-square value of the electric field at the sensor’s location? Get solution
78. During the testing of a new light bulb, a sensor is placed 42.1 cm from the bulb. It records an intensity of 191.4 W/m2 for the radiation emitted by the bulb. What is the root-mean-square value of the magnetic field at the sensor’s location? Get solution
80. During the testing of a new light bulb, a sensor is placed 17.7 cm from the bulb. It records a root-mean-square value of 279.9 V/m for the electric field of the radiation emitted from the bulb. What is the intensity of that radiation at the sensor’s location? Get solution
81. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two polarizers on the telescope. Th e first polarizer has a polarizing angle of 28.1° relative to the horizontal, and the second has a polarizing angle of 88.6°. By what fraction is the intensity of the incident sunlight reduced by the polarizers? Get solution
82. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two polarizers on the telescope. The first polarizer has a polarizing angle of 38.3° relative to the horizontal. If the astronomers want to reduce the intensity of the sunlight by a factor of 0.7584, what polarizing angle should the second polarizer have with the horizontal? Assume that this angle is greater than that of the first polarizer. Get solution
83. To visually examine sunspots through a telescope, astronomers have to reduce the intensity of the sunlight to avoid harming their retinas. They accomplish this intensity reduction by mounting two linear polarizers on the telescope. The second polarizer has a polarizing angle of 110.6° relative to the horizontal. If the astronomers want to reduce the intensity of the sunlight by a factor of 0.7645, what polarizing angle should the first polarizer have with the horizontal? Assume that this angle is smaller than that of the second polarizer. Get solution
