Transcript A parallel-plate capacitor has closely spaced circular

Chapter 30: Maxwell’s Equations and
Electromagnetic Waves
Section 30-1: Maxwell’s Displacement
Current
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
A. 136 mT
B. 256 mT
C. 16.5 mT
D. 457 mT
E. 88.3 mT
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
A. 136 mT
B. 256 mT
C. 16.5 mT
D. 457 mT
E. 88.3 mT
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
A. 5.65 ×1011 N · m2/(C · s)
B. 11.3 × 1011 N · m2/(C · s)
C. 2.45 × 1011 N · m2/(C · s)
D. 12.4 × 1011 N · m2/(C · s)
E. 1.76 × 1011 N · m2/(C · s)
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
A. 5.65 ×1011 N · m2/(C · s)
B. 11.3 × 1011 N · m2/(C · s)
C. 2.45 × 1011 N · m2/(C · s)
D. 12.4 × 1011 N · m2/(C · s)
E. 1.76 × 1011 N · m2/(C · s)
An ac voltage is applied across a capacitor.
Which figure best represents the magnetic
field between the capacitor?
An ac voltage is applied across a capacitor.
Which figure best represents the magnetic
field between the capacitor?
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?
A. 1.2 T
B. 1.6.2 T
C. 3.2 T
D. 72 T
E. None of these is correct.
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?
A. 1.2 T
B. 1.6.2 T
C. 3.2 T
D. 72 T
E. None of these is correct.
Chapter 30: Maxwell’s Equations and
Electromagnetic Waves
Section 30-2: Maxwell’s Equations
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.
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.
If the existence of magnetic monopoles should ever
be confirmed, which of the following equations
would have to be altered?
Qinside
A.  En dA 
s
0
B.
B
s
n
dA  0
 
Bn
C.  E  dl   
dA
c
s t
 
En
D.  B  dl   0 I   0 0 
dA
c
s t
E. All would st ill apply.
If the existence of magnetic monopoles should ever
be confirmed, which of the following equations
would have to be altered?
Qinside
A.  En dA 
s
0
B.
B
s
n
dA  0
 
Bn
C.  E  dl   
dA
c
s t
 
En
D.  B  dl   0 I   0 0 
dA
c
s t
E. All would st ill apply.
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.
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.
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.
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.
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.
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.
Chapter 30: Maxwell’s Equations and
Electromagnetic Waves
Section 30-3: The Wave Equation for
Electromagnetic Waves
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 + wt.
C. The speed of an electromagnetic wave traveling
in a vacuum is given by (0m0)–1/2.
D. The magnitude of E in an electromagnetic wave
is greater than the B magnitude of by a factor
of c.
E. All of these statements are true.
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 + wt.
C. The speed of an electromagnetic wave traveling
in a vacuum is given by (0m0)–1/2.
D. The magnitude of E in an electromagnetic wave
is greater than the B magnitude of by a factor
of c.
E. All of these statements are true.
Which of the following functions satisfy the
one-dimensional wave equation?
A. y(x, t) = y0 cos(kx – wt)
B. y(x, t) = y0 sin(kx – wt)
C. y(x, t) = y0 sin(kx – wt) + B cos(kx – wt)
D. y(x, t) = y0 (sin kx) · B(cos wt)
E. All of these functions satisfy the onedimensional wave equation.
Which of the following functions satisfy the
one-dimensional wave equation?
A. y(x, t) = y0 cos(kx – wt)
B. y(x, t) = y0 sin(kx – wt)
C. y(x, t) = y0 sin(kx – wt) + B cos(kx – wt)
D. y(x, t) = y0 (sin kx) · B(cos wt)
E. All of these functions satisfy the
one- dimensional wave equation.
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 magnitude of E in an electromagnetic
wave is greater than the B magnitude of
by a factor of c.
E. All of the above statements are true.
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 magnitude of E in an
electromagnetic wave is greater than
the B magnitude of by a factor of c.
E. All of the above statements are true.
An elect romagnetic wave is propagating in the
 iˆdirectionand its elect ricfield is given by

E  E0 sin (kx  t ) ˆj. T hecorresponding magnetic
field wave is (where B0  E0 / c)

A. B  B0 sin(kx  t ) iˆ.

B. B  B0 sin kx  t  kˆ.

C. B  B0 coskx  t  ˆj.

D. B   B0 sin kx  t  kˆ.

E. B   B cos(kx  t ) kˆ.
0
An elect romagnetic wave is propagating in the
 iˆdirectionand its elect ricfield is given by

E  E0 sin (kx  t ) ˆj. T hecorresponding magnetic
field wave is (where B0  E0 / c)

A. B  B0 sin(kx  t ) iˆ.

B. B  B0 sin kx  t  kˆ.

C. B  B0 coskx  t  ˆj.

D. B   B0 sin kx  t  kˆ.

E. B   B cos(kx  t ) kˆ.
0
Chapter 30: Maxwell’s Equations and
Electromagnetic Waves
Section 30-4: Electromagnetic Radiation
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
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
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
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
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
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
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
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
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
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
Light wave A has twice the frequency of light
wave B. The wavelength of light wave A is
_____ that of light wave B.
A. equal to
B. twice
C. four times
D. half
E. one
Light wave A has twice the frequency of light
wave B. The wavelength of light wave A is
_____ that of light wave B.
A. equal to
B. twice
C. four times
D. half
E. one
Arrange the following types of
electromagnetic radiation in order of
increasing wavelength: gamma rays,
infrared light, ultraviolet light, 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
Arrange the following types of
electromagnetic radiation in order of
increasing wavelength: gamma rays,
infrared light, ultraviolet light, 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
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.
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.
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
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
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) 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
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) 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
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.
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.
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.
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.
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
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
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.
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.
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
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
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
A. 32.1 nV
B. 84.3 nV
C. 66.7 nV
D. 178 nV
E. 643 nV
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
A. 32.1 nV
B. 84.3 nV
C. 66.7 nV
D. 178 nV
E. 643 nV
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?
+ axis

1
2
3
4
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.
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?
+ axis

1
2
3
4
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.
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?
+
axis

1
2
3
4
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.
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?
+
axis

1
2
3
4
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.
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 Earth’s orbit? The radius of
the Earth’s orbit is 1.50  1011 m.
A. 550 m2
B. 625 m2
C. 1100 m2
D. 2500 m2
E. None of these is correct.
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 Earth’s orbit? The radius of
the Earth’s orbit is 1.50  1011 m.
A. 550 m2
B. 625 m2
C. 1100 m2
D. 2500 m2
E. None of these is correct.
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.
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.
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.
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.
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.
A. 1.1 J
B. 3.0 × 1023 J
C. 3.5 J
D. 4.6 J
E. 2.2 J
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.
A. 1.1 J
B. 3.0 × 1023 J
C. 3.5 J
D. 4.6 J
E. 2.2 J