Chapter 30: Maxwell’s Equations and Electromagnetic Waves

1
Chapter 30 Maxwells Equations and
Electromagnetic Waves

• Section 30-1 Maxwells Displacement Current

2
A parallel-plate capacitor has closely spaced
circular plates of radius R 2.00 cm. Charge is
flowing onto the positive plate at the rate I
dQ/dt 1.36 A. The magnetic field at a distance
r 2.00 cm from the axis of the plates is
approximately

• 136 mT
• 256 mT
• 16.5 mT
• 457 mT
• 88.3 mT

3
A parallel-plate capacitor has closely spaced
circular plates of radius R 2.00 cm. Charge is
flowing onto the positive plate at the rate I
dQ/dt 1.36 A. The magnetic field at a distance
r 2.00 cm from the axis of the plates is
approximately

• 136 mT
• 256 mT
• 16.5 mT
• 457 mT
• 88.3 mT

4
Charge is flowing onto one plate of a
parallel-plate capacitor and off the other plate
at a rate of 5.00 A. The rate at which the
electric field between the plates is changing is
approximately

• 5.65 1011 N m2/(C s)
• 11.3 1011 N m2/(C s)
• 2.45 1011 N m2/(C s)
• 12.4 1011 N m2/(C s)
• 1.76 1011 N m2/(C s)

5
Charge is flowing onto one plate of a
parallel-plate capacitor and off the other plate
at a rate of 5.00 A. The rate at which the
electric field between the plates is changing is
approximately

• 5.65 1011 N m2/(C s)
• 11.3 1011 N m2/(C s)
• 2.45 1011 N m2/(C s)
• 12.4 1011 N m2/(C s)
• 1.76 1011 N m2/(C s)

6
An ac voltage is applied across a capacitor.
Which figure best represents the magnetic field
between the capacitor?
7
An ac voltage is applied across a capacitor.
Which figure best represents the magnetic field
between the capacitor?
8
An ac voltage, V 20 V sin (1000 rad/s t) is
applied across a capacitor of capacitance C 40
?F. The capacitor is made of two circular plate
each of radius r 5 cm. What is the peak
magnetic field at the circumference of the
capacitor?

• 1.2 ?T
• 1.6.2 ?T
• 3.2 ?T
• 72 ?T
• None of these is correct.

9
An ac voltage, V 20 V sin (1000 rad/s t) is
applied across a capacitor of capacitance C 40
?F. The capacitor is made of two circular plate
each of radius r 5 cm. What is the peak
magnetic field at the circumference of the
capacitor?

• 1.2 ?T
• 1.6.2 ?T
• 3.2 ?T
• 72 ?T
• None of these is correct.

10
Chapter 30 Maxwells Equations and
Electromagnetic Waves

• Section 30-2 Maxwells Equations

11
Which of the following statements contradicts one
of Maxwell's equations?

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

12
Which of the following statements contradicts one
of Maxwell's equations?

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

13
If the existence of magnetic monopoles should
ever be confirmed, which of the following
equations would have to be altered?
14
If the existence of magnetic monopoles should
ever be confirmed, which of the following
equations would have to be altered?
15
Maxwell's equations

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

16
Maxwell's equations

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

17
Which of the following statements is false?

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

18
Which of the following statements is false?

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

19
Which of the following statements is true?

• A changing electric field induces a magnetic
  field.
• A changing magnetic field induces an electric
  field.
• Maxwells equations predict the speed of light.
• Maxwells equations predict that light is made up
  of oscillating electric and magnetic waves.
• All the above statements are true.

20
Which of the following statements is true?

• A changing electric field induces a magnetic
  field.
• A changing magnetic field induces an electric
  field.
• Maxwells equations predict the speed of light.
• Maxwells equations predict that light is made up
  of oscillating electric and magnetic waves.
• All the above statements are true.

21
Chapter 30 Maxwells Equations and
Electromagnetic Waves

• Section 30-3 The Wave Equation for
  Electromagnetic Waves

22
Which of the following statements is true?

• Both the B and the E components of an
  electromagnetic wave satisfy the wave equation.
• The phase of a wave traveling in the negative z
  direction is kz wt.
• The speed of an electromagnetic wave traveling in
  a vacuum is given by (?0m0)1/2.
• The magnitude of E in an electromagnetic wave is
  greater than the B magnitude of by a factor of
  c.
• All of these statements are true.

23
Which of the following statements is true?

• Both the B and the E components of an
  electromagnetic wave satisfy the wave equation.
• The phase of a wave traveling in the negative z
  direction is kz wt.
• The speed of an electromagnetic wave traveling in
  a vacuum is given by (?0m0)1/2.
• The magnitude of E in an electromagnetic wave is
  greater than the B magnitude of by a factor of
  c.
• All of these statements are true.

24
Which of the following functions satisfy the
one-dimensional wave equation?

• y(x, t) y0 cos(kx wt)
• y(x, t) y0 sin(kx wt)
• y(x, t) y0 sin(kx wt) B cos(kx wt)
• y(x, t) y0 (sin kx) B(cos wt)
• All of these functions satisfy the one-
  dimensional wave equation.

25
Which of the following functions satisfy the
one-dimensional wave equation?

• y(x, t) y0 cos(kx wt)
• y(x, t) y0 sin(kx wt)
• y(x, t) y0 sin(kx wt) B cos(kx wt)
• y(x, t) y0 (sin kx) B(cos wt)
• All of these functions satisfy the one-
  dimensional wave equation.

26
Which of the following statements is true?

• Maxwell's equations apply only to fields that are
  constant in time.
• Electromagnetic waves are longitudinal waves.
• The electric and magnetic fields are out of phase
  in an electromagnetic wave.
• The magnitude of E in an electromagnetic wave is
  greater than the B magnitude of by a factor of
  c.
• All of the above statements are true.

27
Which of the following statements is true?

• Maxwell's equations apply only to fields that are
  constant in time.
• Electromagnetic waves are longitudinal waves.
• The electric and magnetic fields are out of phase
  in an electromagnetic wave.
• The magnitude of E in an electromagnetic wave is
  greater than the B magnitude of by a factor of
  c.
• All of the above statements are true.

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30
Chapter 30 Maxwells Equations and
Electromagnetic Waves

• Section 30-4 Electromagnetic Radiation

31
The visible portion of the electromagnetic
spectrum is closest to which of the following
intervals?

• 200 to 500 nm
• 300 to 600 nm
• 400 to 700 nm
• 500 to 800 nm
• 600 to 900 nm

32
The visible portion of the electromagnetic
spectrum is closest to which of the following
intervals?

• 200 to 500 nm
• 300 to 600 nm
• 400 to 700 nm
• 500 to 800 nm
• 600 to 900 nm

33
Electromagnetic waves that have a wavelength of
300 m in free space have a frequency of

• 1 103 Hz
• 5 105 Hz
• 1 106 Hz
• 9 106 Hz
• 1 1011 Hz

34
Electromagnetic waves that have a wavelength of
300 m in free space have a frequency of

• 1 103 Hz
• 5 105 Hz
• 1 106 Hz
• 9 106 Hz
• 1 1011 Hz

35
What is the frequency of 555-nm light?

• 16.7 kHz
• 5.40 1014 Hz
• 5.40 1015 Hz
• 1.70 107 Hz
• 5.40 1017 Hz

36
What is the frequency of 555-nm light?

• 16.7 kHz
• 5.40 1014 Hz
• 5.40 1015 Hz
• 1.70 107 Hz
• 5.40 1017 Hz

37
The wavelength of a 150-MHz television signal is
approximately

• 1.0 m
• 1.5 m
• 2.0 m
• 2.0 cm
• 50 cm

38
The wavelength of a 150-MHz television signal is
approximately

• 1.0 m
• 1.5 m
• 2.0 m
• 2.0 cm
• 50 cm

39
The wavelength of a 63.7-MHz electromagnetic wave
is approximately

• 1.0 m
• 4.7 m
• 6.8 m
• 7.2 cm
• 50 cm

40
The wavelength of a 63.7-MHz electromagnetic wave
is approximately

• 1.0 m
• 4.7 m
• 6.8 m
• 7.2 cm
• 50 cm

41
Light wave A has twice the frequency of light
wave B. The wavelength of light wave A is _____
that of light wave B.

• equal to
• twice
• four times
• half
• one

42
Light wave A has twice the frequency of light
wave B. The wavelength of light wave A is _____
that of light wave B.

• equal to
• twice
• four times
• half
• one

43
Arrange the following types of electromagnetic
radiation in order of increasing wavelength
gamma rays, infrared light, ultraviolet light,
visible light.

• Gamma rays are not electromagnetic radiation.
• gamma rays, infrared, visible, ultraviolet
• gamma rays, ultraviolet, visible, infrared
• visible, ultraviolet, infrared, gamma rays
• ultraviolet, visible, infrared, gamma rays

44
Arrange the following types of electromagnetic
radiation in order of increasing wavelength
gamma rays, infrared light, ultraviolet light,
visible light.

• Gamma rays are not electromagnetic radiation.
• gamma rays, infrared, visible, ultraviolet
• gamma rays, ultraviolet, visible, infrared
• visible, ultraviolet, infrared, gamma rays
• ultraviolet, visible, infrared, gamma rays

45
Of X rays, infrared radiation, and radio waves,
which has the longest wavelength and which the
shortest?

• X rays have the longest, radio waves the
  shortest.
• X rays have the longest, infrared radiation the
  shortest.
• Radio waves have the longest, X rays the
  shortest.
• Radio waves have the longest, infrared radiation
  the shortest.
• Infrared radiation has the longest, X rays the
  shortest.

46
Of X rays, infrared radiation, and radio waves,
which has the longest wavelength and which the
shortest?

• X rays have the longest, radio waves the
  shortest.
• X rays have the longest, infrared radiation the
  shortest.
• Radio waves have the longest, X rays the
  shortest.
• Radio waves have the longest, infrared radiation
  the shortest.
• Infrared radiation has the longest, X rays the
  shortest.

47
Which of the following groups is arranged in
order of increasing wavelength?

• infrared, ultraviolet, microwaves
• X rays, visible, infrared
• gamma rays, ultraviolet, X rays
• microwaves, gamma rays, visible
• infrared, ultraviolet, gamma rays

48
Which of the following groups is arranged in
order of increasing wavelength?

• infrared, ultraviolet, microwaves
• X rays, visible, infrared
• gamma rays, ultraviolet, X rays
• microwaves, gamma rays, visible
• infrared, ultraviolet, gamma rays

49
There are many different regions to the
electromagnetic spectrum. These include, (a)
visible light, (b) gamma-rays, (c) infra-red, (d)
micro-waves, (e) radio-waves, (f) ultra-violet,
and (g) X-rays. Put them in order of increasing
wavelength, starting with the shortest wavelength
first.

• bgdafge
• bgfadce
• bgafcde
• bgfacde
• bgafdce

50
There are many different regions to the
electromagnetic spectrum. These include, (a)
visible light, (b) gamma-rays, (c) infra-red, (d)
micro-waves, (e) radio-waves, (f) ultra-violet,
and (g) X-rays. Put them in order of increasing
wavelength, starting with the shortest wavelength
first.

• bgdafge
• bgfadce
• bgafcde
• bgfacde
• bgafdce

51
Which of the following statements about light in
a vacuum is incorrect?

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

52
Which of the following statements about light in
a vacuum is incorrect?

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

53
A beam of light is propagating in the x
direction. The electric-field vector

• can oscillate in any arbitrary direction in
  space.
• must oscillate in the z direction.
• must oscillate in the yz plane.
• must oscillate in the x direction.
• must have a steady component in the x direction.

54
A beam of light is propagating in the x
direction. The electric-field vector

• can oscillate in any arbitrary direction in
  space.
• must oscillate in the z direction.
• must oscillate in the yz plane.
• must oscillate in the x direction.
• must have a steady component in the x direction.

55
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.

• electric field electric
• electric field magnetic
• magnetic field magnetic
• magnetic field electric
• electric and magnetic fields electric

56
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.

• electric field electric
• electric field magnetic
• magnetic field magnetic
• magnetic field electric
• electric and magnetic fields electric

57
Which of the following does not result in the
production of electromagnetic waves?

• Charges moving at a constant velocity.
• Charges that are accelerating or decelerating.
• Charges moving around in a circle.
• Electrons that make a transition from one atomic
  level to another.
• An oscillating electric current.

58
Which of the following does not result in the
production of electromagnetic waves?

• Charges moving at a constant velocity.
• Charges that are accelerating or decelerating.
• Charges moving around in a circle.
• Electrons that make a transition from one atomic
  level to another.
• An oscillating electric current.

59
The nearest star to us, Alpha Centauri, is 4.30
light-years away. What is this distance in
kilometers?

• 4.1 1010 km
• 4.1 1013 km
• 4.1 1016 km
• 6.8 1011 km
• 6.8 1014 km

60
The nearest star to us, Alpha Centauri, is 4.30
light-years away. What is this distance in
kilometers?

• 4.1 1010 km
• 4.1 1013 km
• 4.1 1016 km
• 6.8 1011 km
• 6.8 1014 km

61
You are using an antenna consisting of a single
loop of wire of radius 15.0 cm to detect
electromagnetic waves for which Erms 0.200
V/m. If the wave frequency is 600 Hz, the rms
value of the emf induced in the loop is
approximately

• 32.1 nV
• 84.3 nV
• 66.7 nV
• 178 nV
• 643 nV

62
You are using an antenna consisting of a single
loop of wire of radius 15.0 cm to detect
electromagnetic waves for which Erms 0.200
V/m. If the wave frequency is 600 Hz, the rms
value of the emf induced in the loop is
approximately

• 32.1 nV
• 84.3 nV
• 66.7 nV
• 178 nV
• 643 nV

63
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?

• 1 sinusoidal wave in the plane of the dipole.
• 2 sinusoidal wave perpendicular to the plane of
  the dipole.
• 3 circular wave perpendicular to the plane of
  the dipole.
• 4 circular wave in the plane of the dipole.
• None of these is correct.

64
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?

• 1 sinusoidal wave in the plane of the dipole.
• 2 sinusoidal wave perpendicular to the plane of
  the dipole.
• 3 circular wave perpendicular to the plane of
  the dipole.
• 4 circular wave in the plane of the dipole.
• None of these is correct.

65
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?

• 1 sinusoidal wave in the plane of the dipole.
• 2 sinusoidal wave perpendicular to the plane of
  the dipole.
• 3 circular wave perpendicular to the plane of
  the dipole.
• 4 circular wave in the plane of the dipole.
• None of these is correct.

66
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?

• 1 sinusoidal wave in the plane of the dipole.
• 2 sinusoidal wave perpendicular to the plane of
  the dipole.
• 3 circular wave perpendicular to the plane of
  the dipole.
• 4 circular wave in the plane of the dipole.
• None of these is correct.

67
The Sun radiates about 3.83 ? 1026 W of power.
How large should a perfectly reflecting solar
sail be on a space ship of mass 50 kg to provide
an acceleration of 10-4 m/s2 at the Earths
orbit? The radius of the Earths orbit is 1.50 ?
1011 m.

• 550 m2
• 625 m2
• 1100 m2
• 2500 m2
• None of these is correct.

68
The Sun radiates about 3.83 ? 1026 W of power.
How large should a perfectly reflecting solar
sail be on a space ship of mass 50 kg to provide
an acceleration of 10-4 m/s2 at the Earths
orbit? The radius of the Earths orbit is 1.50 ?
1011 m.

• 550 m2
• 625 m2
• 1100 m2
• 2500 m2
• None of these is correct.

69
Electromagnetic waves are produced when

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

70
Electromagnetic waves are produced when

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

71
The polar plot of the intensity of
electromagnetic radiation from an electric-dipole
antenna shows that the intensity is

• a maximum at ? 0º.
• a minimum at ? 90º.
• a maximum at ? 90º.
• independent of the angle ?.
• None of these is correct.

72
The polar plot of the intensity of
electromagnetic radiation from an electric-dipole
antenna shows that the intensity is

• a maximum at ? 0º.
• a minimum at ? 90º.
• a maximum at ? 90º.
• independent of the angle ?.
• None of these is correct.

73
The 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.

• 1.1 J
• 3.0 1023 J
• 3.5 J
• 4.6 J
• 2.2 J

74
The 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.

• 1.1 J
• 3.0 1023 J
• 3.5 J
• 4.6 J
• 2.2 J