Section 34.1 Maxwell S Equations and Hertz S Discoveries

Chapter 34 Problems nonmagnetic substance is v  1/ 0 0 , where κ is the dielectric constant of the 1, 2, 3 = straightforward, intermediate, substance. Determine the speed of light in challenging water, which has a dielectric constant at optical frequencies of 1.78. Section 34.1 Maxwell’s Equations and Hertz’s Discoveries 4. An electromagnetic wave in vacuum has an electric field amplitude of 220 V/m. Note: Assume that the medium is Calculate the amplitude of the vacuum unless specified otherwise. corresponding magnetic field.

5. Figure 34.3 shows a plane 1. A very long, thin rod carries electric electromagnetic sinusoidal wave charge with the linear density 35.0 nC/m. It propagating in the x direction. Suppose that lies along the x axis and moves in the x the wavelength is 50.0 m, and the electric direction at a speed of 15.0 Mm/s. (a) Find field vibrates in the xy plane with an the electric field the rod creates at the point amplitude of 22.0 V/m. Calculate (a) the (0, 20.0 cm, 0). (b) Find the magnetic field it frequency of the wave and (b) the creates at the same point. (c) Find the force magnitude and direction of B when the exerted on an electron at this point, moving electric field has its maximum value in the with a velocity of (240î) Mm/s. negative y direction. (c) Write an expression for B with the correct unit vector, with Section 34.2 Plane Electromagnetic Waves numerical values for Bmax, k, and ω, and with its magnitude in the form 2. (a) The distance to the North Star, Polaris, is approximately 6.44 × 1018 m. If B  B coskx  ωt Polaris were to burn out today, in what max year would we see it disappear? (b) How long does it take for sunlight to reach the 6. Write down expressions for the Earth? (c) How long does it take for a electric and magnetic fields of a sinusoidal microwave radar signal to travel from the plane electromagnetic wave having a Earth to the Moon and back? (d) How long frequency of 3.00 GHz and traveling in the does it take for a radio wave to travel once positive x direction. The amplitude of the around the Earth in a great circle, close to electric field is 300 V/m. the planet’s surface? (e) How long does it take for light to reach you from a lightning 7. In SI units, the electric field in an stroke 10.0 km away? electromagnetic wave is described by

E  100sin 1.00107 x  ωt 3. The speed of an electromagnetic y   wave traveling in a transparent Find (a) the amplitude of the corresponding Section 34.3 Energy Carried by magnetic field oscillations, (b) the Electromagnetic Waves wavelength λ, and (c) the frequency f. 11. How much electromagnetic energy 8. Verify by substitution that the per cubic meter is contained in sunlight, if following equations are solutions to the intensity of sunlight at the Earth’s Equations 34.8 and 34.9, respectively: surface under a fairly clear sky is 1 000 W/m2?

E  Emax coskx  ωt

B  Bmax coskx  ωt 12. An AM radio station broadcasts isotropically (equally in all directions) with 9. Review problem. A standing-wave an average power of 4.00 kW. A dipole interference pattern is set up by radio receiving antenna 65.0 cm long is at a waves between two metal sheets 2.00 m location 4.00 miles from the transmitter. apart. This is the shortest distance between Compute the amplitude of the emf that is the plates that will produce a standing- induced by this signal between the ends of wave pattern. What is the fundamental the receiving antenna. frequency? 13. What is the average magnitude of 10. A microwave oven is powered by an the Poynting vector 5.00 miles from a radio electron tube called a magnetron, which transmitter broadcasting isotropically with generates electromagnetic waves of an average power of 250 kW? frequency 2.45 GHz. The microwaves enter the oven and are reflected by the walls. The 14. A monochromatic light source emits standing-wave pattern produced in the 100 W of electromagnetic power uniformly oven can cook food unevenly, with hot in all directions. (a) Calculate the average spots in the food at antinodes and cool electric-field energy density 1.00 m from the spots at nodes, so a turntable is often used source. (b) Calculate the average magnetic- to rotate the food and distribute the energy. field energy density at the same distance If a microwave oven intended for use with from the source. (c) Find the wave intensity a turntable is instead used with a cooking at this location. dish in a fixed position, the antinodes can appear as burn marks on foods such as 15. A community plans to build a carrot strips or cheese. The separation facility to convert solar radiation to distance between the burns is measured to electrical power. They require 1.00 MW of be 6 cm ± 5%. From these data, calculate the power, and the system to be installed has speed of the microwaves. an efficiency of 30.0% (that is, 30.0% of the solar energy incident on the surface is converted to useful energy that can power the community). What must be the effective area of a perfectly absorbing surface used in 19. In a region of free space the electric ^ such an installation, assuming sunlight has field at an instant of time is E = (80.0 i + 32.0 2 a constant intensity of 1 000 W/m ? ^ ^ j – 64.0k )N/C and the magnetic field is B = ^ ^ ^ 16. Assuming that the antenna of a 10.0- (0.200 i + 0.080 0 j + 0.290k )μT. (a) Show kW radio station radiates spherical that the two fields are perpendicular to electromagnetic waves, compute the each other. (b) Determine the Poynting maximum value of the magnetic field 5.00 vector for these fields. km from the antenna, and compare this value with the surface magnetic field of the 20. Let us model the electromagnetic Earth. wave in a microwave oven as a plane traveling wave moving to the left, with an 17. The filament of an incandescent intensity of 25.0 kW/m2. An oven contains lamp has a 150-Ω resistance and carries a two cubical containers of small mass, each direct current of 1.00 A. The filament is 8.00 full of water. One has an edge length of 6.00 cm long and 0.900 mm in radius. (a) cm and the other, 12.0 cm. Energy falls Calculate the Poynting vector at the surface perpendicularly on one face of each of the filament, associated with the static container. The water in the smaller electric field producing the current and the container absorbs 70.0% of the energy that current’s static magnetic field. (b) Find the falls on it. The water in the larger container magnitude of the static electric and absorbs 91.0%. (That is, the fraction 0.3 of magnetic fields at the surface of the the incoming microwave energy passes filament. through a 6-cm thickness of water, and the fraction (0.3)(0.3) = 0.09 passes through a 18. One of the weapons being 12-cm thickness.) Find the temperature considered for the “Star Wars” antimissile change of the water in each container over a system is a laser that could destroy ballistic time interval of 480 s. Assume that a missiles. When a high-power laser is used negligible amount of energy leaves either in the Earth’s atmosphere, the electric field container by heat. can ionize the air, turning it into a conducting plasma that reflects the laser 21. A lightbulb filament has a resistance light. In dry air at 0°C and 1 atm, electric of 110 Ω. The bulb is plugged into a breakdown occurs for fields with standard 120-V (rms) outlet, and emits amplitudes above about 3.00 MV/m. (a) 1.00% of the electric power delivered to it What laser beam intensity will produce by electromagnetic radiation of frequency f. such a field? (b) At this maximum intensity, Assuming that the bulb is covered with a what power can be delivered in a filter that absorbs all other frequencies, find cylindrical beam of diameter 5.00 mm? the amplitude of the magnetic field 1.00 m from the bulb. 22. A certain microwave oven contains a magnetron that has an output of 700 W of microwave power for an electrical input power of 1.40 kW. The microwaves are entirely transferred from the magnetron into the oven chamber through a waveguide, which is a metal tube of rectangular cross section with width 6.83 cm and height 3.81 cm. (a) What is the efficiency of the magnetron? (b) Assuming that the food is absorbing all the microwaves produced by the magnetron and that no energy is reflected back into the waveguide, find the direction and magnitude of the Poynting vector, averaged over time, in the waveguide near the entrance to the oven chamber. (c) What is the maximum electric field at this point? Philippe Plailly/SPL/Photo Researchers

23. High-power lasers in factories are Figure P34.23: A laser cutting device used to cut through cloth and metal (Fig. mounted on a robot arm is being used to P34.23). One such laser has a beam cut through a metallic plate. diameter of 1.00 mm and generates an electric field having an amplitude of 0.700 24. A 10.0-mW laser has a beam MV/m at the target. Find (a) the amplitude diameter of 1.60 mm. (a) What is the of the magnetic field produced, (b) the intensity of the light, assuming it is uniform intensity of the laser, and (c) the power across the circular beam? (b) What is the delivered by the laser. average energy density of the beam?

25. 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. (d) Compare the value found in part (c) to the 30. Given that the intensity of solar value of the solar intensity given in radiation incident on the upper atmosphere Example 34.5. of the Earth is 1 340 W/m2, determine (a) the intensity of solar radiation incident on Section 34.4 Momentum and Radiation Mars, (b) the total power incident on Mars, Pressure and (c) the radiation force that acts on the planet if it absorbs nearly all of the light. (d) 26. A 100-mW laser beam is reflected Compare this force to the gravitational back upon itself by a mirror. Calculate the attraction between Mars and the Sun. (See force on the mirror. Table 13.2.)

27. A radio wave transmits 25.0 W/m2 of 31. A plane electromagnetic wave has an power per unit area. A flat surface of area intensity of 750 W/m2. A flat, rectangular A is perpendicular to the direction of surface of dimensions 50 cm × 100 cm is propagation of the wave. Calculate the placed perpendicular to the direction of the radiation pressure on it, assuming the wave. The surface absorbs half of the surface is a perfect absorber. energy and reflects half. Calculate (a) the total energy absorbed by the surface in 1.00 28. A possible means of space flight is to min and (b) the momentum absorbed in place a perfectly reflecting aluminized sheet this time. into orbit around the Earth and then use the light from the Sun to push this “solar sail.” 32. A uniform circular disk of mass 24.0 Suppose a sail of area 6.00 × 105 m2 and g and radius 40.0 cm hangs vertically from mass 6 000 kg is placed in orbit facing the a fixed, frictionless, horizontal hinge at a Sun. (a) What force is exerted on the sail? point on its circumference. A horizontal (b) What is the sail’s acceleration? (c) How beam of electromagnetic radiation with long does it take the sail to reach the Moon, intensity 10.0 MW/m2 is incident on the 3.84 × 108 m away? Ignore all gravitational disk in a direction perpendicular to its effects, assume that the acceleration surface. The disk is perfectly absorbing, and calculated in part (b) remains constant, and the resulting radiation pressure makes the assume a solar intensity of 1 340 W/m2. disk rotate. Find the angle through which the disk rotates as it reaches its new 29. A 15.0-mW helium–neon laser (λ = equilibrium position. (Assume that the 632.8 nm) emits a beam of circular cross radiation is always perpendicular to the section with a diameter of 2.00 mm. (a) Find surface of the disk.) the maximum electric field in the beam. (b) What total energy is contained in a 1.00-m Section 34.5 Production of length of the beam? (c) Find the momentum Electromagnetic Waves by an Antenna carried by a 1.00-m length of the beam. 33. Figure 34.10 shows a Hertz antenna demonstrated that the current creates a (also known as a halfwave antenna, because magnetic field on both sides of the sheet, its length is λ/2). The antenna is located far parallel to the sheet and perpendicular to enough from the ground that reflections do the current, with magnitude B = ½μ0Js. If the not significantly affect its radiation pattern. current oscillates in time according to Most AM radio stations, however, use a Marconi antenna, which consists of the top ^ ^ J s  J max cosωtj  J max cos ωtj half of a Hertz antenna. The lower end of this (quarter-wave) antenna is connected to the sheet radiates an electromagnetic wave Earth ground, and the ground itself serves as shown in Figure P34.37. The magnetic as the missing lower half. What are the field of the wave is described by the wave heights of the Marconi antennas for radio ^ stations broadcasting at (a) 560 kHz and (b) function B = ½μ0Jmax[cos(kx – ωt)]k . (a) Find 1 600 kHz? the wave function for the electric field in the wave. (b) Find the Poynting vector as a 34. Two hand-held radio transceivers function of x and t. (c) Find the intensity of with dipole antennas are separated by a the wave. (d) What If? If the sheet is to emit large fixed distance. If the transmitting radiation in each direction (normal to the 2 antenna is vertical, what fraction of the plane of the sheet) with intensity 570 W/m , maximum received power will appear in what maximum value of sinusoidal current the receiving antenna when it is inclined density is required? from the vertical by (a) 15.0°? (b) 45.0°? (c) 90.0°?

35. Two radio-transmitting antennas are separated by half the broadcast wavelength and are driven in phase with each other. In which directions are (a) the strongest and (b) the weakest signals radiated?

36. Review problem. Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation Figure P34.37: Representation of the plane produced by a proton moving in a circle of electromagnetic wave radiated by an radius R perpendicular to a magnetic field infinite current sheet lying in the yz plane. of magnitude B. The vector B is in the z direction, the vector E is in the y direction, and the direction of 37. A very large flat sheet carries a wave motion is along x. Both vectors have uniformly distributed electric current with magnitudes proportional to cos(kx – ωt). current per unit width Js. Example 30.6 far away is the object that reflected the Section 34.6 The Spectrum of wave? Electromagnetic Waves 44. This just in! An important news 38. Classify waves with frequencies of 2 announcement is transmitted by radio Hz, 2 kHz, 2 MHz, 2 GHz, 2 THz, 2 PHz, 2 waves to people sitting next to their radios EHz, 2 ZHz, and 2 YHz on the 100 km from the station, and by sound electromagnetic spectrum. Classify waves waves to people sitting across the with wavelengths of 2 km, 2 m, 2 mm, 2 newsroom, 3.00 m from the newscaster. μm, 2 nm, 2 pm, 2 fm, and 2 am. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s. 39. The human eye is most sensitive to light having a wavelength of 5.50 × 10–7 m, 45. The United States Navy has long which is in the green-yellow region of the proposed the construction of extremely visible electromagnetic spectrum. What is low-frequency (ELF) communication the frequency of this light? systems. Such waves could penetrate the oceans to reach distant submarines. 40. Compute an order-of-magnitude Calculate the length of a quarter- estimate for the frequency of an wavelength antenna for a transmitter electromagnetic wave with wavelength generating ELF waves of frequency 75.0 Hz. equal to (a) your height; (b) the thickness of How practical is this? this sheet of paper. How is each wave classified on the electromagnetic spectrum? 46. What are the wavelength ranges in (a) the AM radio band (540–1 600 kHz), and 41. What are the wavelengths of (b) the FM radio band (88.0–108 MHz)? electromagnetic waves in free space that have frequencies of (a) 5.00 × 1019 Hz and Additional Problems (b) 4.00 × 109 Hz? 47. Assume that the intensity of solar 42. Suppose you are located 180 m from radiation incident on the cloudtops of the a radio transmitter. (a) How many Earth is 1 340 W/m2. (a) Calculate the total wavelengths are you from the transmitter if power radiated by the Sun, taking the the station calls itself 1 150 AM? (The AM average Earth–Sun separation to be 1.496 × band frequencies are in kilohertz.) (b) What 1011 m. (b) Determine the maximum values If? What if this station is 98.1 FM? (The FM of the electric and magnetic fields in the band frequencies are in megahertz.) sunlight at the Earth’s location.

43. A radar pulse returns to the receiver 48. The intensity of solar radiation at the after a total travel time of 4.00 × 10–4 s. How top of the Earth’s atmosphere is 1 340 W/m2. Assuming that 60% of the incoming solar energy reaches the Earth’s surface and density of 1.50 g/cm3. Let the particle be assuming that you absorb 50% of the located 3.75 × 1011 m from the Sun, and use incident energy, make an order-of- 214 W/m2 as the value of the solar intensity magnitude estimate of the amount of solar at that point.) energy you absorb in a 60-min sunbath. 51. A dish antenna having a diameter of 49. Review problem. In the absence of 20.0 m receives (at normal incidence) a cable input or a satellite dish, a television radio signal from a distant source, as shown set can use a dipole-receiving antenna for in Figure P34.51. The radio signal is a VHF channels and a loop antenna for UHF continuous sinusoidal wave with channels (Fig. Q34.12). The UHF antenna amplitude Emax = 0.200 μV/m. Assume the produces an emf from the changing antenna absorbs all the radiation that falls magnetic flux through the loop. The TV on the dish. (a) What is the amplitude of the station broadcasts a signal with a frequency magnetic field in this wave? (b) What is the f, and the signal has an electric-field intensity of the radiation received by this amplitude Emax and a magnetic-field antenna? (c) What is the power received by amplitude Bmax at the location of the the antenna? (d) What force is exerted by receiving antenna. (a) Using Faraday’s law, the radio waves on the antenna? derive an expression for the amplitude of the emf that appears in a single-turn circular loop antenna with a radius r, which is small compared with the wavelength of the wave. (b) If the electric field in the signal points vertically, what orientation of the loop gives the best reception?

50. Consider a small, spherical particle of radius r located in space a distance R from the Sun. (a) Show that the ratio

Frad/Fgrav is proportional to 1/r, where Frad is the force exerted by solar radiation and Fgrav is the force of gravitational attraction. (b) The result of part (a) means that, for a Figure P34.51 sufficiently small value of r, the force exerted on the particle by solar radiation 52. One goal of the Russian space exceeds the force of gravitational attraction. program is to illuminate dark northern Calculate the value of r for which the cities with sunlight reflected to Earth from a particle is in equilibrium under the two 200-m diameter mirrored surface in orbit. forces. (Assume that the particle has a Several smaller prototypes have already perfectly absorbing surface and a mass been constructed and put into orbit. (a) be continuously exposed to the radiation. Assume that sunlight with intensity 1 340 Compare the answer to part (a) with this W/m2 falls on the mirror nearly standard. perpendicularly and that the atmosphere of the Earth allows 74.6% of the energy of sunlight to pass through it in clear weather. What is the power received by a city when the space mirror is reflecting light to it? (b) The plan is for the reflected sunlight to cover a circle of diameter 8.00 km. What is the intensity of light (the average magnitude of the Poynting vector) received by the city? (c) This intensity is what percentage of the vertical component of sunlight at Saint Petersburg in January, when the sun reaches an angle of 7.00° Amos Morgan/Getty Images above the horizon at noon? Figure P34.54 53. In 1965, Arno Penzias and Robert 55. A linearly polarized microwave of Wilson discovered the cosmic microwave wavelength 1.50 cm is directed along the radiation left over from the Big Bang positive x axis. The electric field vector has expansion of the Universe. Suppose the a maximum value of 175 V/m and vibrates energy density of this background radiation in the xy plane. (a) Assume that the is 4.00 × 10–14 J/m3. Determine the magnetic field component of the wave can corresponding electric field amplitude. be written in the form B = Bmax sin(kx – ωt) and give values for B , k, and ω. Also, 54. A hand-held cellular telephone max determine in which plane the magnetic operates in the 860- to 900-MHz band and field vector vibrates. (b) Calculate the has a power output of 0.600 W from an average value of the Poynting vector for antenna 10.0 cm long (Fig. P34.54). (a) Find this wave. (c) What radiation pressure the average magnitude of the Poynting would this wave exert if it were directed at vector 4.00 cm from the antenna, at the normal incidence onto a perfectly reflecting location of a typical person’s head. Assume sheet? (d) What acceleration would be that the antenna emits energy with imparted to a 500-g sheet (perfectly cylindrical wave fronts. (The actual reflecting and at normal incidence) with radiation from antennas follows a more dimensions of 1.00 m × 0.750 m? complicated pattern.) (b) The ANSI/IEEE C95.1-1991 maximum exposure standard is 56. The Earth reflects approximately 0.57 mW/cm2 for persons living near 38.0% of the incident sunlight from its cellular telephone base stations, who would clouds and surface. (a) Given that the mass of 1.00 μg and a density of 0.200 intensity of solar radiation is 1 340 W/m2, g/cm3. Determine the radiation intensity what is the radiation pressure on the Earth, needed to support the bead. (b) If the beam in pascals, at the location where the Sun is has a radius of 0.200 cm, what is the power straight overhead? (b) Compare this to required for this laser? normal atmospheric pressure at the Earth’s surface, which is 101 kPa. 60. Lasers have been used to suspend spherical glass beads in the Earth’s 57. An astronaut, stranded in space 10.0 gravitational field. (a) A black bead has a m from his spacecraft and at rest relative to mass m and a density ρ. Determine the it, has a mass (including equipment) of 110 radiation intensity needed to support the kg. Because he has a 100-W light source that bead. (b) If the beam has a radius r, what is forms a directed beam, he considers using the power required for this laser? the beam as a photon rocket to propel himself continuously toward the spacecraft. 61. A microwave source produces (a) Calculate how long it takes him to reach pulses of 20.0-GHz radiation, with each the spacecraft by this method. (b) What If? pulse lasting 1.00 ns. A parabolic reflector Suppose, instead, that he decides to throw with a face area of radius 6.00 cm is used to the light source away in a direction focus the microwaves into a parallel beam opposite the spacecraft. If the mass of the of radiation, as shown in Figure P34.61. The light source is 3.00 kg and, after being average power during each pulse is 25.0 thrown, it moves at 12.0 m/s relative to the kW. (a) What is the wavelength of these recoiling astronaut, how long does it take microwaves? (b) What is the total energy for the astronaut to reach the spacecraft? contained in each pulse? (c) Compute the average energy density inside each pulse. 58. Review problem. A 1.00-m-diameter (d) Determine the amplitude of the electric mirror focuses the Sun’s rays onto an and magnetic fields in these microwaves. absorbing plate 2.00 cm in radius, which (e) Assuming this pulsed beam strikes an holds a can containing 1.00 L of water at absorbing surface, compute the force 20.0°C. (a) If the solar intensity is 1.00 exerted on the surface during the 1.00-ns kW/m2, what is the intensity on the duration of each pulse. absorbing plate? (b) What are the maximum magnitudes of the fields E and B? (c) If 40.0% of the energy is absorbed, how long does it take to bring the water to its boiling point?

59. Lasers have been used to suspend spherical glass beads in the Earth’s gravitational field. (a) A black bead has a Figure P34.61 incident on the black disk, and the mirror 62. The electromagnetic power radiated disk is completely shielded. Calculate the by a nonrelativistic moving point charge q angle between the equilibrium positions of having an acceleration a is the horizontal bar when the beam is switched from “off” to “on.” q 2 a 2 = 3 6 0c 65. A “laser cannon” of a spacecraft has a beam of cross-sectional area A. The maximum electric field in the beam is E. where ε0 is the permittivity of free space and c is the speed of light in vacuum. (a) The beam is aimed at an asteroid that is Show that the right side of this equation has initially moving in the direction of the units of watts. (b) An electron is placed in a spacecraft. What is the acceleration of the constant electric field of magnitude 100 asteroid relative to the spacecraft if the laser N/C. Determine the acceleration of the beam strikes the asteroid perpendicular to electron and the electromagnetic power its surface, and the surface is nonreflecting? radiated by this electron. (c) What If? If a The mass of the asteroid is m. Ignore the proton is placed in a cyclotron with a radius acceleration of the spacecraft. of 0.500 m and a magnetic field of magnitude 0.350 T, what electromagnetic 66. A plane electromagnetic wave varies power does this proton radiate? sinusoidally at 90.0 MHz as it travels along the +x direction. The peak value of the 63. A thin tungsten filament of length electric field is 2.00 mV/m, and it is directed 1.00 m radiates 60.0 W of power in the form along the ± y direction. (a) Find the of electromagnetic waves. A perfectly wavelength, the period, and the maximum absorbing surface in the form of a hollow value of the magnetic field. (b) Write cylinder of radius 5.00 cm and length 1.00 expressions in SI units for the space and m is placed concentrically with the time variations of the electric field and of filament. Calculate the radiation pressure the magnetic field. Include numerical acting on the cylinder. (Assume that the values and include subscripts to indicate radiation is emitted in the radial direction, coordinate directions. (c) Find the average and ignore end effects.) power per unit area that this wave carries through space. (d) Find the average energy 64. The torsion balance shown in Figure density in the radiation (in joules per cubic 34.8 is used in an experiment to measure meter). (e) What radiation pressure would radiation pressure. The suspension fiber this wave exert upon a perfectly reflecting exerts an elastic restoring torque. Its torque surface at normal incidence? constant is 1.00 × 10–11 N · m/degree, and the length of the horizontal rod is 6.00 cm. The Note: Section 20.7 introduced beam from a 3.00-mW helium–neon laser is electromagnetic radiation as a mode of energy transfer. The following three problems use ideas introduced both there and in the current chapter. 67. Eliza is a black cat with four black emissivity for visible light is 0.900 and its kittens: Penelope, Rosalita, Sasha, and emissivity for infrared light is 0.700. Timothy. Eliza’s mass is 5.50 kg, and each Assume that light from the noon Sun is kitten has mass 0.800 kg. One cool night all incident perpendicular to the glass with an five sleep snuggled together on a mat, with intensity of 1 000 W/m2, and that no water their bodies forming one hemisphere. (a) enters or leaves the box. Find the steady- Assuming that the purring heap has state temperature of the interior of the box. uniform density 990 kg/m3, find the radius (b) What If? The couple builds an identical of the hemisphere. (b) Find the area of its box with no water tubes. It lies flat on the curved surface. (c) Assume the surface ground in front of the house. They use it as temperature is uniformly 31.0°C and the a cold frame, where they plant seeds in emissivity is 0.970. Find the intensity of early spring. Assuming the same noon Sun radiation emitted by the cats at their curved is at an elevation angle of 50.0°, find the surface, and (d) the radiated power from steady-state temperature of the interior of this surface. (e) You may think of the this box when its ventilation slots are emitted electromagnetic wave as having a tightly closed. single predominant frequency (of 31.2 THz). Find the amplitude of the electric field just outside the surface of the cozy pile, and (f) the amplitude of the magnetic field. (g) Are the sleeping cats charged? Are they current-carrying? Are they magnetic? Are they a radiation source? Do they glow in the dark? Give an explanation for your answers so that they do not seem © Bill Banaszewski/Visuals Unlimited contradictory. (h) What If? The next night the kittens all sleep alone, curling up into Figure P34.68 separate hemispheres like their mother. Find the total radiated power of the family. 69. Review problem. The study of (For simplicity, we ignore throughout the Creation suggests a Creator with an cats’ absorption of radiation from the inordinate fondness for beetles and for environment.) small red stars. A small red star radiates electromagnetic waves with power 6.00 × 23 68. Review problem. (a) An elderly 10 W, which is only 0.159% of the couple has a solar water heater installed on luminosity of the Sun. Consider a spherical the roof of their house (Fig. P34.68). The planet in a circular orbit around this star. heater consists of a flat closed box with Assume the emissivity of the planet is equal extraordinarily good thermal insulation. Its for infrared and for visible light. Assume interior is painted black, and its front face is the planet has a uniform surface made of insulating glass. Assume that its temperature. Identify the projected area over which the planet absorbs starlight and the radiating area of the planet. If beetles thrive at a temperature of 310 K, what should be the radius of the planet’s orbit?