Deck 31: Maxwells Equations and Electromagnetic Waves

Question 1

In the radiation field from an antenna, the electric and magnetic fields are

A)perpendicular to one another.
B)anti-parallel to one another.
C)anti-perpendicular to one another.
D)parallel to one another.
E)never in any geometric arrangement with respect to one another.

Answer 1

perpendicular to one another.

Question 2

Electromagnetic waves do not require a medium to be transmitted.

Answer 2

True

Question 3

Electromagnetic waves are longitudinal.

Answer 3

False

Question 4

A changing electric field will produce a

A)current.
B)gravitational field.
C)magnetic field.
D)radiation field.
E)none of the given answers

Question 5

Write Maxwell's Equations in the integral form for free space.

Question 6

In using Ampere's law, the integral must be evaluated

A)around a path that lies in a plane.
B)in a clockwise direction.
C)around a closed path.
D)around a circular path.
E)in a counter-clockwise direction.

Question 7

It can be concluded from Gauss's law for magnetism that

A)south magnetic poles do not exist.
B)isolated magnetic poles sometimes exist.
C)north magnetic poles do not exist.
D)magnetic poles are pairs of electric charges.
E)isolated magnetic poles do not exist.

Question 8

An electric field is produced by a

A)constant magnetic field.
B)changing magnetic field.
C)either a constant or a changing magnetic field.
D)none of the given answers

Question 9

Electromagnetic waves are

A)transverse.
B)circular waves.
C)alternating between longitudinal and transverse.
D)surface waves.
E)longitudinal.

Question 10

The ratio of the electric field to the magnetic field in the electromagnetic wave is the speed of the light.

Question 11

The electric energy density in an electromagnetic wave is higher than its magnetic energy density.

Question 12

Far from their source, electromagnetic waves are

A)elliptical waves.
B)longitudinal waves.
C)plane waves.
D)spherical waves.
E)circular waves.

Question 13

Gauss's law for magnetism tells us that the

A)net magnetic flux through a surface is zero.
B)net magnetic flux is zero.
C)net magnetic flux through a closed surface is zero.
D)magnetic flux is zero.
E)magnetic flux out of a surface is zero.

Question 14

An electromagnetic wave is a result of electric and magnetic fields acting together.

Question 15

In an electromagnetic wave the and fields are oriented such that

A)they are parallel to one another and perpendicular to the direction of wave propagation.
B)they are parallel to one another and parallel to the direction of wave propagation.
C)they are perpendicular to one another and perpendicular to the direction of wave propagation.
D)they are perpendicular to one another and parallel to the direction of wave propagation.
E)None of the above answers is correct.

Question 16

Electromagnetic waves are transverse in nature.

Question 17

Electromagnetic waves in a vacuum travel with the speed of light.

Question 18

Accelerating electric charges give rise to electromagnetic waves.

Question 19

Just as a changing magnetic field produces an electric field, a changing electric field produces a magnetic field.

Question 20

Electromagnetic waves are a result of a stationary electric field and a changing magnetic field.

Question 21

The speed of light in a vacuum is

A)299,792,458 m/s.
B)the basis for the meter.
C)a defined value instead of a measured value.
D)none of the above
E)all of the above

Question 22

Which one of the following is not an electromagnetic wave?

A)UV
B)infrared
C)radio waves
D)sound waves
E)gamma rays

Question 23

An electromagnetic wave is propagating towards the west. At a certain moment the direction of the magnetic field vector associated with this wave points vertically up. What is the direction of the electric field vector?

A)Horizontal and pointing south
B)Vertical and pointing down
C)Horizontal and pointing north
D)Vertical and pointing up
E)Horizontal and pointing east

Question 24

The right hand rule for the direction of propagation of the electromagnetic waves is to

A)point the forefinger of your right hand toward E vector, middle finger toward the B vector, and the thumb will represent the propagation.
B)point the middle finger of your right hand toward the E vector, the forefinger toward the B vector, and the thumb will represent the direction of propagation.
C)point the fingers of your right hand toward the E vector, curl your fingers towards the B vector, and the thumb will point the direction of propagation.
D)point the fingers of your left hand toward the E vector, curl your fingers towards the B vector, and the thumb will point the direction of propagation.
E)None of the other answers is correct.

Question 25

A particle of interplanetary dust is close to the Sun and interacts with the Sun's gravitational field as well as with the light emitted by the Sun. If it only interacts appreciably with the Sun, can it be pushed away from the Sun instead of being pulled towards it?

A)No, the gravitational force will always dominate if the object is large enough.
B)No, the gravitational force will always dominate if the object is close enough.
C)Yes, if the object is small enough, radiation pressure will win over.
D)Yes, but the object must be very large so that it can gain enough radiation pressure.
E)None of the previous answers is correct.

Question 26

A parallel-plate capacitor, made of two circular plates of radius R = 10 cm, is connected in series with a resistor of resistance R = 100 Ω and a battery of emf E = 10 V. What is the maximum value of the magnetic field induced by the displacement current between the plates, at a distance r = 5 cm from the axis of the plates while the capacitor is being charged?

A)3 × 10^-7 T
B)5 × 10^-7 T
C)2 × 10^-7 T
D)1 × 10^-7 T
E)4 × 10^-7 T

Question 27

If the magnetic field in an EM wave is in the x-direction and the electric field in the wave is in the y-direction, the wave is traveling in the

A)x-y plane.
B)direction halfway between the x- and y-directions.
C)z-direction.
D)x-direction.
E)negative z-direction.

Question 28

FIGURE 31-1
An electromagnetic wave propagates along the +y direction as shown in Fig. 31-1. If the E-field at the origin is along the +z direction, what is the direction of the B-field?

A)+z
B)-z
C)+y
D)+x
E)-x

Question 29

Which one of the following is the correct order of the electromagnetic spectrum from low to high frequencies?

A)radio waves, infrared, microwaves, UV, visible, X-rays, gamma rays
B)radio waves, UV, X-rays, microwaves, infrared, visible, gamma rays
C)radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays
D)radio waves, microwaves, visible, X-rays, infrared, UV, gamma rays
E)radio waves, infrared, X-rays, microwaves, UV, visible, gamma rays

Question 30

The force per unit area exerted by an electromagnetic wave is called the

A)energy density.
B)power.
C)intensity.
D)radiation pressure.
E)radiation field.

Question 31

Which one of the following is the correct representation of the electromagnetic waves from longer wavelength to shorter wavelength?

A)radio waves, infrared, microwaves, UV, visible, X-rays, gamma rays
B)radio waves, UV, X-rays, microwaves, infrared, visible, gamma rays
C)radio waves, microwaves, visible, X-rays, infrared, UV, gamma rays
D)radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays
E)radio waves, infrared, X-rays, microwaves, UV, visible, gamma rays

Question 32

Using Maxwell's equations it can be shown that electromagnetic waves have a speed in free space of

A)(ε_Oμ_O)^-3/2.
B)(ε_Oμ_O)^-1/2.
C)ε_Oμ_O.
D)(ε_Oμ_O)^-2.
E)(ε_Oμ_O)^-1.

Question 33

FIGURE 31-2
For an xyz coordinate system shown in Fig. 31-2, if the E-vector is in the +z direction, and the B-vector is in the +x direction, what is the direction of propagation of the electromagnetic waves?

A)+x
B)-x
C)+y
D)-y
E)+z

Question 34

The first successful determination of the finite speed of light is credited to

A)Galileo.
B)Roemer.
C)Einstein.
D)Newton.
E)Franklin.

Question 35

Two objects are in all respects identical except for the fact that one was coated with a substance that is an excellent reflector of light while the other was coated with a substance that is a perfect absorber of light. You place both objects at the same distance from a powerful light source so they both receive the same amount of energy U from the light. The linear momentum these objects will receive is such that:

A)The reflecting objects receives a larger amount of momentum.
B)Both objects receive the same amount of momentum.
C)The reflecting object receives a smaller amount of momentum.
D)None of the previous answers is correct.

Question 36

A parallel-plate capacitor , made of two circular plates of radius R = 10 cm, is being charged. What is the magnitude of the induced magnetic field induced by the displacement current between the plates of the capacitor at a distance r = 2 cm from the axis of the plates at a time when the electric field varies at the rate dE/dt = 2 × 10¹² V/m s?

A)0.7 × 10^-7 T
B)2.2 × 10^-7 T
C)8.1 × 10^-7 T
D)3.5 × 10^-7 T
E)1.3 × 10^-7 T

Question 37

The energy per unit volume in an EM wave is

A)equally divided between the electric and magnetic fields.
B)almost entirely in the electric field.
C)indeterminate.
D)almost entirely in the magnetic field.
E)zero.

Question 38

Of the components of the electromagnetic spectrum listed below, which is associated with the shortest wavelengths?

A)microwaves
B)infrared light
C)gamma rays
D)x-rays
E)ultraviolet light

Question 39

An AM radio station indicates its location on the dial as "1030" what?

A)Hz
B)Hz/s
C)kHz
D)GHz
E)MHz

Question 40

If an electromagnetic wave has its magnetic field oscillating in the vertical direction, the direction of oscillation of the electric field is

A)east-west.
B)horizontal.
C)vertical.
D)north-south.
E)circular.

Question 41

An electromagnetic wave with components E_y = E_o sin(kx - ωt) and B_z = B_o sin(kx - ωt) is a wave traveling in the

A)negative x-direction.
B)x-direction.
C)y-direction.
D)z-direction.
E)cannot be determined with the information given

Question 42

The wavelength of a certain portion of microwaves is 40 mm. What is its frequency?

A)40 GHz
B)4.0 GHz
C)0.75 GHz
D)75 GHz
E)7.5 GHz

Question 43

If the visible wavelengths of light range from 400 nm to 750 nm, what is the highest frequency associated with visible light?

A)3.0 × 10⁸ Hz
B)7.5 × 10¹⁴ Hz
C)2.3 × 10²⁰ Hz
D)4.0 × 10¹⁴ Hz
E)5.0 × 10⁸ Hz

Question 44

The wavelength of an electromagnetic wave is 600 nm. What is its frequency?

A)200 × 10¹² Hz
B)300 × 10¹² Hz
C)400 × 10¹² Hz
D)500 × 10¹² Hz
E)600 × 10¹² Hz

Question 45

A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the lowest frequency associated with this portion of the spectrum?

A)1.50 × 10¹⁴ Hz
B)7.50 × 10¹³ Hz
C)7.50 × 10¹⁴ Hz
D)7.50 × 10¹⁵ Hz
E)1.50 × 10¹⁵ Hz

Question 46

The electric field of a plane progressive electromagnetic wave in a vacuum is given by E_x = E_osin(kz - ωt). What is the corresponding magnetic field?

A)B_y = sin(kz - ωt)
B)B_y = cos(kz - ωt)
C)B_y = - sin(kz - ωt)
D)B_x = c E_o cos(kz - ωt)
E)B_y = - cos(kz - ωt)

Question 47

If the electric field and magnetic field of an EM wave are given by E = E_o sin(kx - ωt) and B = B_o sin(kx - ωt), and if the value of E_o is 5.1 x 10^-5 V/m, what is the value of B_o?

A)1.7 × 10¹⁴ T
B)1.7 × 10³ T
C)1.7 × 10^-14 T
D)1.7 × 10⁴ T
E)1.7 × 10^-13 T

Question 48

The magnetic field of a plane progressive electromagnetic wave in a vacuum is given by B_z = B_ocos(ky - ωt). What is the corresponding expression for the electric field?

A)E_x = cB_osin(ky - ωt)
B)E_x = - cB_ocos(ky - ωt)
C)E_z = cB_osin(ky - ωt)
D)E_x = cB_ocos(ky - ωt)
E)E_x = - cB_osin(ky - ωt)

Question 49

A cordless phone operates at 900 MHz. What is the associated wavelength?

A)900 m
B)0.25 m
C)300 m
D)3.3 m
E)0.33 m

Question 50

The value of the electric field for a certain type of electromagnetic wave is 570 N/C. What is the value of the magnetic field for that wave?

A)2.91 × 10^-6 T
B)1.90 × 10^-6 T
C)1.10 × 10^-6 T
D)1.41 × 10^-6 T
E)2.41 × 10^-6 T

Question 51

The value of the magnetic field for a certain type of electromagnetic wave is 2.12 μT. What is the value of the electric field for that wave?

A)636 V/m
B)636 N/C
C)636 J/Cm
D)All of the answers given are correct.
E)None of the answers given are correct.

Question 52

A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the highest frequency associated with this portion of the spectrum?

A)1.50 × 10¹⁴ Hz
B)7.50 × 10¹³ Hz
C)7.50 × 10¹⁴ Hz
D)7.50 × 10¹⁵ Hz
E)1.50 × 10¹⁵ Hz

Question 53

The frequency of a microwave signal is 9.76 GHz. What is its wavelength in meters?

A)3.07 × 10^-2 m
B)2.07 × 10^-2 m
C)1.07 × 10^-2 m
D)5.07 × 10^-2 m
E)4.07 × 10^-2 m

Question 54

An electromagnetic wave with components E_y = E_o sin(kx - ωt) and B_z = B_o sin(kx - ωt) is a wave with a frequency of

A)k.
B)ω/2π.
C)k/ω.
D)ω.
E)ω/π.

Question 55

A plane electromagnetic wave propagates in a vacuum in the z-direction. The wave has a wavelength of 10 m and the electric field is along the +x direction and has an amplitude of is 0.20 V/m, with one maximum at x = 0 and t = 0. What is the mathematical expression for the magnetic field?

A)B_y = 0.067 × 10^-8sin[(0.63 m^-1)z - (2.1 × 10^-9 s^-1)t] T
B)B_y = 0.067 × 10^-8sin[(0.63 m^-1)z + (2.1 × 10^-9 s^-1)t] T
C)B_y = 0.067 × 10^-8cos[(0.63 m^-1)z + (1.9 × 10⁸ s^-1)t] T
D)B_y = 0.067 × 10^-8cos[(10 m^-1)z - (2.1 × 10^-9 s^-1)t] T
E)B_y = 0.067 × 10^-8cos[(0.63 m^-1)z - (1.9 × 10^-8 s^-1)t] T

Question 56

The distance between the two planets is 1.6 × 10⁶ m. How much time would the light signal take to go from one planet to the other?

A)1.9 × 10^-2 s
B)0.45 × 10^-2 s
C)0.53 × 10^-2 s
D)1.3 × 10^-2 s
E)None of the other answers is correct.

Question 57

An FM radio station broadcasts at 96.7 MHz. What is the wavelength associated with this broadcast?

A)3.1 m
B)0.32 m
C)2.9 × 10¹⁴ m
D)2.9 × 10¹⁶ m
E)not enough information given

Question 58

The electric field of a plane electromagnetic pulse in a vacuum is given by E_x = E_o . What is the corresponding expression for the magnetic field?

A)B_y =

B)B_y =

C)B_y =

D)B_y =

E)B_y =

Question 59

An electromagnetic wave with components E_y = E_o sin(kx - ωt) and B_z = B_o sin(kx - ωt) is a wave traveling with a speed of

A)ω.
B)ω/k.
C)k.
D)k/ω.
E)ω/k².

Question 60

The electric field of a plane standing electromagnetic wave in a vacuum is given by E_y = E_osin(kx)cos(ωt). What is the corresponding expression for the magnetic field?

A)B_z = cos(kx)cos(ωt)
B)B_z = - sin(kx)cos(ωt)
C)B_z = sin(kx)cos(ωt)
D)B_z = - cos(kx)sin(ωt)
E)B_z = cos(kx)sin(ωt)

Question 61

The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T. What is the intensity of the wave?

A)1.0 × 10^-13 W/m²
B)1.5 × 10^-5 W/m²
C)3.0 × 10^-5 W/m²
D)2.0 × 10^-13 W/m²
E)7.5 × 10⁵ W/m²

Question 62

Near the earth the intensity of radiation from the Sun is 1350 W/m². What volume of space in this region contains 1.0 J of energy?

A)4.5 × 10^-6 m³
B)3.3 × 10² m³
C)7.4 × 10^-4 m³
D)1.4 × 10³ m³
E)2.2 × 10⁵ m³

Question 63

What is the distance traveled by a beam of light in a time of 2.0 ms?

A)6.0 × 10⁵ m
B)0.66 × 10⁵ m
C)90 m
D)70 m
E)60 m

Question 64

If a beam of radiation has an intensity of 120 W/m², what is the maximum value of E?

A)1.5 × 10³ V/m
B)0.000001 T
C)1.0 × 10^-6 V/m
D)3.0 × 10² V/m
E)3.2 × 10^-3 V/m

Question 65

An electromagnetic wave has a magnetic field of rms value 3.0 × 10^-6 T. What is the intensity of the wave?

A)0.1 × 10³ W/m²
B)3.0 × 10³ W/m²
C)1.1 × 10³ W/m²
D)2.1 × 10³ W/m²
E)1.5 × 10³ W/m²

Question 66

The average magnetic energy density of an electromagnetic wave is 8.95 × 10^-5 J/m³. What is the magnetic field component of this wave?

A)12.0 μT
B)13.0 μT
C)14.0 μT
D)15.0 μT
E)16.0 μT

Question 67

The average intensity of the sunlight in Miami, Florida, is 1040 W/m². What is the average value of the radiation pressure due to this sunlight in Miami?

A)2.28 × 10^-6 N/m²
B)1.63 × 10^-6 N/m²
C)7.83 × 10^-6 N
D)3.46 × 10^-6 N/m²
E)9.78 × 10^-6 N/m²

Question 68

How far does a beam of light travel in one full year?

A)80 × 10¹² m
B)95 × 10¹⁴ m
C)30 × 10⁸ m
D)20 × 10¹⁵ m
E)36 × 10¹⁶ m

Question 69

A laser with a power of 1.0 mW has a beam radius of 1.0 mm. What is the peak value of the electric field in that beam?

A)490 V/m
B)840 V/m
C)65 V/m
D)120 V/m
E)22 V/m

Question 70

The momentum of 1 J of energy in an electromagnetic wave is

A)1.5 × 10^-9 kg∙m/s.
B)3 × 10^-9 kg∙m/s.
C)1 kg m/s.
D)1 × 10-17 kg∙m/s.
E)1000 kg m/s.

Question 71

A beam of light travels a distance of 2900 m. How much time does it take?

A)9.7 s
B)9.7 ms
C)9.7 μs
D)9.7 ns
E)9.7 ps

Question 72

The intensity of an electromagnetic wave is 8 × 10⁷ W/m². What is the amplitude of the magnetic field of this wave?

A)8.2 × 10^-4 T
B)3.3 × 10^-7 T
C)10 T
D)14 T
E)5.8 × 10^-4 T

Question 73

The intensity of solar radiation near the earth is 1.4 × 10³ W/m². What force is exerted by solar radiation impinging normally on a 5.0 m² perfectly reflecting panel of an artificial satellite orbiting the earth?

A)1.4 × 10⁴ N
B)9.4 × 10^-5 N
C)1.4 × 10^-4 N
D)2.3 × 10^-5 N
E)4.7 × 10^-5 N

Question 74

The magnetic field component of the electromagnetic wave is 15.0 μT. What is the magnetic energy density of the wave?

A)2.26 × 10^-4 J/m³
B)8.95 × 10^-5 J/m²
C)1.79 × 10^-4 J/m³
D)4.47 × 10^-4 J/m²
E)9.72 × 10^-5 J/m³

Question 75

The total electromagnetic power emitted by the Sun is 3.8 ×10²⁶ W. What is the radiation pressure near the orbit of Mercury, which has an orbital radius of 5.8 × 10¹⁰ m?

A)3 × 10^-5 N/m²
B)3 × 10^-7 N/m²
C)3 × 10^-8 N/m²
D)3 × 10^-4 N/m²
E)3 × 10^-6 N/m²

Question 76

The wavelength of a certain portion of an electromagnetic wave is 314 nm. What is its frequency and classification?

A)9.55 × 10¹⁴ Hz, ultraviolet
B)9.55 × 10¹⁴ Hz, X-ray
C)8.44 × 10¹⁵ Hz, X-ray
D)8.44 × 10¹⁵ Hz, ultraviolet
E)9.55 × 10¹⁵ Hz, ultraviolet