Chapter 34

Electromagnetic Waves

Multiple Choice

1. The Earth is 1.49 × 1011 meters from the sun. If the solar radiation at the top of the Earth’s atmosphere is 1340 W/m2, what is the total power output of the sun?

a. 7.10 × 1027 W b. 2.20 × 1030 W c. 6.62 × 1026 W d. 3.74 × 1026 W e. 2.98 × 1025 W

2. If the radiant energy from the sun comes in as a plane EM wave of intensity 1340 W/m2, calculate the peak values of E and B.

a. 300 V/m, 10–4 T b. 1000 V/m, 3.35 × 10–6 T c. 225 V/m, 1.6 × 10–3 T d. 111 V/m, 3 × 10–5 T e. 711 V/m, 2.37 × 10–6 T

3. If the maximum E-component of an electromagnetic wave is 600 V/m, what is the maximum B-component?

a. 1.4 T b. 1.8 × 10–5 T c. 2.0 × 10–6 T d. 1.0 × 10–3 T e. 1.6 × 10–10 T

4. Find the force exerted by reflecting sunlight off a reflecting aluminum sheet in space if the area normal to the sunlight is 10 000 m2 and the solar intensity is 1350 W/m2.

a. 0.72 N b. 0.09 N c. 9 N d. 45 N e. 0.18 N

237

238 CHAPTER 34

5. What is the average value of the magnitude of the Poynting vector S at 1 meter from a 100-watt lightbulb radiating in all directions?

a. 1 W/m2 b. 4 W/m2 c. 2 W/m2 d. 8 W/m2 e. 12 W/m2

6. A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain. What is the intensity of the signal at a distance of 10 km?

a. 8 × 10–5 W/m2 b. 8 × 10–6 W/m2 c. 3 × 10–3 W/m2 d. 0.8 W/m2 e. 2.5 × 10–5 W/m2

7. How much electromagnetic energy is contained in each cubic meter near the Earth’s surface if the intensity of sunlight under clear skies is 1000 W/m2?

a. 3.3 × 10–6 J b. 3.3 J c. 0.003 J d. 10–4 J e. 3.0 × 105 J

8. At a distance of 10 km from a radio transmitter, the amplitude of the E-field is 0.20 volts/meter. What is the total power emitted by the radio transmitter?

a. 10 kW b. 67 kW c. 140 kW d. 245 kW e. 21 kW

9. What is the maximum radiation pressure exerted by sunlight in space (S = 1350 W/m2) on a flat black surface?

a. 2.25 × 10–5 Pa b. 0.06 Pa c. 7 × 10–4 Pa d. 4.5 × 10–6 Pa e. 9.0 × 10–6 Pa

Electromagnetic Waves 239

10. What is the maximum radiation pressure exerted by sunlight in space (S = 1350 W/m2) on a highly polished silver surface?

a. 1.4 × 10–2 Pa b. 0.12 Pa c. 9.0 × 10–6 Pa d. 4.5 × 10–5 Pa e. 2.3 × 10–6 Pa

11. Find the frequency of X-rays of wavelength 1 Å = 10–10 m.

a. 3 × 1018 Hz b. 3 × 1010 MHz c. 6 × 109 Hz d. 3 × 108 Hz e. 3 × 1020 Hz

12. Green light has a wavelength of 5.4 × 10–7 m. What is the frequency of this EM-wave in air?

a. 5.55 × 1014 Hz b. 6.00 × 1011 Hz c. 9.00 × 108 Hz d. 3.00 × 1010 MHz e. 1.80 × 1015 Hz

13. An FM radio station broadcasts at 98.6 MHz. What is the wavelength of the radiowaves?

a. 60.8 m b. 6.08 m c. 3.04 m d. 0.314 m e. 0.33 cm

14. What should be the height of a dipole antenna (of dimensions 1/4 wavelength) if it is to transmit 1200 kHz radiowaves?

a. 11.4 m b. 60 cm c. 1.12 m d. 62.5 m e. 250 m

240 CHAPTER 34

15. The magnetic field of a plane-polarized electromagnetic wave moving in the

z-direction is given by B = 1.2 × 10–6 sin ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛810×

−240

7tzπ2 in SI units. What is

the maximum E-field?

a. 1000 V/m b. 180 V/m c. 81 V/m d. 360 V/m e. 0.40 V/m

16. The magnetic field of a plane-polarized electromagnetic wave moving in the

z-direction is given by B = 1.2 × 10–6 sin ⎥⎥⎤

⎢⎢⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ ×−

810

2402

7tzπ⎦⎣

in SI units. What is

the frequency of the wave?

a. 500 MHz b. 250 kHz c. 1.25 MHz d. 10 mHz e. 300 MHz

17. The magnetic field of a plane-polarized electromagnetic wave moving in the

z-direction is given by B = 1.2 × 10–6 sin ⎥⎥⎦⎢

⎢⎣

⎟⎠

⎜⎝ 8240

2⎤⎡⎟⎞

⎜⎛ 10×

−7tzπ in SI units. What is

the wavelength of the EM wave?

a. 120 m b. 240 m c. 60 m d. 100 m e. 360 m

18. The magnetic field of a plane-polarized electromagnetic wave moving in the

z-direction is given by B = 1.2 × 10–6 sin ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛810×

−240

7tzπ2 in SI units. What is

the speed of the EM wave?

a. 3 × 108 m/s b. 100 m/s c. 106 m/s d. 2 × 107 m/s e. 2 × 108 m/s

Electromagnetic Waves 241

19. The magnetic field of a plane-polarized electromagnetic wave moving in the

z-direction is given by B = 1.2 × 10–6 sin ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛810×

−240

7tzπ2 in SI units. Find the

average power per square meter carried by the EM wave.

a. 720 W b. 172 W c. 500 W d. 2 × 107 W e. 86 W

20. A solar cell has a light-gathering area of 10 cm2 and produces 0.2 A at 0.8 V (DC) when illuminated with S = 1000 W/m2 sunlight. What is the efficiency of the solar cell?

a. 16% b. 7% c. 23% d. 4% e. 32%

21. High frequency alternating current is passed through a solenoid that contains a solid copper core insulated from the coils of the solenoid. Which statement is correct?

a. A copper core remains cool no matter what the frequency of the current in the solenoid is.

b. The copper core remains cool because the induced emf is parallel to the solenoid axis and fluctuates rapidly.

c. The copper core heats up because an emf parallel to the solenoid axis is induced in the core.

d. The copper core heats up because circular currents around its axis are induced in the core.

e. The copper core heats up because the electric field induced in the copper is parallel to the magnetic field produced by the solenoid.

22. In an electromagnetic wave, 1) how are the electric and magnetic field directions related and 2) how is the direction of travel determined from their directions? (c is the velocity of the light wave.)

a. E || B; cc

= BE×BE×

.

EB×cb. E || B; = .

EB×c

c. E ⊥ B; cc

= B×EBE×

.

d. E ⊥ B; cc

= EBEB

××

.

e. E = B/c; cc

= EBEB

××

.

242 CHAPTER 34

23. The intensity of radiation reaching the earth from the sun is 1350 W/m2. The earth’s radius is 6.4 × 106 m. How big a force does this radiation exert on the earth? (Assume it is all absorbed.)

a. 5.8 × 108 N b. 1.2 × 109 N c. 2.3 × 109 N d. 4.6 × 109 N e. 1.7 × 1017 N

24. The speed of light is given by the value of

00μεa. .

00μεb. .

c. 00με

1.

d. 00με

1.

0

0

με

e. .

25. The magnetic field amplitude in an electromagnetic wave in vacuum is related to the electric field amplitude by = B

cE

a. .

b. c

E.

c. . Ed. cE . e. . cE

2212 mN/C 1085. ⋅× − 20Eε26. Since 0 , the units of are 8=ε

a. 3msJ⋅

.

b. 3msN⋅

.

3mJ

c. .

d. 3mN

.

e. 3mW

.

Electromagnetic Waves 243

27. When E and B are the amplitudes of the electric and magnetic fields in an electromagnetic wave in vacuum, the total average energy density in the wave is

a. 204

1Eε .

b. 202

1Eε .

c. . 20Eε

d. 0

2

μB

.

e. 0μ

EB.

28. In the atmosphere, the shortest wavelength electromagnetic waves are called

a. microwaves. b. infrared waves. c. ultraviolet waves. d. X-rays. e. gamma rays.

29. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the pressure of solar radiation on sphere 2 to that on sphere 1 is a. 0.25. b. 0.50. c. 1.0. d. 2.0. e. 4.0.

30. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the gravitational force exerted by the sun on sphere 1 to the pressure of solar radiation on sphere 1 is T1; the ratio for sphere 2 is T2. The ratio of T2 to T1 is a. 0.25. b. 0.50. c. 1.0. d. 2.0. e. 4.0.

31. Magnetic fields are produced by

a. constant electric currents. b. electric currents that vary sinusoidally with time. c. time-varying electric fields. d. all of the above. e. only (a) and (b) above.

244 CHAPTER 34

32. At every instant the ratio of the magnitude of the electric to the magnetic field in an electromagnetic wave in vacuum is equal to

a. the speed of radio waves. b. the speed of light. c. the speed of gamma rays. d. all of the above. e. only (a) and (b) above.

33. A spherical particle of density ρ = 5.00

gcm2 and 2.00 mm radius is located at the

same distance from the Sun as the Earth. RSE = 1.50×1011 m .

G = 6.67 ×10−11

Nm2

kg2 . S = 1300

Wm2 . MS = 1.99 ×1030 kg . If the particle absorbs

100 percent of the sunlight reaching it, the ratio of the force exerted by the solar radiation to the force of gravity exerted on the particle by the Sun is

a. 5.8×10−5 . b. 0.58. c. 1.0. d. 1.7. e. 1.7 ×104 .

34. You can raise the temperature of an object with

a. microwaves. b. infrared waves. c. ultraviolet rays. d. all of the above. e. only (a) and (b) above.

35. An open circuit consists of a 12 μF parallel plate capacitor charged to 200 V and a Ω10 resistor. At the instant when a switch closes the circuit (with no battery in it) the displacement current between the plates of the capacitor is

a. 1.2 μA .

b. 2.4 ×10−4 A . c. 2.4 mA. d. 10 A. e. 20 A.

Electromagnetic Waves 245

Open-Ended Problems

36. Near the surface of the planet, the Earth’s magnetic field is about 0.5 × 10–4 T. How much energy is stored in 1 m3 of the atmosphere because of this field?

37. The sun radiates energy at a rate of 3.86 × 1026 W. Its radius is 7.0 × 108 m. If the distance from the Earth to the sun is 1.5 × 1011 m, what is the intensity of solar radiation at the top of the Earth’s atmosphere?

38. A possible means of spaceflight is to place a perfectly reflecting aluminized sheet into Earth orbit and use the light from the sun to push this solar sail. If a huge sail of area 6 × 105 m2 and mass 6000 kg were placed into orbit and turned toward the sun, what would be the force exerted on the sail? (Assume a solar intensity of 1380 W/m2.)

246 CHAPTER 34

Electromagnetic Waves 247

Chapter 34

Electromagnetic Waves

1. d

2. b

3. c

4. b

5. d

6. a

7. a

8. b

9. d

10. c

11. a

12. a

13. c

14. d

15. d

16. c

17. b

18. a

19. b

20. a

21. d

22. c

23. a

24. c

25. a

26. c

27. b

28. e

29. a

30. c

31. d

32. d

33. e

34. d

35. e

36. 9.9 × 10–4 J

37. 1400 W/m2

38. 5.52 N

248 CHAPTER 34