chapter 30: maxwell ’ s equations and electromagnetic waves section 30-1: maxwell’s displacement...

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, 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

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?

apply. still wouldAll E.

inside

EI ldB

Q dA E

If the existence of magnetic monopoles should ever be confirmed, which of the following equations would have to be altered?

apply. still wouldAll E.

inside

EI ldB

Q dA E

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.

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.

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.

Section 30-3: The Wave Equation for Electromagnetic Waves

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.

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.

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 one- dimensional 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.

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.

E. All of the above statements are 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.

E. All of the above statements are true.

)/ (where is wavefield

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by given is field electric its anddirection ˆ

in the gpropagatin is waveneticelectromagAn

jtkxEE

.ˆ)cos( E.

.ˆsin D.

.ˆcos C.

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.ˆ)sin( A.

ktkxBB

jtkxBB

ktkxBB

itkxBB

)/ (where is wavefield

magnetic ingcorrespond The .ˆ)(sin

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.ˆ)cos( E.

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ktkxBB

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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) ultra-violet, 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) ultra-violet, 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

1 2 3 4

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.

1 2 3 4

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?

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?

dipole. D. 4 – circular wave in the plane of the dipole. E. None of these is correct.

1 2 3 4

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?

dipole. D. 4 – circular wave in the plane of the dipole. E. None of these is correct.

1 2 3 4

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

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

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.

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.

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.

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.

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

chapter 30: maxwell ’ s equations and electromagnetic waves section 30-1: maxwell’s displacement...

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