Solved: A laptop computer communicates with a router

Refer to Figure 24.1. Between the times indicated in parts c and d in the drawing, what is the direction of the magnetic field at the point P for the electromagnetic wave being generated? Is it directed (a) upward along the length of the wire, (b) downward along the length of the wire, (c) into the plane of the paper, or (d) out of the plane of the paper?

A transmitting antenna is located at the origin of an x, y, z axis system and broadcasts an electromagnetic wave whose electric field oscillates along the y axis. The wave travels along the x axis. Three possible wire loops are available for use with an LC-tuned circuit to detect this wave: (a) a loop that lies in the xy plane, (b) a loop that lies in the xz plane, and (c) a loop that lies in the yz plane. Which one of the loops will detect the wave?

Why does the peak value of the emf induced in a loop antenna (see Figure 24.5) depend on the frequency of the electromagnetic wave?

Find the range in wavelengths (in vacuum) for visible light in the frequency range between 4.0  1014 Hz (red light) and 7.9  1014 Hz (violet light). Express the answers in nanometers.

As we have discussed in Section 17.3, diffraction is the ability of a wave to bend around an obstacle or around the edges of an opening. Based on that discussion, which type of radio wave would you expect to bend more readily around an obstacle such as a building, (a) an AM radio wave or (b) an FM radio wave?

A supernova is a violent explosion that occurs at the death of certain stars. For a few days after the explosion, the intensity of the emitted light can become a billion times greater than that of our own sun. After several years, however, the intensity usually returns to zero. Supernovae are relatively rare events in the universe; only six have been observed in our galaxy within the past 400 years. A supernova that occurred in a neighboring galaxy, approximately 1.66  1021 m away, was recorded in 1987. Figure 24.13 shows a photograph of the sky (a) before and (b) a few hours after the explosion. Astronomers say that viewing an event like the supernova is like looking back in time. Which one of the following statements correctly describes what we see when we view such events? (a) The nearer the event is to the earth, the further back in time we are looking. (b) The farther the event is from the earth, the further back in time we are looking

The frequency of electromagnetic wave A is twice that of electromagnetic wave B. For these two waves, what is the ratio A/B of the wavelengths in a vacuum? (a) A/B 2, because wave A has twice the speed that wave B has. (b) A/B 2, because wave A has one-half the speed that wave B has. (c) A/B , because wave A has one-half the speed that wave B has. (d) A/B , because wave A has twice the speed that wave B has. (e) A/B , because both waves have the same speed. 1 2 1 2 1 2

Sunlight enters the top of the earths atmosphere with an electric field whose rms value is Erms 720 N/C. Find (a) the average total energy density of this electromagnetic wave and (b) the rms value of the sunlights magnetic field.

Figure 24.16 shows a tiny source that is emitting light uniformly in all directions. At a distance of 2.50 m from the source, the rms electric field strength of the light is 19.0 N/C. Assuming that the light does not reflect from anything in the environment, determine the average power of the light emitted by the source.

If both the electric and magnetic fields of an electromagnetic wave double in magnitude, how does the intensity of the wave change? The intensity (a) decreases by a factor of four (b) decreases by a factor of two (c) increases by a factor of two (d) increases by a factor of four (e) increases by a factor of eight.

Suppose that the electric field of an electromagnetic wave decreases in magnitude. Does the magnitude of the magnetic field (a) increase, (b) decrease, or (c) remain the same?

Police use radar guns and the Doppler effect to catch speeders. Figure 24.17 illustrates a moving car approaching a stationary police car. A radar gun emits an electromagnetic wave that reflects from the oncoming car. The reflected wave returns to the police car with a frequency (measured by on-board equipment) that is different from the emitted frequency. One such radar gun emits a wave whose frequency is 8.0  109 Hz. When the speed of the car is 39 m/s and the approach is essentially head-on, what is the difference between the frequency of the wave returning to the police car and that emitted by the radar gun?

The drawing shows three situationsA, B, and Cin which an observer and a source of electromagnetic waves are moving along the same line. In each case the source emits a wave of the same frequency. The arrows in each situation denote velocity vectors relative to the ground and have magnitudes of either v or 2v. Rank the magnitudes of the frequencies of the observed waves in descending order (largest first).

What value of  should be used in Figure 24.21, so that the average intensity of the polarized light reaching the photocell will be one-tenth the average intensity of the unpolarized light?

As explained earlier, no light reaches the photocell in Figure 24.21 when the polarizer and the analyzer are crossed. Suppose that a third piece of polarizing material is inserted between the polarizer and analyzer, as in Figure 24.24a. With the insert in place, will light reach the photocell when (a) 0, (b) 90, or (c) is between 0 and 90? Conc

Malus law applies to the setup in Figure 24.21, which shows the analyzer rotated through an angle and the polarizer held fixed. Does Malus law apply when the analyzer is held fixed and the polarizer is rotated?

In Example 7, we saw that when the angle between the polarizer and analyzer is 63.4, the average intensity of the transmitted light drops to one-tenth of the average intensity of the incident unpolarized light. What happens to the light intensity that is not transmitted?

The drawing shows two sheets of polarizing material. The transmission axis of one is vertical, and that of the other makes an angle of 45 with the vertical. Unpolarized light shines on this arrangement first from the left and then from the right. From which direction does at least some light pass through both sheets? (a) From the left (b) From the right (c) From either direction (d) From neither direction What is the answer when the light is horizontally polarized? What is the answer when the light is vertically polarized?

You are sitting upright on the beach near a lake on a sunny day, wearing Polaroid sunglasses. When you lie down on your side, facing the lake, the sunglasses dont work as well as they do while you are sitting upright. Why not?

Figure 24.31 shows the popular dish antenna that receives digital TV signals from a satellite. The average intensity of the electromagnetic wave that carries a particular TV program is W/m2 , and the circular aperture of the antenna has a radius of r 15 cm. (a) Determine the electromagnetic energy delivered to the dish during a one-hour program. (b) What is the average energy density of the electromagnetic wave?

How is the average power passing through the circular aperture of the antenna related to the average intensity of the TV signal?

How much energy does the antenna receive in a time t?

What is the average energy density, or average energy per unit volume, of the electromagnetic wave?

The light beam in Figure 24.32 passes through a polarizer whose transmission axis makes an angle with the vertical. The beam is partially polarized and partially unpolarized, and the average intensity of the incident light is the sum of the average intensity of the polarized light and the average intensity of the unpolarized light; The intensity of the transmitted light is also the sum of two parts: As the polarizer is rotated clockwise, the intensity of the transmitted light has a minimum value of when and has a maximum value of when the angle is (a) What is the intensity of the incident light that is unpolarized? (b) What is the intensity of the incident light that is polarized?

How is related to S0, unpolar?

How is related to S0, polar?

The minimum transmitted intensity is 2.0 W/m2 . Why isnt it 0 W/m2?

The drawing shows an x, y, z coordinate system. A circular loop of wire lies in the z, x plane and, when used with an LC-tuned circuit, detects an electromagnetic wave. Which one of the following statements is correct? (a) The wave travels along the x axis, and its electric field oscillates along the y axis. (b) The wave travels along the z axis, and its electric field oscillates along the x axis. (c) The wave travels along the z axis, and its electric field oscillates along the y axis. (d) The wave travels along the y axis, and its electric field oscillates along the x axis. (e) The wave travels along the y axis, and its electric field oscillates along the z axis.

An electromagnetic wave travels in a vacuum. The wavelength of the wave is tripled. How is this accomplished? (a) By tripling the frequency of the wave (b) By tripling the speed of the wave (c) By reducing the frequency of the wave by a factor of three (d) By reducing the speed of the wave by a factor of three (e) By tripling the magnitudes of the electric and magnetic fields that comprise the wave

An electromagnetic wave is traveling in a vacuum. The magnitudes of the electric and magnetic fields of the wave are ______, and the electric and magnetic energies carried by the wave are ______. (a) equal, proportional (but not equal) to each other (b) proportional (but not equal) to each other, equal (c) equal, equal (d) proportional (but not equal) to each other, unequal

The drawing shows four situationsA, B, C, and Din which an observer and a source of electromagnetic waves can move along the same line. In each case the source emits a wave of the same frequency, and in each case only the source or the observer is moving. The arrow in each situation denotes the velocity vector, which has the same magnitude in each situation. When there is no arrow, the observer or the source is stationary. Rank the frequencies of the observed electromagnetic waves in descending order (largest first) according to magnitude. (a) A and B (a tie), C and D (a tie) (b) C and D (a tie), A and B (a tie) (c) A and D (a tie), B and C (a tie) (d) B and D (a tie), A and C (a tie) (e) B and C (a tie), A and D (a tie) A Observer Source B C D

The drawing shows two sheets of polarizing material. Polarizer 1 has its transmission axis aligned vertically, and polarizer 2 has its transmission axis aligned at an angle of 45 with respect to the vertical. Light that is completely polarized along the vertical direction is incident either from the far left or from the far right. In either case, the average intensity of the incident light is the same. Which one of the following statements is true concerning the average intensity of the light that is transmitted by the pair of sheets? (a) When the light is incident from either the left or the right, the transmitted intensity is one-half the incident intensity. (b) When the light is incident from either the left or the right, the transmitted intensity is one-fourth the incident intensity. (c) When the light is incident from the left, the transmitted intensity is one-half the incident intensity; when the light is incident from the right, the transmitted intensity is zero. (d) When the light is incident from the left, the transmitted intensity is onefourth the incident intensity; when the light is incident from the right, the transmitted intensity is one-half the incident intensity. (e) When the light is incident from the left, the transmitted intensity is one-half the incident intensity; when the light is incident from the right, the transmitted intensity is one-fourth the incident intensity

The team monitoring a space probe exploring the outer solar system finds that radio transmissions from the probe take 2.53 hours to reach earth. How distant (in meters) is the probe?

(a) Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is 3.85  108 m. Find the time it took for his voice to reach the earth via radio waves. (b) Someday a person will walk on Mars, which is 5.6  1010 m from the earth at the point of closest approach. Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves

In astronomy, distances are often expressed in light-years. One light-year is the distance traveled by light in one year. The distance to Alpha Centauri, the closest star other than our own sun that can be seen by the naked eye, is 4.3 light-years. Express this distance in meters

FM radio stations use radio waves with frequencies from 88.0 to 108 MHz to broadcast their signals. Assuming that the inductance in Figure 24.4 has a value of 6.00  107 H, determine the range of capacitance values that are needed so the antenna can pick up all the radio waves broadcasted by FM stations.

In a traveling electromagnetic wave, the electric field is represented mathematically as where E0 is the maximum field strength. This equation is an adaptation of Equation 16.3. (a) What is the frequency of the wave? (b) This wave and the wave that results from its reflection can form a standing wave, in a way similar to that in which standing waves can arise on a string (see Section 17.5). What is the separation between adjacent nodes in the standing wave?

A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.25 m and consists of 450 turns. The transmitted radio wave has a frequency of 1.2 MHz. The magnetic field of the wave is parallel to the normal to the coil and has a maximum value of 2.0  1013 T. Using Faradays law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna during this time.

A truck driver is broadcasting at a frequency of 26.965 MHz with a CB (citizens band) radio. Determine the wavelength of the electromagnetic wave being used. The speed of light is c 2.9979  108 m/s.

In a dentists office an X-ray of a tooth is taken using X-rays that have a frequency of 6.05  1018 Hz. What is the wavelength in vacuum of these X-rays?

In a certain UHF radio wave, the shortest distance between positions at which the electric and magnetic fields are zero is 0.34 m. Determine the frequency of this UHF radio wave.

FM radio waves have frequencies between 88.0 and 108.0 MHz. Determine the range of wavelengths for these waves.

Magnetic resonance imaging, or MRI (see Section 21.7), and positron emission tomography, or PET scanning (see Section 32.6), are two medical diagnostic techniques. Both employ electromagnetic waves. For these waves, find the ratio of the MRI wavelength (frequency 6.38  107 Hz) to the PET scanning wavelength (frequency 1.23  1020 Hz).

A certain type of laser emits light that has a frequency of 5.2  1014 Hz. The light, however, occurs as a series of short pulses, each lasting for a time of 2.7  1011 s. (a) How many wavelengths are there in one pulse? (b) The light enters a pool of water. The frequency of the light remains the same, but the speed of the light slows down to 2.3  108 m/s. How many wavelengths are there now in one pulse?

Two radio waves are used in the operation of a cellular telephone. To receive a call, the phone detects the wave emitted at one frequency by the transmitter station or base unit. To send your message to the base unit, your phone emits its own wave at a different frequency. The difference between these two frequencies is fixed for all channels of cell phone operation. Suppose that the wavelength of the wave emitted by the base unit is 0.34339 m and the wavelength of the wave emitted by the phone is 0.36205 m. Using a value of 2.9979  108 m/s for the speed of light, determine the difference between the two frequencies used in the operation of a cell phone

A positively charged object with a mass of 0.115 kg oscillates at the end of a spring, generating ELF (extremely low frequency) radio waves that have a wavelength of 4.80  107 m. The frequency of these radio waves is the same as the frequency at which the object oscillates. What is the spring constant of the spring?

Review Conceptual Example 3 for information pertinent to this problem. When we look at the star Polaris (the North Star), we are seeing it as it was 680 years ago. How far away from us (in meters) is Polaris?

Figure 24.12 illustrates Michelsons setup for measuring the speed of light with the mirrors placed on Mt. San Antonio and Mt. Wilson in California, which are 35 km apart. Using a value of 3.00  108 m/s for the speed of light, find the minimum angular speed (in rev/s) for the rotating mirror

Two astronauts are 1.5 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship?

A laptop computer communicates with a router wirelessly, by means of radio signals. The router is connected by cable directly to the Internet. The laptop is 8.1 m from the router, and is downloading text and images from the Internet at an average rate of 260 Mbps, or 260 megabits per second. (A bit, or binary digit, is the smallest unit of digital information.) On average, how many bits are downloaded to the laptop in the time it takes the wireless signal to travel from the router to the laptop?

A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler effect to catch speeders. A lidar gun uses an infrared laser and emits a precisely timed series of pulses of infrared electromagnetic waves. The time for each pulse to travel to the speeding vehicle and return to the gun is measured. In one situation a lidar gun in a stationary police car observes a difference of 1.27  107 s in roundtrip travel times for two pulses that are emitted 0.450 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle

A politician holds a press conference that is televised live. The sound picked up by the microphone of a TV news network is broadcast via electromagnetic waves and heard by a television viewer. This viewer is seated 2.3 m from his television set. A reporter at the press conference is located 4.1 m from the politician, and the sound of the words travels directly from the celebritys mouth, through the air, and into the reporters ears. The reporter hears the words exactly at the same instant that the television viewer hears them. Using a value of 343 m/s for the speed of sound, determine the maximum distance between the television set and the politician. Ignore the small distance between the politician and the microphone. In addition, assume that the only delay between what the microphone picks up and the sound being emitted by the television set is that due to the travel time of the electromagnetic waves used by the network.

A mirror faces a cliff located some distance away. Mounted on the cliff is a second mirror, directly opposite the first mirror and facing toward it. A gun is fired very close to the first mirror. The speed of sound is 343 m/s. How many times does the flash of the gunshot travel the round-trip distance between the mirrors before the echo of the gunshot is heard?

A laser emits a narrow beam of light. The radius of the beam is 1.0  103 m, and the power is 1.2  103 W. What is the intensity of the laser beam?

An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is 1.23  109 W/m2 . What is the rms value of (a) the electric field and (b) the magnetic field in the electromagnetic wave emitted by the laser?

The maximum strength of the magnetic field in an electromagnetic wave is 3.3  106 T. What is the maximum strength of the waves electric field?

The microwave radiation left over from the Big Bang explosion of the universe has an average energy density of 4  1014 J/m3 . What is the rms value of the electric field of this radiation?

On a cloudless day, the sunlight that reaches the surface of the earth has an intensity of about 1.0  103 W/m2 . What is the electromagnetic energy contained in 5.5 m3 of space just above the earths surface?

Multiple-Concept Example 5 discusses the principles used in this problem. A neodymium-glass laser emits short pulses of highintensity electromagnetic waves. The electric field of such a wave has an rms value of Erms 2.0  109 N/C. Find the average power of each pulse that passes through a 1.6  105 -m2 surface that is perpendicular to the laser beam.

Consult Multiple-Concept Example 5 to review the concepts on which this problem depends. A light bulb emits light uniformly in all directions. The average emitted power is 150.0 W. At a distance of 5.00 m from the bulb, determine (a) the average intensity of the light, (b) the rms value of the electric field, and (c) the peak value of the electric field.

Multiple-Concept Example 5 provides some pertinent background for this problem. The mean distance between earth and the sun is 1.50  1011 m. The average intensity of solar radiation incident on the upper atmosphere of the earth is 1390 W/m2 . Assuming that the sun emits radiation uniformly in all directions, determine the total power radiated by the sun.

A stationary particle of charge q 2.6  108 C is placed in a laser beam (an electromagnetic wave) whose intensity is 2.5  103 W/m2 . Determine the magnitudes of the (a) electric and (b) magnetic forces exerted on the charge. If the charge is moving at a speed of 3.7  104 m/s perpendicular to the magnetic field of the electromagnetic wave, find the magnitudes of the (c) electric and (d) magnetic forces exerted on the particle.

The power radiated by the sun is 3.9  1026 W. The earth orbits the sun in a nearly circular orbit of radius 1.5  1011 m. The earths axis of rotation is tilted by 27 relative to the plane of the orbit (see the drawing), so sunlight does not strike the equator perpendicularly. What power strikes a 0.75-m2 patch of flat land at the equator at point Q?

An electromagnetic wave strikes a 1.30-cm2 section of wall perpendicularly. The rms value of the waves magnetic field is determined to be 6.80  104 T. How long does it take for the wave to deliver 1850 J of energy to the wall?

A heat lamp emits infrared radiation whose rms electric field is Erms 2800 N/C. (a) What is the average intensity of the radiation? (b) The radiation is focused on a persons leg over a circular area of radius 4.0 cm. What is the average power delivered to the leg? (c) The portion of the leg being irradiated has a mass of 0.28 kg and a specific heat capacity of 3500 J/(kg C ). How long does it take to raise its temperature by 2.0 C ? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

A gamma-ray telescope intercepts a pulse of gamma radiation from a magnetar, a type of star with a spectacularly large magnetic field. The pulse lasts 0.24 s and delivers 8.4  106 J of energy perpendicularly to the 75-m2 surface area of the telescopes detector. The magnetar is thought to be 4.5  1020 m (about 50 000 light-years) from earth, and to have a radius of 9.0  103 m. Find the magnitude of the rms magnetic field of the gamma-ray pulse at the surface of the magnetar, assuming that the pulse radiates uniformly outward in all directions.

A distant galaxy emits light that has a wavelength of 434.1 nm. On earth, the wavelength of this light is measured to be 438.6 nm. (a) Decide whether this galaxy is approaching or receding from the earth. Give your reasoning. (b) Find the speed of the galaxy relative to the earth.

Multiple-Concept Example 6 reviews the concepts that play a role in this problem. A speeder is pulling directly away and increasing his distance from a police car that is moving at 25 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 7.0  109 Hz. The wave reflects from the speeders car and returns to the police car, where its frequency is measured to be 320 Hz less than the emitted frequency. Find the speeders speed with respect to the ground.

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the galactic center is receding from the earth at a relative speed of uG 1.6  106 m/s. Relative to the center, the tangential speed is v T 0.4  106 m/s E for locations A and B, which are equidistant from the center. When the frequencies of the light coming from regions A and B are measured on earth, they are not the same and each is different from the emitted frequency of 6.200  1014 Hz. Find the measured frequency for the light from (a) region A and (b) region B.

The drawing shows three situationsA, B, and Cin which an observer and a source of electromagnetic waves are moving along the same line. In each case the source emits a wave that has a frequency of 4.57  1014 Hz. The arrows in each situation denote velocity vectors of the observer and source relative to the ground and have the magnitudes indicated (v or 2v), where the speed v is 1.50  106 m/s. Calculate the observed frequency in each of the three cases.

Unpolarized light whose intensity is 1.10 W/m2 is incident on the polarizer in Figure 24.21. (a) What is the intensity of the light leaving the polarizer? (b) If the analyzer is set at an angle of  75 with respect to the polarizer, what is the intensity of the light that reaches the photocell? 4

The drawing shows three polarizer/analyzer pairs. The incident light beam for each pair is unpolarized and has the same average intensity of 48 W/m2 . Find the average intensity of the transmitted beam for each of the three cases (A, B, and C) shown in the drawing.

The average intensity of light emerging from a polarizing sheet is 0.764 W/m2 , and the average intensity of the horizontally polarized light incident on the sheet is 0.883 W/m2 . Determine the angle that the transmission axis of the polarizing sheet makes with the horizontal.

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 94% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet. What angle does the transmission axis of the second sheet make with the vertical?

Review Conceptual Example 8 before solving this problem. Suppose that unpolarized light of intensity 150 W/m2 falls on the polarizer in Figure 24.24a, and the angle  in the drawing is 30.0 . What is the light intensity reaching the photocell?

The drawing shows light incident on a polarizer whose transmission axis is parallel to the z axis. The polarizer is rotated clockwise through an angle . The average intensity of the incident light is 7.0 W/m2 . Determine the average intensity of the transmitted light for each of the six cases shown in the table. Intensity of Transmitted Light Incident Light 0 35 (a) Unpolarized (b) Polarized parallel to z axis (c) Polarized parallel to y axis 4

For each of the three sheets of polarizing material shown in the drawing, the orientation of the transmission axis is labeled relative to the vertical. The incident beam of light is unpolarized and has an intensity of 1260.0 W/m2 . What is the intensity of the beam transmitted through the three sheets when 1 19.0 , 2 55.0 , and 3 100.0 ? In

Before attempting this problem, review Conceptual Example 8. The intensity of the light that reaches the photocell in Figure 24.24a is 110 W/m2 , when  23 . What would be the intensity reaching the photocell if the analyzer were removed from the setup, everything else remaining the same?

More than one analyzer can be used in a setup like the one in Figure 24.21, each analyzer following the previous one. Suppose that the transmission axis of the first analyzer is rotated 27 relative to the transmission axis of the polarizer, and that the transmission axis of each additional analyzer is rotated 27 relative to the transmission axis of the previous one. What is the minimum number of analyzers needed for the light reaching the photocell to have an intensity that is reduced by at least a factor of 100 relative to the intensity of the light striking the first analyzer?

The drawing shows four sheets of polarizing material, each with its transmission axis oriented differently. Light that is polarized in the vertical direction is incident from the left and has an average intensity of 27 W/m2 . Determine the average intensity of the light that emerges on the right in the drawing when sheet A alone is removed, when sheet B alone is removed, when sheet C alone is removed, and when sheet D alone is removed.

Obtain the wavelengths in vacuum for (a) blue light whose frequency is 6.34  1014 Hz, and (b) orange light whose frequency is 4.95  1014 Hz. Express your answers in nanometers (1 nm 109 m).

from 315 to 945 N/C. (a) Determine the wave intensities for the two values of the electric field. (b) What is the magnitude of the magnetic field associated with each electric field? (c) Determine the wave intensity for each value of the magnetic field.

An AM station is broadcasting a radio wave whose frequency is 1400 kHz. The value of the capacitance in Figure 24.4 is 8.4  1011 F. What must be the value of the inductance in order that this station can be tuned in by the radio?

The human eye is most sensitive to light with a frequency of about 5.5  1014 Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across the width of your thumb, a distance of about 2.0 cm?

A future space station in orbit about the earth is being powered by an electromagnetic beam from the earth. The beam has a cross-sectional area of 135 m2 and transmits an average power of 1.20  104 W. What are the rms values of the (a) electric and (b) magnetic fields?

Multiple-Concept Example 6 explores the concepts that are involved in this problem. Suppose that the police car in that example is moving to the right at 27 m/s, while the speeder is coming up from behind at a speed of 39 m/s, both speeds being with respect to the ground. Assume that the electromagnetic wave emitted by the radar gun has a frequency of 8.0  109 Hz. Find the difference between the frequency of the wave that returns to the police car after reflecting from the speeders car and the original frequency emitted by the police car.

In experiment 1, unpolarized light falls on the polarizer in Figure 24.21. The angle of the analyzer is  60.0 . In experiment 2, the unpolarized light is replaced by light of the same intensity, but the light is polarized along the direction of the polarizers transmission axis. By how many additional degrees must the analyzer be rotated so that the light falling on the photocell will have the same intensity as it did in experiment 1? Explain whether  is increased or decreased by this additional number of degrees.

The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 1.5  1010 T. The wave passes perpendicularly through an open window, the area of which is 0.20 m2 . How much energy does this wave carry through the window during a 45-s phone call?

Equation 16.3, y A sin (2f t  2x/), gives the mathematical representation of a wave oscillating in the y direction and traveling in the positive x direction. Let y in this equation equal the electric field of an electromagnetic wave traveling in a vacuum. The maximum electric field is A 156 N/C, and the frequency is f 1.50  108 Hz. Plot a graph of the electric field strength versus position, using for x the following values: 0, 0.50, 1.00, 1.50, and 2.00 m. Plot this graph for (a) a time t 0 s and (b) a time t that is one-fourth of the waves period. * 58

A beam of polarized light with an average intensity of 15 W/m2 is sent through a polarizer. The transmission axis makes an angle of 25 with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.

An argon-ion laser produces a cylindrical beam of light whose average power is 0.750 W. How much energy is contained in a 2.50-m length of the beam?

What fraction of the power radiated by the sun is intercepted by the planet Mercury? The radius of Mercury is 2.44  106 m, and its mean distance from the sun is 5.79  1010 m. Assume that the sun radiates uniformly in all directions.

The drawing shows an edge-on view of the solar panels on a communications satellite. The dashed line specifies the normal to Additional Problems 767 the panels. Sunlight strikes the panels at an angle  with respect to the normal. If the solar power impinging on the panels is 2600 W when  65 , what is it when  25 ? **

Suppose that the light falling on the polarizer in Figure 24.21 is partially polarized (average intensity and partially unpolarized (average intensity . The total incident intensity is and the percentage polarization is When the polarizer is rotated in such a situation, the intensity reaching the photocell varies between a minimum value of and a maximum value of Show that the percentage polarization can be expressed as 100 (Smax  Smin)/(Smax Smin).