Deck 10: Maxwells Equations and Electromagnetic Waves

Question 1

An AC voltage, V = 20 V sin (1000 rad/s t) is applied across a capacitor of capacitance C = 40 $\mu$ 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 $\mu$ T
B) 1.6.2 $\mu$ T
C) 3.2 $\mu$ T
D) 72 $\mu$ T
E) None of these is correct.

Answer 1

3.2 $\mu$ T

Question 2

Maxwell generalized Ampère's law to read from which the displacement current is defined as

A)
B)
C)
D)
E)

Answer 2

Question 3

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 and are equal in magnitude in an electromagnetic wave.
E) None of these statements is true.

Answer 3

None of these statements is true.

Question 4

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

A)

B)

C)

D)
E) all would still apply

Question 5

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 6

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)

Question 7

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

Question 8

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 9

A parallel-plate capacitor has closely spaced circular plates of radius R = 3.00 cm. Charge is flowing onto the positive plate at the rate I = dQ/dt = 3.65 A. The magnetic field at a distance r = 1.50 cm from the axis of the plates is approximately

A) 135 mT
B) 256 $\mu$ T
C) 1.35 $\mu$ T
D) 457 mT
E) 88.3 $\mu$ T

Question 10

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 11

Which of the following statements is true?

A) Both the and the components of an electromagnetic wave satisfy the wave equation.
B) The phase of a wave traveling in the negative z direction is kz + $\omega$ t.
C) The speed of an electromagnetic wave traveling in a vacuum is given by $\varepsilon$ ₀ $\mu$ ₀)^-1/2.
D) The magnitude of is greater than the magnitude of by a factor of c.
E) All of these statements are true.

Question 12

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 13

The electric field of an electro-magnetic wave is given by E_y = 25 sin(2.4 *10⁶ $\pi$ (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 14

Charge is flowing onto one plate of a parallel-plate capacitor and off the other plate at a rate of 2.50 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) 2.82 * 10¹¹ N · m²/(C · s)
D) 12.4 * 10¹¹ N · m²/(C · s)
E) 1.76 * 10¹¹ N · m²/(C · s)

Question 15

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 16

The electric field of an electro-magnetic wave is given by E_y = 25 sin(2.4* 10⁶ $\pi$ (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 17

The electric field in a region of space varies according to
E = (1.25 N/C) sin 1500t
Where t is in seconds. The maximum displacement current through a 2.00-m² area perpendicular to E is approximately

A) 3.32 nA
B) 13.3 nA
C) 66.4 nA
D) 16.6 nA
E) 33.2 nA

Question 18

The electric field in a region of space varies according to
E = (0.25 N/C) sin 3000t
Where t is in seconds. The maximum displacement current through a 1.00-m² area perpendicular to E is approximately

A) 3.32 nA
B) 13.3 nA
C) 26.6 nA
D) 6.64 nA
E) 11.8 nA

Question 19

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

A) y(x, t) = y₀ cos(kx - $\omega$ t)
B) y(x, t) = y₀ sin(kx - $\omega$ t)
C) y(x, t) = y₀ sin(kx - $\omega$ t) + B cos(kx - $\omega$ t)
D) y(x, t) = y₀ (sin kx) · B(cos $\omega$ t)
E) All of these functions satisfy the one-dimensional wave equation.

Question 20

An electromagnetic wave is propagating in the direction and its electric field is given by . The corresponding magnetic field wave is (where B₀ = E₀/c)

A) .
B) .
C) .
D) .
E) .

Question 21

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 22

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 23

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-fourth

Question 24

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 25

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 26

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 27

The left part of the figure shows an 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 28

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 29

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 30

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 F* 10⁶ Hz
E) 1 *10¹¹ Hz

Question 31

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

Question 32

The frequency range for FM broadcasts is from 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 33

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 34

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

Question 35

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 $\mu$ V
B) 84.3 $\mu$ V
C) 66.7 $\mu$ V
D) 178 $\mu$ V
E) 643 $\mu$ V

Question 36

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 37

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

Question 38

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 39

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

Question 40

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 $\in$ ₀ = 8.85 * 10^-12 C²/N · m² and the permeability of free space µ₀ = 4 $\pi$ 0 * 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 41

An astronaut is stranded in space a distance of 50 m from her spaceship. She carries a 5-kW laser gun. If the total mass of the astronaut, space suit, and laser gun is 90 kg, approximately how long will it take her to reach her ship if she points the laser gun directly away from it?

A) 3.2 h
B) 6.5 h
C) 13 h
D) 2.3 * 10⁴ h
E) 3.2 * 10⁴ s

Question 42

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 $\mu$ J/m³
B) 1.59 $\mu$ J/m³
C) 3.18 $\mu$ J/m³
D) 6.78 $\mu$ J/m³
E) 5.21 $\mu$ J/m³

Question 43

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

Question 44

The Sun radiates about 3.83 *10²⁶ W of power. What is the force resulting from the solar radiation on Earth? The radius of Earth's orbit is 1.50 *10¹¹ m and the radius of Earth is 6.37 *10⁶ m. Assume that all the radiation is absorbed by Earth.

A) 1.8 *10⁸ N
B) 2.9 * 10⁸ N
C) 5.8 * 10⁸ N
D) 8.8 * 10⁹ N
E) None of these is correct.

Question 45

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 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.

Question 46

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 47

An electromagnetic wave of intensity 100 W/m² is incident normally on a square black card whose sides are 25 cm. If the card absorbs all of the radiation incident on it, the approximate force exerted by the wave on this card is

A) 64 nN
B) 16 nN
C) 42 nN
D) 10 nN
E) None of these is correct.

Question 48

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

A) 50 nPa
B) 2.0 nPa
C) 8.0 nPa
D) 16 nPa
E) 4.0 nPa

Question 49

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

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

Question 50

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

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

Question 51

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 52

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

A) 71 nT
B) 0.35 $\mu$ T
C) 0.14 $\mu$ T
D) 0.20 $\mu$ T
E) 0.10 $\mu$ T

Question 53

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 54

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 55

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 56

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 57

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

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 58

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 59

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 60

An electromagnetic wave of intensity 100 W/m² is incident normally on a square white card whose sides are 25 cm. If the card reflects all of the radiation incident on it, the approximate force exerted by the wave on this card is

A) 64 nN
B) 16 nN
C) 42 nN
D) 10 nN
E) None of these is correct.

Question 61

The intensity of solar radiation on Earth is about 1.4 *10³ W/m². How many 50-W light bulbs 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