Deck 22: Electromagnetic Waves

Question 1

Which of the following does not result in the production of electromagnetic waves?

A) charges moving at a constant velocity
B) charges that are accelerating or decelerating
C) charges moving around in a circle
D) electrons that make a transition from one atomic level to another
E) an oscillating electric current

Answer 1

charges moving at a constant velocity

Question 2

Which of the following statements about light in a vacuum is incorrect?

A) Light always travels with the same speed c regardless of the motion of the source or observer.
B) Light has wavelike properties.
C) Light has particlelike properties.
D) Light is an electromagnetic wave with its electric-field vector pointing parallel to the direction of propagation.
E) Light can be plane polarized.

Answer 2

Light is an electromagnetic wave with its electric-field vector pointing parallel to the direction of propagation.

Question 3

The nearest star to us, Alpha Centauri, is 4.30 light years away. What is this distance in kilometers?

A) 4.1 × 10¹⁰ km
B) 4.1 × 10¹³ km
C) 4.1 × 10¹⁶ km
D) 6.8 × 10¹¹ km
E) 6.8 × 10¹⁴ km

Answer 3

4.1 × 10¹³ km

Question 4

The electric field of an electromagnetic wave is given by E_y = 25 sin 2.4 × 10⁶ π x - 3.0 × 10⁸t)). What is the wavelength of the wave?

A) 4.8 × 10⁷ m
B) 2.1 × 10^-8 m
C) 2.1 × 10^-7 m
D) 8.3 × 10^-7 m
E) 7.5 × 10^-6 m

Question 5

The electric field of an electromagnetic wave is given by E_y = 25 sin 2.4 × 10⁶ π x - 3.0 × 10⁸t)). What is the frequency of the wave?

A) 4.8 × 10⁷ s^-1
B) 3.6 × 10¹⁴ s^-1
C) 1.2 × 10⁶ s^-1
D) 2.3 × 10¹⁵ s^-1
E) None of the above.

Question 6

The left part of the figure shows a dipole oscillating in a sinusoidal function. Which of the curves best represents the magnetic field along the axis of the dipole centered about the dipole?

A) 1 - sinusoidal wave in the plane of the dipole
B) 2 - sinusoidal wave perpendicular to the plane of the dipole
C) 3 - circular wave perpendicular to the plane of the dipole; the intensity propagates in a sinusoidal function
D) 4 - circular wave in the plane of the dipole.; the intensity propagates in a sinusoidal function
E) None of these is correct.

Question 7

The wavelength of a 63.7-MHz electromagnetic wave is approximately

A) 1.0 m.
B) 4.7 m.
C) 6.8 m.
D) 7.2 cm.
E) 50 cm.

Question 8

The frequency range for FM broadcasts is 87.9 - 107.9 MHz in the U.S. In terms of wavelengths, the range corresponds to

A) 87.9 - 107.9 m.
B) 2.78 - 3.41 m.
C) 83.3 - 102.3 m.
D) 12.4 - 19.5 m.
E) None of these is correct.

Question 9

What is the frequency of 555-nm light?

A) 16.7 kHz
B) 5.40 × 10¹⁴ Hz
C) 5.40 × 10¹⁵ Hz
D) 1.70 × 10⁷ Hz
E) 5.40 × 10¹⁷ Hz

Question 10

Of x rays, infrared radiation, and radio waves, which has the longest wavelength and which the shortest?

A) X rays have the longest, radio waves the shortest.
B) X rays have the longest, infrared radiation the shortest.
C) Radio waves have the longest, x rays the shortest.
D) Radio waves have the longest, infrared radiation the shortest.
E) Infrared radiation has the longest, x rays the shortest.

Question 11

The left part of the figure shows a dipole oscillating in a sinusoidal function. Which of the curves best represents the electric field along the axis of the dipole?

A) 1 - sinusoidal wave in the plane of the dipole
B) 2 - sinusoidal wave perpendicular to the plane of the dipole
C) 3 - circular wave perpendicular to the plane of the dipole
D) 4 - circular wave in the plane of the dipole
E) None of these is correct.

Question 12

Which of the following functions satisfy the one-dimensional wave equation?

A) yx, t) = y₀ coskx - ωt)
B) yx, t) = y₀ sinkx - ωt)
C) yx, t) = y₀ sinkx - ωt) + B coskx - ωt)
D) yx, t) = y₀ sin kx) · Bcos ωt)
E) All of these functions satisfy the one-dimensional wave equation.

Question 13

Electromagnetic waves that have a wavelength of 300 m in free space have a frequency of

A) 1 × 10^-3 Hz.
B) 5 × 10⁵ Hz.
C) 1 × 10⁶ Hz.
D) 9 × 10⁶ Hz.
E) 1 × 10¹¹ Hz.

Question 14

Arrange the following types of electromagnetic radiation in order of increasing wavelength: gamma rays, infrared light, ultraviolet light, and visible light.

A) Gamma rays are not electromagnetic radiation.
B) gamma rays, infrared, visible, ultraviolet
C) gamma rays, ultraviolet, visible, infrared
D) visible, ultraviolet, infrared, gamma rays
E) ultraviolet, visible, infrared, gamma rays

Question 15

Which of the following statements is true?

A) Both the B and the E components of an electromagnetic wave satisfy the wave equation.
B) The phase of a wave traveling in the negative z direction is kz + ωt.
C) The speed of an electromagnetic wave traveling in a vacuum is given by ε₀μ₀)^-1/2.
D) The magnitude of E is greater than the magnitude of B by a factor of c.
E) All of these statements are true.

Question 16

The wavelength of a 150-MHz television signal is approximately

A) 1.0 m.
B) 1.5 m.
C) 2.0 m.
D) 2.0 cm.
E) 50 cm.

Question 17

A beam of light is propagating in the x direction. The electric-field vector

A) can oscillate in any arbitrary direction in space.
B) must oscillate in the z direction.
C) must oscillate in the yz plane.
D) must oscillate in the x direction.
E) must have a steady component in the x direction.

Question 18

Which of the following statements is true?

A) Maxwell's equations apply only to fields that are constant in time.
B) Electromagnetic waves are longitudinal waves.
C) The electric and magnetic fields are out of phase in an electromagnetic wave.
D) The electric- and magnetic-field vectors E and B are equal in magnitude in an electromagnetic wave.
E) None of these statements is true.

Question 19

The visible portion of the electromagnetic spectrum is closest to which of the following intervals?

A) 200 to 500 nm
B) 300 to 600 nm
C) 400 to 700 nm
D) 500 to 800 nm
E) 600 to 900 nm

Question 20

Light that has a wavelength of 600 nm has a frequency of

A) 5.0 × 10¹⁵ Hz.
B) 5.0 × 10¹⁴ Hz.
C) 5.0 × 10⁶ Hz.
D) 1.2 × 10⁵ Hz.
E) 1.2 × 10¹⁴ Hz.

Question 21

Electromagnetic waves are produced when

A) free electric charges accelerate.
B) conduction electrons move with a constant drift velocity in a conductor.
C) a conductor moves with constant velocity through a magnetic field.
D) electrons bound to atoms and molecules make transitions to higher energy states.
E) All of these are correct.

Question 22

Which of the following statements is true?

A) A changing electric field induces a magnetic field.
B) A changing magnetic field induces an electric field.
C) Maxwell's equations predict the speed of light.
D) Maxwell's equations predict that light is made up of oscillating electric and magnetic waves.
E) All the above statements are true.

Question 23

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away at most) from Earth is the spaceship?

A) 7.5 × 10⁸ m
B) 15 × 10⁸ m
C) 30 × 10⁸ m
D) 45 × 10⁸ m
E) The spaceship is on the Moon.

Question 24

Communications satellites are usually placed in geosynchronous orbits, a distance of 4.43 × 10⁷ m from the center of Earth. What is the time lag for a signal sent from one point on Earth's surface to another via such a satellite? The radius of Earth R_E = 6.370 × 10⁶ m.)

A) 0.13 s
B) 0.25 s
C) 0.51 s
D) 0.29 s
E) 0.15 s

Question 25

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A) very much greater.
B) a little greater.
C) the same.
D) a little less.
E) very much less.

Question 26

Maxwell's equations

A) imply that the electric field due to a point charge varies inversely as the square of the distance from the charge.
B) describe how electric field lines diverge from a positive charge and converge on a negative charge.
C) assert that the flux of the magnetic field vector is zero through any closed surface.
D) describe the experimental observation that magnetic field lines do not diverge from any point space or converge to any point.
E) All of these are correct.

Question 27

Which of the following statements contradicts one of Maxwell's equations?

A) A changing magnetic field produces an electric field.
B) The net magnetic flux through a closed surface depends on the current inside.
C) A changing electric field produces a magnetic field.
D) The net electric flux through a closed surface depends on the charge inside.
E) None of these statements contradict any of Maxwell's equations.

Question 28

A common unit of length in astronomy is the parsec, where 1 parsec = 3.26 light years. How many seconds does it take a radio signal to travel one parsec through space?

A) 1.03 × 10⁸ s
B) 9.71 × 10⁸ s
C) 9.71 × 10⁷ s
D) 1.72 × 10⁶ s
E) None of the above.

Question 29

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m. If the wave frequency is 600 Hz, the rms value of the emf induced in the loop is approximately

A) 32.1 nV.
B) 84.3 nV.
C) 66.7 nV.
D) 178 nV.
E) 643 nV.

Question 30

Which of the following groups is arranged in order of increasing wavelength?

A) infrared, ultraviolet, microwaves
B) x rays, visible, infrared
C) gamma rays, ultraviolet, x rays
D) microwaves, gamma rays, visible
E) infrared, ultraviolet, gamma rays

Question 31

Which of the following statements is false?

A) Isolated electric charges exist.
B) Electric field lines diverge from positive charges and converge on negative charges.
C) The flux of the magnetic-field vector is zero through any closed surface.
D) Isolated magnetic poles exist.
E) Changing electric fields induce changing magnetic fields.

Question 32

Ultrafast pulse lasers can emit pulses of the order 10 fs. The length of each pulse that is 10 fs long is

A) 1.0 μm.
B) 2.0 μm.
C) 3.0 μm.
D) 9.0 μm.
E) 12.0 μm.

Question 33

It has been suggested that a fundamental physical unit of time is the time required for light to traverse the diameter of the nucleus of an atom approximately 3 × 10^-13 m). This unit of time is approximately

A) 1 s.
B) 10^-4 s.
C) 2 × 10^-20 s.
D) 10^-21 s.
E) 10^-23 s.

Question 34

There are many different regions to the electromagnetic spectrum. These include a) visible light, b) gamma-rays, c) infrared, d) microwaves, e) radio waves, f) ultraviolet, and g) x rays. Put them in order of increasing wavelength, starting with the shortest wavelength first.

A) bgdafge
B) bgfadce
C) bgafcde
D) bgfacde
E) bgafdce

Question 35

Ultrafast pulse lasers can emit pulses of the order 10 fs. If each pulse that is 10 fs long and the wavelength of the laser is 500 nm, the number of wavelengths in each pulse is

A) 6.
B) 10.
C) 12.
D) 50.
E) 120.

Question 36

The polar plot of the intensity of electromagnetic radiation from an electric-dipole antenna shows that the intensity is

A) a maximum at θ = 0º.
B) a minimum at θ = 90º.
C) a maximum at θ = 90º.
D) independent of the angle θ.
E) None of these is correct.

Question 37

How long does it take light to travel across the width of a Pb nucleus of radius 7.1 fm?

A) 2.4 × 10^-23 s
B) 1.2 × 10^-23 s
C) 2.4 × 10^-20 s
D) 4.7 × 10^-23 s
E) None of the above.

Question 38

For a particular electromagnetic plane wave, the electric field's amplitude is 0.54 V/m. What is the magnetic field's amplitude?

A) 0.54 T
B) 1.8 x 10^-9 T
C) 5.56 x 10⁸ T
D) 1.62 x 10⁸ T
E) 1.85 T

Question 39

You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m. If the wave frequency is 600 kHz, the rms value of the emf induced in the loop is approximately

A) 32.1 μV.
B) 84.3 μV.
C) 66.7 μV.
D) 178 μV.
E) 643 μV.

Question 40

An AC voltage is applied across a capacitor. Which figure best represents the magnetic field between the capacitor?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 41

The detection of radio waves can be accomplished with either a dipole antenna or a loop antenna. The dipole antenna detects the _____ of the wave, and the loop antenna detects the _____ field of the wave.

A) electric field; electric
B) electric field; magnetic
C) magnetic field; magnetic
D) magnetic field; electric
E) electric and magnetic fields; electric

Question 42

The rms value of the electric field in an electromagnetic wave is E_rms = 200 V/m. The intensity of this wave is approximately

A) 53.1 W/m².
B) 106 W/m².
C) 1.59 × 10¹⁰ W/m².
D) 3.18 × 10¹⁰ W/m².
E) 1.70 kW/m².

Question 43

A 60-W lightbulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a lightbulb is emitted as electromagnetic radiation, what is the maximum value of the electric field at a distance of 2.0 m from the lightbulb?

A) 43 V/m
B) 0.11 mV/m
C) 21 V/m
D) 60 V/m
E) 30 V/m

Question 44

Which of the following is NOT one of Maxwell's equations?

A) Gauss's Law for Electric Fields
B) Gauss's Law for Magnetic Fields
C) Maxwell-Ampere's Law
D) Lenz's Law
E) Faraday's Law

Question 45

Earth is about 28,000 light years from the center of the Milky Way Galaxy. If a supernova explosion occurred approximately 14,000 light years away from us and released 2.0 × 10⁴⁶ J of energy in a sudden burst of light, how much energy would enter one of your pupils? Assume the diameter of a pupil to be about 4 mm. For comparison, our Sun radiates approximately 4 × 10²⁶ J/s.)

A) 1.1 J
B) 3.0 × 10²³ J
C) 3.5 J
D) 4.6 J
E) 2.2 J

Question 46

A 60-W lightbulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a lightbulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2.00 m from the lightbulb?

A) 15 W/m²
B) 4.8 W/m²
C) 2.4 W/m²
D) 0.60 W/m²
E) 1.2 W/m²

Question 47

The frequency of a particular electromagnetic wave is 5.00 x 10¹⁴ Hz. What is the energy of an individual photon in that wave?

A) 5.00 x 10¹⁴ J
B) 3.32 x 10^-19 J
C) 6.00 x 10^-7 J
D) 2.00 x 10^-15 J
E) 5.00 x 10^-14 J

Question 48

The intensity of solar radiation on Earth is about 1.4 × 10³ W/m². How many 50-W lightbulbs would you have to arrange in an array 3 m from you in order to obtain the same intensity as the Sun?

A) 8.0 × 10²
B) 5.3 × 10²
C) 3.2 × 10³
D) 1.0 × 10⁷
E) 1.6 × 10³

Question 49

The intensity of a laser beam is 450 W/m2. What is the rms value of the electric field of this laser beam? The permittivity of free space ϵ₀ = 8.85 × 10^-12 C²/N · m² and the permeability of free space µ₀ = 4π× 10^-7 N/A².)

A) 1.7 × 10⁵ V/m
B) 5.8 × 10² V/m
C) 3.4 × 10⁵ V/m
D) 4.1 × 10² V/m
E) 1.3 × 10³ V/m

Question 50

The rms value of the magnitude of the magnetic field in an electromagnetic wave is B_rms = 0.378 T. The average energy density of this wave is approximately

A) 114 kJ/m³.
B) 28.4 kJ/m³.
C) 31.8 kJ/m³.
D) 67.8 kJ/m³.
E) 56.9 kJ/m³.

Question 51

The rms value of the electric field in an electromagnetic wave is E_rms = 600 V/m. The average energy density of this wave is approximately

A) 0.796 μJ/m³.
B) 1.59 μJ/m³.
C) 3.18 μJ/m³.
D) 6.78 μJ/m³.
E) 5.21 μJ/m³.

Question 52

The rms value of the magnitude of the magnetic field in an electromagnetic wave is B_rms = 0.137 T. The intensity of this wave is approximately

A) 2.39 × 10¹² W/m².
B) 4.77 × 10¹² W/m².
C) 9.54 × 10¹² W/m².
D) 2.27 × 10¹² W/m².
E) 1.56 × 10¹² W/m².

Question 53

A 60-W lightbulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a lightbulb is emitted as electromagnetic radiation, what is the maximum value of the magnetic field at a distance of 2.0 m from the lightbulb?

A) 71 nT
B) 0.35 μT
C) 0.14 μT
D) 0.20 μT
E) 0.10 μT