Solved: Consider a bright star in our night sky. Assume

A spherical interplanetary grain of dust of radius 0.2 mm is at a distance r1 from the Sun. The gravitational force exerted by the Sun on the grain just balances the force due to radiation pressure from the Suns light. (i) Assume the grain is moved to a distance 2r1 from the Sun and released. At this location, what is the net force exerted on the grain? (a) toward the Sun (b) away from the Sun (c) zero (d) impossible to determine without knowing the mass of the grain (ii) Now assume the grain is moved back to its original location at r1, compressed so that it crystallizes into a sphere with significantly higher density, and then released. In this situation, what is the net force exerted on the grain? Choose from the same possibilities as in part (i).

A small source radiates an electromagnetic wave with a single frequency into vacuum, equally in all directions. (i) As the wave moves, does its frequency (a) increase, (b) decrease, or (c) stay constant? Using the same choices, answer the same question about (ii) its wavelength, (iii) its speed, (iv) its intensity, and (v) the amplitude of its electric field.

A typical microwave oven operates at a frequency of 2.45 GHz. What is the wavelength associated with the electromagnetic waves in the oven? (a) 8.20 m (b) 12.2 cm (c) 1.20 3 108 m (d) 8.20 3 1029 m (e) none of those answers

A student working with a transmitting apparatus like Heinrich Hertzs wishes to adjust the electrodes to generate electromagnetic waves with a frequency half as large as before. (i) How large should she make the effective capacitance of the pair of electrodes? (a) four times larger than before (b) two times larger than before (c) one-half as large as before (d) one-fourth as large as before (e) none of those answers (ii) After she makes the required adjustment, what will the wavelength of the transmitted wave be? Choose from the same possibilities as in part (i).

Assume you charge a comb by running it through your hair and then hold the comb next to a bar magnet. Do the electric and magnetic fields produced constitute an electromagnetic wave? (a) Yes they do, necessarily. (b) Yes they do because charged particles are moving inside the bar magnet. (c) They can, but only if the electric field of the comb and the magnetic field of the magnet are perpendicular. (d) They can, but only if both the comb and the magnet are moving. (e) They can, if either the comb or the magnet or both are accelerating.

Which of the following statements are true regarding electromagnetic waves traveling through a vacuum? More than one statement may be correct. (a) All waves have the same wavelength. (b) All waves have the same frequency. (c) All waves travel at 3.00 3 108 m/s. (d) The electric and magnetic fields associated with the waves are perpendicular to each other and to the direction of wave propagation. (e) The speed of the waves depends on their frequency.

A plane electromagnetic wave with a single frequency moves in vacuum in the positive x direction. Its amplitude is uniform over the yz plane. (i) As the wave moves, does its frequency (a) increase, (b) decrease, or (c) stay constant? Using the same choices, answer the same question about (ii) its wavelength, (iii) its speed, (iv) its intensity, and (v) the amplitude of its magnetic field

Assume the amplitude of the electric field in a plane electromagnetic wave is E1 and the amplitude of the magnetic field is B1. The source of the wave is then adjusted so that the amplitude of the electric field doubles to become 2E1. (i) What happens to the amplitude of the magnetic field in this process? (a) It becomes four times larger. (b) It becomes two times larger. (c) It can stay constant. (d) It becomes one-half as large. (e) It becomes one-fourth as large. (ii) What happens to the intensity of the wave? Choose from the same possibilities as in part (i).

An electromagnetic wave with a peak magnetic field magnitude of 1.50 3 1027 T has an associated peak electric field of what magnitude? (a) 0.500 3 10215 N/C (b) 2.00 3 1025 N/C (c) 2.20 3 104 N/C (d) 45.0 N/C (e) 22.0 N/C

i) Rank the following kinds of waves according to their wavelength ranges from those with the largest typical or average wavelength to the smallest, noting any cases of equality: (a) gamma rays (b) microwaves (c) radio waves (d) visible light (e) x-rays (ii) Rank the kinds of waves according to their frequencies from highest to lowest. (iii) Rank the kinds of waves according to their speeds in vacuum from fastest to slowest.

Consider an electromagnetic wave traveling in the positive y direction. The magnetic field associated with the wave at some location at some instant points in the negative x direction as shown in Figure OQ34.11. What is the direction of the electric field at this position and at this instant? (a) the positive x direction (b) the positive y direction (c) the positive z direction (d) the negative z direction (e) the negative y direction

An empty plastic or glass dish being removed from a microwave oven can be cool to the touch, even when food on an adjoining dish is hot. How is this phenomenon possible?

What new concept did Maxwells generalized form of Ampres law include?

A radar pulse returns to the transmitterreceiver after a total travel time of 4.00 3 1024 s. How far away is the object that reflected the wave?

Figure P34.15 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 50.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m. Calculate (a) the frequency of the wave and (b) the magnetic field B S when the electric field has its maximum value in the negative y direction. (c) Write an expression for B S with the correct unit vector, with numerical values for Bmax, k, and v, and with its magnitude in the form B 5 Bmax cos (kx 2 vt)

Verify by substitution that the following equations are solutions to Equations 34.15 and 34.16, respectively: E 5 E max cos (kx 2 vt) B 5 Bmax cos (kx 2 vt)

Review. A microwave oven is powered by a magnetron, an electronic device that generates electromagnetic waves of frequency 2.45 GHz. The microwaves enter the oven and are reflected by the walls. The standing-wave pattern produced in the oven can cook food unevenly, with hot spots in the food at antinodes and cool spots at nodes, so a turntable is often used to rotate the food and distribute the energy. If a microwave oven intended for use with a turntable is instead used with a cooking dish in a fixed position, the antinodes can appear as burn marks on foods such as carrot strips or cheese. The separation distance between the burns is measured to be 6 cm 6 5%. From these data, calculate the speed of the microwaves

Why is the following situation impossible? An electromagnetic wave travels through empty space with electric and magnetic fields described by E 5 9.00 3 103 cos [(9.00 3 106)x 2 (3.00 3 1015)t ] B 5 3.00 3 1025 cos [(9.00 3 106)x 2 (3.00 3 1015)t ] where all numerical values and variables are in SI units

In SI units, the electric field in an electromagnetic wave is described by E y 5 100 sin (1.00 3 107 x 2 vt) Find (a) the amplitude of the corresponding magnetic field oscillations, (b) the wavelength l, and (c) the frequency f.

At what distance from the Sun is the intensity of sunlight three times the value at the Earth? (The average EarthSun separation is 1.496 3 1011 m.)

If the intensity of sunlight at the Earths surface under a fairly clear sky is 1 000 W/m2, how much electromagnetic energy per cubic meter is contained in sunlight?

The power of sunlight reaching each square meter of the Earths surface on a clear day in the tropics is close to 1 000 W. On a winter day in Manitoba, the power concentration of sunlight can be 100 W/m2. Many human activities are described by a power per unit area on the order of 102 W/m2 or less. (a) Consider, for example, a family of four paying $66 to the electric company every 30 days for 600 kWh of energy carried by electrical transmission to their house, which has floor dimensions of 13.0 m by 9.50 m. Compute the power per unit area used by the family. (b) Consider a car 2.10 m wide and 4.90 m long traveling at 55.0 mi/h using gasoline having heat of combustion 44.0 MJ/kg with fuel economy 25.0 mi/gal. One gallon of gasoline has a mass of 2.54 kg. Find the power per unit area used by the car. (c) Explain why direct use of solar energy is not practical for running a conventional automobile. (d) What are some uses of solar energy that are more practical?

A community plans to build a facility to convert solar radiation to electrical power. The community requires 1.00 MW of power, and the system to be installed has 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). Assuming sunlight has a constant intensity of 1 000 W/m2, what must be the effective area of a perfectly absorbing surface used in such an installation?

In a region of free space, the electric field at an instant of time is E S 5 180.0i ^ 1 32.0j ^ 2 64.0k^ 2 N/C and the magnetic field is B S 5 10.200i ^ 1 0.080 0j ^ 1 0.290k^ 2 mT. (a) Show that the two fields are perpendicular to each other. (b) Determine the Poynting vector for these fields.

When a high-power laser is used in the Earths atmosphere, the electric field associated with the laser beam can ionize the air, turning it into a conducting plasma that reflects the laser light. In dry air at 0C and 1 atm, electric breakdown occurs for fields with amplitudes above about 3.00 MV/m. (a) What laser beam intensity will produce such a field? (b) At this maximum intensity, what power can be delivered in a cylindrical beam of diameter 5.00 mm?

Review. Model the electromagnetic wave in a microwave oven as a plane traveling wave moving to the left, with an intensity of 25.0 kW/m2. An oven contains two cubical containers of small mass, each full of water. One has an edge length of 6.00 cm, and the other, 12.0 cm. Energy falls perpendicularly on one face of each container. The water in the smaller container absorbs 70.0% of the energy that falls on it. The water in the larger container absorbs 91.0%. That is, the fraction 0.300 of the incoming microwave energy passes through a 6.00-cm thickness of water, and the fraction (0.300)(0.300) 5 0.090 passes through a 12.0-cm thickness. Assume a negligible amount of energy leaves either container by heat. Find the temperature change of the water in each container over a time interval of 480 s.

High-power lasers in factories are used to cut through cloth and metal (Fig. P34.27). One such laser has a beam diameter of 1.00 mm and generates an electric field having an amplitude of 0.700 MV/m at the target. Find (a) the amplitude of the magnetic field produced, (b) the intensity of the laser, and (c) the power delivered by the laser

Consider a bright star in our night sky. Assume its distance from the Earth is 20.0 light-years (ly) and its power output is 4.00 3 1028 W, about 100 times that of the Sun. (a) Find the intensity of the starlight at the Earth. (b) Find the power of the starlight the Earth intercepts. One light-year is the distance traveled by light through a vacuum in one year.

What is the average magnitude of the Poynting vector 5.00 mi from a radio transmitter broadcasting isotropically (equally in all directions) with an average power of 250 kW?

Assuming the antenna of a 10.0-kW radio station radiates spherical electromagnetic waves, (a) compute the maximum value of the magnetic field 5.00 km from the antenna and (b) state how this value compares with the surface magnetic field of the Earth.

Review. An AM radio station broadcasts isotropically (equally in all directions) with an average power of 4.00 kW. A receiving antenna 65.0 cm long is at a location 4.00 mi from the transmitter. Compute the amplitude of the emf that is induced by this signal between the ends of the receiving antenna.

At what distance from a 100-W electromagnetic wave point source does E max 5 15.0 V/m?

The filament of an incandescent lamp has a 150-V resistance and carries a direct current of 1.00 A. The filament is 8.00 cm long and 0.900 mm in radius. (a) Calculate the Poynting vector at the surface of the filament, associated with the static electric field producing the current and the currents static magnetic field. (b) Find the magnitude of the static electric and magnetic fields at the surface of the filament.

At one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.80 mT. 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 Suns radiation.

A 25.0-mW laser beam of diameter 2.00 mm is reflected at normal incidence by a perfectly reflecting mirror. Calculate the radiation pressure on the mirror.

A radio wave transmits 25.0 W/m2 of power per unit area. A flat surface of area A is perpendicular to the direction of propagation of the wave. Assuming the surface is a perfect absorber, calculate the radiation pressure on it.

A 15.0-mW heliumneon laser emits a beam of circular cross section with a diameter of 2.00 mm. (a) Find the maximum electric field in the beam. (b) What total energy is contained in a 1.00-m length of the beam? (c) Find the momentum carried by a 1.00-m length of the beam.

A heliumneon laser emits a beam of circular cross section with a radius r and a power P. (a) Find the maximum electric field in the beam. (b) What total energy is contained in a length , of the beam? (c) Find the momentum carried by a length , of the beam.

A uniform circular disk of mass m 5 24.0 g and radius r 5 40.0 cm hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference as shown in Figure P34.39a. A beam of electromagnetic radiation with intensity 10.0 MW/m2 is incident on the disk in a direction perpendicular to its surface. The disk is perfectly absorbing, and the resulting radiation pressure makes the disk rotate. Assuming the radiation is always perpendicular to the surface of the disk, find the angle u through which the disk rotates from the vertical as it reaches its new equilibrium position shown in Figure 34.39b.

The intensity of sunlight at the Earths distance from the Sun is 1 370 W/m2. Assume the Earth absorbs all the sunlight incident upon it. (a) Find the total force the Sun exerts on the Earth due to radiation pressure. (b) Explain how this force compares with the Suns gravitational attraction.

A plane electromagnetic wave of intensity 6.00 W/m2, moving in the x direction, strikes a small perfectly reflecting pocket mirror, of area 40.0 cm2, held in the yz plane. (a) What momentum does the wave transfer to the mirror each second? (b) Find the force the wave exerts on the mirror. (c) Explain the relationship between the answers to parts (a) and (b).

Assume the intensity of solar radiation incident on the upper atmosphere of the Earth is 1 370 W/m2 and use data from Table 13.2 as necessary. Determine (a) the intensity of solar radiation incident on Mars, (b) the total power incident on Mars, and (c) the radiation force that acts on that planet if it absorbs nearly all the light. (d) State how this force compares with the gravitational attraction exerted by the Sun on Mars. (e) Compare the ratio of the gravitational force to the light-pressure force exerted on the Earth and the ratio of these forces exerted on Mars, found in part (d).

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this solar sail. Suppose a sail of area A 5 6.00 3 105 m2 and mass m 5 6.00 3 103 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1 370 W/m2. (a) What force is exerted on the sail? (b) What is the sails acceleration? (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval required for the sail to reach the Moon, 3.84 3 108 m away, starting from rest at the Earth.

Extremely low-frequency (ELF) waves that can penetrate the oceans are the only practical means of communicating with distant submarines. (a) Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 75.0 Hz into air. (b) How practical is this means of communication?

A Marconi antenna, used by most AM radio stations, consists of the top half of a Hertz antenna (also known as a half-wave antenna because its length is l/2). The lower end of this Marconi (quarter-wave) antenna is connected to Earth ground, and the ground itself serves as the missing lower half. What are the heights of the Marconi antennas for radio stations broadcasting at (a) 560 kHz and (b) 1 600 kHz?

A large, flat sheet carries a uniformly distributed electric current with current per unit width Js. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B 5 1 2m0 Js. If the current is in the y direction and oscillates in time according to Jmax 1cos vt 2 j ^ 5 Jmax 3cos 12vt2 4 j ^ the sheet radiates an electromagnetic wave. Figure P34.46 shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function B S 5 1 2m0 Jmax 3cos 1kx 2 vt2 4 k (a) Find the wave function for the electric field of the wave to the right of the sheet. (b) Find the Poynting vector as a function of x and t. (c) Find the intensity of the wave. (d)What If? If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 570W/m2, what maximum value of sinusoidal current density is required?

Review. Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.350 T

Review. Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton of mass mp moving in a circular path perpendicular to a magnetic field of magnitude B.

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

Compute an order-of-magnitude estimate for the frequency of an electromagnetic wave with wavelength equal to (a) your height and (b) the thickness of a sheet of paper. How is each wave classified on the electromagnetic spectrum?

What are the wavelengths of electromagnetic waves in free space that have frequencies of (a) 5.00 3 1019 Hz and (b) 4.00 3 109 Hz?

An important news announcement is transmitted by radio waves to people sitting next to their radios 100 km from the station and by sound waves to people sitting across the newsroom 3.00 m from the newscaster. Taking the speed of sound in air to be 343 m/s, who receives the news first? Explain.

In addition to cable and satellite broadcasts, television stations still use VHF and UHF bands for digitally broadcasting their signals. Twelve VHF television channels (channels 2 through 13) lie in the range of frequencies between 54.0 MHz and 216 MHz. Each channel is assigned a width of 6.00 MHz, with the two ranges 72.076.0 MHz and 88.0174 MHz reserved for non-TV purposes. (Channel 2, for example, lies between 54.0 and 60.0 MHz.) Calculate the broadcast wavelength range for (a) channel 4, (b) channel 6, and (c) channel 8.

Classify waves with frequencies of 2 Hz, 2 kHz, 2 MHz, 2 GHz, 2 THz, 2 PHz, 2 EHz, 2 ZHz, and 2 YHz on the electromagnetic spectrum. Classify waves with wavelengths of 2 km, 2 m, 2 mm, 2 mm, 2 nm, 2 pm, 2 fm, and 2 am.

Assume the intensity of solar radiation incident on the cloud tops of the Earth is 1 370 W/m2. (a) Taking the average EarthSun separation to be 1.496 3 1011 m, calculate the total power radiated by the Sun. Determine the maximum values of (b) the electric field and (c) the magnetic field in the sunlight at the Earths location

In 1965, Arno Penzias and Robert Wilson discovered the cosmic microwave radiation left over from the big bang expansion of the Universe. Suppose the energy density of this background radiation is 4.00 3 10214 J/m3. Determine the corresponding electric field amplitude

The eye is most sensitive to light having a frequency of 5.45 3 1014 Hz, which is in the green-yellow region of the visible electromagnetic spectrum. What is the wavelength of this light?

Write expressions for the electric and magnetic fields of a sinusoidal plane electromagnetic wave having an electric field amplitude of 300 V/m and a frequency of 3.00 GHz and traveling in the positive x direction.

One goal of the Russian space program is to illuminate dark northern cities with sunlight reflected to the Earth from a 200-m diameter mirrored surface in orbit. Several smaller prototypes have already been constructed and put into orbit. (a) Assume that sunlight with intensity 1 370 W/m2 falls on the mirror nearly perpendicularly and that the atmosphere of the Earth allows 74.6% of the energy of sunlight to pass though 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 St. Petersburg in January, when the sun reaches an angle of 7.00 above the horizon at noon?

A microwave source produces pulses of 20.0-GHz radiation, with each pulse lasting 1.00 ns. A parabolic reflector with a face area of radius 6.00 cm is used to focus the microwaves into a parallel beam of radiation as shown in Figure P34.60. The average power during each pulse is 25.0 kW. (a) What is the wavelength of these microwaves? (b) What is the total energy contained in each pulse? (c) Compute the average energy density inside each pulse. (d) Determine the amplitude of the electric and magnetic fields in these microwaves. (e) Assuming that this pulsed beam strikes an absorbing surface, compute the force exerted on the surface during the 1.00-ns duration of each pulse.

The intensity of solar radiation at the top of the Earths atmosphere is 1 370 W/m2. Assuming 60% of the incoming solar energy reaches the Earths surface and you absorb 50% of the incident energy, make an orderof-magnitude estimate of the amount of solar energy you absorb if you sunbathe for 60 minutes.

Two handheld radio transceivers with dipole antennas are separated by a large, fixed distance. If the transmitting antenna is vertical, what fraction of the maximum received power will appear in the receiving antenna when it is inclined from the vertical (a) by 15.0? (b) By 45.0? (c) By 90.0?

Consider a small, spherical particle of radius r located in space a distance R 5 3.75 3 1011 m from the Sun. Assume the particle has a perfectly absorbing surface and a mass density of r 5 1.50 g/cm3. Use S 5 214 W/m2 as the value of the solar intensity at the location of the particle. Calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation.

Consider a small, spherical particle of radius r located in space a distance R from the Sun, of mass MS . Assume the particle has a perfectly absorbing surface and a mass density r. The value of the solar intensity at the particles location is S. Calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation. Your answer should be in terms of S, R, r, and other constants

A dish antenna having a diameter of 20.0 m receives (at normal incidence) a radio signal from a distant source as shown in Figure P34.65. The radio signal is a continuous sinusoidal wave with amplitude E max 5 0.200 mV/m. Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic field in this wave? (b) What is the intensity of the radiation received by this antenna? (c) What is the power received by the antenna? (d) What force is exerted by the radio waves on the antenna?

The Earth reflects approximately 38.0% of the incident sunlight from its clouds and surface. (a) Given that the intensity of solar radiation at the top of the atmosphere is 1 370 W/m2, find the radiation pressure on the Earth, in pascals, at the location where the Sun is straight overhead. (b) State how this quantity compares with normal atmospheric pressure at the Earths surface, which is 101 kPa.

Review. A 1.00-m-diameter circular mirror focuses the Suns rays onto a circular absorbing plate 2.00 cm in radius, which holds a can containing 1.00 L of water at 20.0C. (a) If the solar intensity is 1.00 kW/m2, what is the intensity on the absorbing plate? At the plate, what are the maximum magnitudes of the fields (b) E S and (c) B S? (d) If 40.0% of the energy is absorbed, what time interval is required to bring the water to its boiling point?

(a) A stationary charged particle at the origin creates an electric flux of 487 N ? m2/C through any closed surface surrounding the charge. Find the electric field it creates in the empty space around it as a function of radial distance r away from the particle. (b) A small source at the origin emits an electromagnetic wave with a single frequency into vacuum, equally in all directions, with power 25.0 W. Find the electric field amplitude as a function of radial distance away from the source. (c) At what distance is the amplitude of the electric field in the wave equal to 3.00 MV/m, representing the dielectric strength of air? (d) As the distance from the source doubles, what happens to the field amplitude? (e) State how the behavior shown in part (d) compares with the behavior of the field in part (a).

Review. (a) A homeowner has a solar water heater installed on the roof of his house (Fig. P34.69). The heater is a flat, closed box with excellent thermal insulation. Its interior is painted black, and its front face is made of insulating glass. Its emissivity for visible light is 0.900, and its emissivity for infrared light is 0.700. Light from the noontime Sun is incident perpendicular to the glass with an intensity of 1 000 W/m2, and no water enters or leaves the box. Find the steadystate temperature of the boxs interior. (b) What If? The homeowner builds an identical box with no water tubes. It lies flat on the ground in front of the house. He uses it as a cold frame, where he plants seeds in early spring. Assuming the same noontime Sun is at an elevation angle of 50.0, find the steady-state temperature of the interior of the box when its ventilation slots are tightly closed.

You may wish to review Sections 16.5 and 17.3 on the transport of energy by string waves and sound. Figure P34.15 is a graphical representation of an electromagnetic wave moving in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 34.24 was generated. (a) Sketch a graph of the electric field in this wave at the instant t 5 0, letting your flat paper represent the xy plane. (b) Compute the energy density uE in the electric field as a function of x at the instant t 5 0. (c) Compute the energy density in the magnetic field uB as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the electric field amplitude. (e) The energy in a shoebox of length l and frontal area A is El 5 el 0 uA dx. (The symbol El for energy in a wavelength imitates the notation of Section 16.5.) Perform the integration to compute the amount of this energy in terms of A, l, Emax, and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point in a time interval defined as the period T 5 1/f of the wave. Find the power the wave carries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Compute this intensity in terms of E max and universal constants. (h) Explain how your result compares with that given in Equation 34.24.

Lasers have been used to suspend spherical glass beads in the Earths gravitational field. (a) A black bead has a radius of 0.500 mm and a density of 0.200 g/cm3. Determine the radiation intensity needed to support the bead. (b) What is the minimum power required for this laser?

Lasers have been used to suspend spherical glass beads in the Earths gravitational field. (a) A black bead has radius r and density r. Determine the radiation intensity needed to support the bead. (b) What is the minimum power required for this laser?

Review. A 5.50-kg black cat and her four black kittens, each with mass 0.800 kg, sleep snuggled together on a mat on a cool night, with their bodies forming a hemisphere. Assume the hemisphere has a surface temperature of 31.0C, an emissivity of 0.970, and a uniform density of 990 kg/m3. Find (a) the radius of the hemisphere, (b) the area of its curved surface, (c) the radiated power emitted by the cats at their curved surface, and (d) the intensity of radiation at this surface. You may think of the emitted electromagnetic wave as having a single predominant frequency. Find (e) the amplitude of the electric field in the electromagnetic wave just outside the surface of the cozy pile and (f) the amplitude of the magnetic field. (g) What If? The next night, the kittens all sleep alone, curling up into separate hemispheres like their mother. Find the total radiated power of the family. (For simplicity, ignore the cats absorption of radiation from the environment.)

The electromagnetic power radiated by a nonrelativistic particle with charge q moving with acceleration a is P 5 q 2 a 2 6pP0c 3 where P0 is the permittivity of free space (also called the permittivity of vacuum) and c is the speed of light in vacuum. (a) Show that the right side of this equation has units of watts. An electron is placed in a constant electric field of magnitude 100 N/C. Determine (b) the acceleration of the electron and (c) the electromagnetic power radiated by this electron. (d) What If? If a proton is placed in a cyclotron with a radius of 0.500 m and a magnetic field of magnitude 0.350 T, what electromagnetic power does this proton radiate just before leaving the cyclotron?

Review. Gliese 581c is the first Earth-like extrasolar terrestrial planet discovered. Its parent star, Gliese 581, is a red dwarf that radiates electromagnetic waves with power 5.00 3 1024 W, which is only 1.30% of the power of the Sun. Assume the emissivity of the planet is equal for infrared and for visible light and the planet has a uniform surface temperature. Identify (a) the projected area over which the planet absorbs light from Gliese 581 and (b) the radiating area of the planet. (c) If an average temperature of 287 K is necessary for life to exist on Gliese 581c, what should the radius of the planets orbit be?

A 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 the average 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?

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 5 Bmax sin (kx 2 vt), give values for (a) Bmax, (b) k, and (c) v. (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 3 0.750 m?

Review. In the absence of cable input or a satellite dish, a television set can use a dipole-receiving antenna for VHF channels and a loop antenna for UHF channels. In Figure CQ34.9, the rabbit ears form the VHF antenna and the smaller loop of wire is the UHF antenna. The UHF antenna produces an emf from the changing magnetic flux through the loop. The television station broadcasts a signal with a frequency f, and the signal has an electric field amplitude Emax and a magnetic field amplitude Bmax at the location of the receiving antenna. (a) Using Faradays law, derive an expression for the amplitude of the emf that appears in a single-turn, circular loop antenna with a radius r that 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?

Review. An astronaut, stranded in space 10.0 m from her spacecraft and at rest relative to it, has a mass (including equipment) of 110 kg. Because she has a 100-W flashlight that forms a directed beam, she considers using the beam as a photon rocket to propel herself continuously toward the spacecraft. (a) Calculate the time interval required for her to reach the spacecraft by this method. (b) What If? Suppose she throws the 3.00-kg flashlight in the direction away from the spacecraft instead. After being thrown, the flashlight moves at 12.0 m/s relative to the recoiling astronaut. After what time interval will the astronaut reach the spacecraft?