Physics Principles with Applications

Douglas C. Giancoli

Chapter 22

Electromagnetic Waves - all with Video Answers

Educators

Chapter Questions

Problem 1

(II) At a given instant, a $1.8-A$ current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1.60 $\mathrm{cm}$ on a side?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 2

(II) A 1200 -nF capacitor with circular parallel plates 2.0 $\mathrm{cm}$ in diameter is accumulating charge at the rate of 35.0 $\mathrm{mC} / \mathrm{s}$ at some instant in time. What will be the magnitude of the induced magnetic field 10.0 $\mathrm{cm}$ radially outward from the center of the plates? What will be the magnitude of the field after the capacitor is fully charged?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 3

(I) If the magnetic field in a traveling EM wave has a peak magnitude of 17.5 $\mathrm{nT}$ at a given point, what is the peak magnitude of the electric field?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 4

(I) In an EM wave traveling west, the $B$ field oscillates vertically and has a frequency of 80.0 $\mathrm{kHz}$ and an rms strength of $6.75 \times 10^{-9} \mathrm{T}$ . What are the frequency and
rms strength of the electric field, and what is its direction? [Hint: see Fig. $22-7.1$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 5

(I) What is the frequency of a microwave whose wave. length is 1.60 $\mathrm{cm} ?$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 6

(1) What is the wavelength of a $29.75 \times 10^{9}$ -Hz radar signal?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 7

(I) An EM wave has frequency $9.66 \times 10^{14} \mathrm{Hz}$ . What is its wavelength, and how would we classify it?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 8

(I) An EM wave has a wavelength of 650 $\mathrm{nm}$ . What is its frequency, and how would we classify it?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 9

(1) How long does it take light to reach us from the Sun, $1.50 \times 10^{8} \mathrm{km}$ away?

Mahmoud Abdelshafy

Mahmoud Abdelshafy

Numerade Educator

Problem 10

(I) A widely used "short-wave" radio broadcast band is referred to as the $49-\mathrm{m}$ band. What is the frequency of a $49-\mathrm{m}$ radio signal?

Gopal Sharma

Numerade Educator

Problem 11

(II) Our nearest star (other than the Sun) is 4.2 light-years away. That is, it takes 4.2 years for the light it emits to reach Earth. How far away is it in meters?

Melissa Walsh

Numerade Educator

Problem 12

(II) A light-year is a measure of distance (not time). How many meters does light travel in a year?

Brandon Fox

Numerade Educator

Problem 13

(II) How long would it take a message sent as radio waves from Earth to reach Mars (a) when nearest Earth, (b) when farthest from Earth? [Hint: see Table $5-2,$ p. $125 . ]$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 14

(II) What is the minimum angular speed at which Michelson's eight-sided mirror would have had to rotate
to reflect light into an observer's eye by succeeding mirror faces (Fig. $22-10 ) ?$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 15

(II) A student wants to scale down Michelson's light- speed experiment to a size that will fit in one room. A sixsided mirror is available, and the stationary mirror can be mounted 12 $\mathrm{m}$ from the rotating mirror. If the arrangement is otherwise as shown in Fig. $22-10$ , at what minimum rate must the mirror rotate?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 16

(II) Who will hear the voice of a singer first-a person in the balcony 50.0 $\mathrm{m}$ away from the stage (Fig. $22-19 )$ , or a person 3000 $\mathrm{km}$ away at home whose ear is next to the
radio? How much sooner? Assume that the microphone is a few centimeters from the singer and the temperature is $20^{\circ} \mathrm{C} .$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 17

(II) Pulsed lasers used in science and medicine produce very short bursts of electromagnetic energy. If the laser light wavelength is 1062 $\mathrm{nm}$ (this corresponds to a Neodymium-YAG laser), and the pulse lasts for 32 picoseconds, how many wavelengths are found within the laser pulse? How short would the pulse need to be to fit only one wavelength?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 18

(I) The $\overrightarrow{\mathbf{E}}$ field in an EM wave in free space has a peak of $21.8 \mathrm{mV} / \mathrm{m} .$ What is the average rate at which this wave bcarries energy across unit area per unit time?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 19

(II) The magnetic field in a traveling EM wave has anrms strength of 28.5 $\mathrm{nT}$ . How long does it take to deliver 235 $\mathrm{J}$ of energy to 1.00 $\mathrm{cm}^{2}$ of a wall that it hits perpendicularly?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 20

(II) How much energy is transported across a $1.00-\mathrm{cm}^{2}$ area per hour by an EM wave whose $E$ field has an rms strength of 38.6 $\mathrm{mV} / \mathrm{m} ?$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 21

(II) A spherically spreading EM wave comes from a 1200 -W source. At a distance of $10.0 \mathrm{m},$ what is the average intensity, and what is the rms value of the electric field?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 22

(II) A 12.8$\cdot \mathrm{m} \mathrm{W}$ laser puts out a narrow beam 1.75 $\mathrm{mm}$ in diameter. What are the average (rms) values of $E$ and $B$ in the beam?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 23

(II) Estimate the average power output of the Sun, given that about 1350 $\mathrm{W} / \mathrm{m}^{2}$ reaches the upper atmosphere of the Earth.

Sachin Rao

Numerade Educator

Problem 24

(II) If the amplitude of the $B$ field of an EM wave is $2.5 \times 10^{-7} \mathrm{T},(a)$ what is the amplitude of the $E$ field? (b) What is the average power per unit area of the EM wave?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 25

(II) A high-energy pulsed laser emits a 1.0 -ns-long pulse of average power $2.8 \times 10^{11} \mathrm{W}$ . The beam is $2.2 \times 10^{-3} \mathrm{m}$ in radius. Determine $(a)$ the energy delivered in each pulse, and $(b)$ the rms value of the electric field.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 26

(II) Estimate the radiation pressure due to a $100 .$ W bulb at a distance of 8.0 $\mathrm{cm}$ from the center of the bulb. Estimate the force exerted on your fingertip if you place it at this point.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 27

(I) What is the range of wavelengths for $(a)$ FM radio $(88 \mathrm{MHz} \text { to } 108 \mathrm{MHz})$ and $(b) \mathrm{AM}$ radio $(535 \mathrm{kHz} \text { to }$
1700 $\mathrm{kHz} ) ?$

Shital Rijal

Numerade Educator

Problem 28

(I) Estimate the wavelength for $1.9 .$ GHz cell phone reception.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 29

(I) Compare 940 on the AM dial to 94 on the FM dial. Which has the longer wavelength, and by what factor is it larger?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 30

(I) What are the wavelengths for two TV channels that broadcast at 54.0 $\mathrm{MHz}$ (Channel 2 ) and 806 $\mathrm{MHz}$ (Channel 69$) ?$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 31

(I) The variable capacitor in the tuner of an AM radio has a capacitance of 2800 $\mathrm{pF}$ when the radio is tuned to a station at 550 $\mathrm{kHz}$ . What must the capacitance be for a station near the other end of the dial, 1610 $\mathrm{kHz}$ ?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 32

(I) The oscillator of a $96.1-\mathrm{MHz}$ FM station has an inductance of 1.8$\mu \mathrm{H}$ . What value must the capacitance be?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 33

(II) A certain FM radio tuning circuit has a fixed capacitor $C=840$ pF. Tuning is done by a variable inductance. What range of values must the inductance have to tune stations from 88 $\mathrm{MHz}$ to 108 $\mathrm{MHz}$ ?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 34

(II) An amateur radio operator wishes to build a receiver that can tune a range from 14.0 $\mathrm{MHz}$ to 15.0 $\mathrm{MHz}$ . A variable capacitor has a minimum capacitance of 82 $\mathrm{pF}$ . (a) What is the required value of the inductance? (b) What is the maximum capacitance used on the variable capacitor?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 35

(II) A satellite beams microwave radiation with a power of 10 $\mathrm{kW}$ toward the Earth's surface, 550 $\mathrm{km}$ away. When the beam strikes Earth, its circular diameter is about 1500 $\mathrm{m}$ . Find the rms electric field strength of the beam.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 36

(III) A 1.60 -m-long FM antenna is oriented parallel to the electric field of an EM wave. How large must the electric field be to produce a $1.00-\mathrm{m} \mathrm{V}$ (rms) voltage between the ends of the antenna? What is the rate of energy transport per square meter?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 37

If the Sun were to disappear or somehow radically change its output, how long would it take for us on Earth to learn about it?

JR

Jared Rogers

Numerade Educator

Problem 38

Light is emitted from an ordinary lightbulb filament in wave-train bursts about $10^{-8} \mathrm{s}$ in duration. What is the length in space of such wave trains?

Mahmoud Abdelshafy

Mahmoud Abdelshafy

Numerade Educator

Problem 39

(a) How long did it take for a message sent from Earth to reach the first astronauts on the Moon? (b) How long will it take for a message from Earth to reach the first astronauts who arrive on Mars; assume Mars is at its closest approach to Earth $\left(78 \times 10^{6} \mathrm{km}\right) ?$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 40

A radio voice signal from the $A$ pollo crew on the Moon (Fig. $22-20$ ) was beamed to a listening crowd from a radio speaker. If you were standing 25 $\mathrm{m}$ from the loud. speaker, what was the total time lag between when you heard the sound and when the sound left the Moon?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 41

Cosmic microwave background radiation fills all space with an average energy density of $4 \times 10^{-14} \mathrm{J} / \mathrm{m}^{3} .(a)$ Find therms value of the electric field associated with this radiation. ( $b )$ How far from a $10-\mathrm{k} \mathrm{W}$ radio transmitter emitting uniformly in all directions would you find a comparable value?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 42

What are $E_{0}$ and $B_{0} 2.00 \mathrm{m}$ from a $95 .$ W light source? Assume the bulb emits radiation of a single frequency uniformly in all directions.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 43

Estimate the rms electric field in the sunlight that hits Mars, knowing that the Earth receives about 1350 $\mathrm{W} / \mathrm{m}^{2}$ and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.

Shital Rijal

Numerade Educator

Problem 44

At a given instant in time, a traveling EM wave is noted to have its maximum magnetic field pointing west and its maximum electric field pointing south. In which direction is the wave traveling? If the rate of energy flow is 560 $\mathrm{W} / \mathrm{m}^{2}$ , what are the maximum values for the two fields?

Zachary Warner

Numerade Educator

Problem 45

Estimate how long an AM antenna would have to be if it were $(a) \frac{1}{2} \lambda$ or $(b) \frac{1}{2} \lambda$ . AM radio is roughly 1 $\mathrm{MHz}$ $(530 \mathrm{kHz} \text { to } 1.7 \mathrm{MHz}) .$

Kyle Godbey

Numerade Educator

Problem 46

How large an emf (rms) will be generated in an antenna that consists of a $380-$ -loop circular coil of wire 2.2 $\mathrm{cm}$ in diameter if the EM wave has a frequency of 810 $\mathrm{kHz}$ and
is transporting energy at an average rate of $1.0 \times 10^{-4} \mathrm{W} / \mathrm{m}^{2}$ at the antenna? [Hint: you can use Eq. $21-5$ for a generator, since it could be applied to an observer moving with the coil so that the magnetic field is oscillating with the frequency $f=\omega / 2 \pi . ]$

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 47

The average intensity of a particular TV station's signal is $1.0 \times 10^{-13} \mathrm{W} / \mathrm{m}^{2}$ when it arrives at a $33 . \mathrm{cm}$ -diameter satellite $\mathrm{TV}$ antenna. (a) Calculate the total energy received by the antenna during 6.0 hours of viewing this station's programs. (b) What are the amplitudes of the $E$ and $B$ fields of the EM wave?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 48

15 $\mathrm{km}$ from a radio station's transmitting antenna, the amplitude of the electric field is 0.12 $\mathrm{V} / \mathrm{m}$ . What is the average power output of the radio station?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 49

The variable capacitance of a radio tuner consists of six plates connected together placed alternately between six other plates, also connected together (Fig. $22-21$ ). Each plate is separated from its neighbor by 1.1 $\mathrm{mm}$ of air. One set of plates can move so that the area of
overlap varies from 1.0 $\mathrm{cm}^{2}$ to 9.0 $\mathrm{cm}^{2}$ . (a) Are these capacitors
connected in series or in parallel? (b) Determine the range of capacitance values. (c) What value of
inductor is needed if the radio is to tune AM stations from 550 $\mathrm{kHz}$ to 1600 $\mathrm{kHz}$ ?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 50

A radio station is allowed to broadcast at an average power not to exceed 25 $\mathrm{k} \mathrm{W}$ . If an electric field amplitude of 0.020 $\mathrm{V} / \mathrm{m}$ is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to hear this station.

Shital Rijal

Numerade Educator

Problem 51

A point source emits light energy uniformly in all directions at an average rate $P_{0}$ with a single frequency $f$ Show that the peak electric field in the wave is given by
$$
E_{0}=\sqrt{\frac{\mu_{0} c P_{0}}{2 \pi r^{2}}}
$$

Zachary Warner

Numerade Educator

Problem 52

Suppose a $50-\mathrm{kW}$ radio station emits EM waves uniformly in all directions. $(a)$ How much energy per second crosses a 1.0$\cdot \mathrm{m}^{2}$ area 100 $\mathrm{m}$ from the transmitting antenna? (b) What is the rms magnitude of the $\overrightarrow{\mathbf{E}}$ field at this point, assuming
the station is operating at full power? (c) What is the voltage induced in a 1.0 -m-long vertical car antenna at this distance?

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 53

Repeat Problem 52 for a distance of 100 $\mathrm{km}$ from the station.

Jheremiah Simon

Jheremiah Simon

Numerade Educator

Problem 54

What is the maximum power level of the radio station of Problem 52 so as to avoid electrical breakdown of air at a distance of 1.0 $\mathrm{m}$ from the antenna? Assume the antenna is a point source. Air breaks down in an electric field of about $3 \times 10^{6} \mathrm{V} / \mathrm{m}$ . [Hint: see Problem 51.1

Jheremiah Simon

Jheremiah Simon

Numerade Educator