Deck 33: Electromagnetic Waves

Question 1

The Maxwell-Ampere Law can be written as $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$ . The term in the equation that relates to the magnetic field produced by the so-called displacement current is

A) $\oint \vec { B } \cdot d \vec { s }$
B) $\mu _ { 0 } I$
C) $\mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$
D) No term in this equation is related to the displacement current.

Answer 1

$\mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$

Question 2

The Maxwell-Ampere Law can be written as; $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$ . The term in the equation that relates to the magnetic field produced by an electric current is

A) $\oint \vec { B } \cdot d \vec { s }$
B) $\mu _ { 0 } I$
C) $\mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$
D) No term in this equation is related to the displacement current.

Answer 2

$\mu _ { 0 } I$

Question 3

Maxwell's equations are a compilation of the fundamental laws needed for a complete mathematical description of the behavior of electric and magnetic fields. The equation that mathematically reflects that there are no isolated magnetic poles is

A) $\oint \vec { E } \cdot d \vec { A } = \frac { Q _ { \text {inside } } } { \varepsilon _ { 0 } }$
B) $\oint \vec { B } \cdot d \vec { A } = 0$
C) $\oint \vec { E } \cdot d \vec { s } = - \frac { d \Phi _ { B } } { d t }$
D) $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$

Answer 3

$\oint \vec { B } \cdot d \vec { A } = 0$

Question 4

Maxwell's equations are a compilation of the fundamental laws needed for a complete mathematical description of the behavior of electric and magnetic fields. The equation that mathematically reflects that a changing magnetic flux induces an electric field is

A) $\oint \vec { E } \cdot d \vec { A } = \frac { Q _ { \text {inside } } } { \varepsilon _ { 0 } }$
B) $\oint \vec { B } \cdot d \vec { A } = 0$
C) $\oint \vec { E } \cdot d \vec { s } = - \frac { d \Phi _ { B } } { d t }$
D) $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$

Question 5

A 4.0-A current is charging a 10.0-mF capacitor. The total displacement current between the capacitor plates is

A) 4.0 A.
B) -4.0 A.
C) 0 A.
D) Not enough information is given to solve this problem.

Question 6

A current is used to charge a capacitor. After the capacitor has been charged, the magnetic field between the plates is

A) given by $B = \frac { \mu _ { 0 } I } { 2 \pi r }$
B) given by $B = \frac { \mu _ { 0 } I ^ { 2 } } { 2 \pi r }$
C) given by $B = \frac { \mu _ { 0 } I } { 2 \pi r ^ { 2 } }$
D) zero.

Question 7

Given that the sun's intensity at the Earth's surface is 1350 W/m², the amount of electrical energy in a cubic meter at the Earth's surface is

A) $1.5 \times 10 ^ { - 6 } \mathrm {~J}$
B) $3.0 \times 10 ^ { - 6 } \mathrm {~J}$
C) $4.5 \times 10 ^ { - 6 } \mathrm {~J}$
D) $6.0 \times 10 ^ { - 6 } \mathrm {~J}$

Question 8

A parallel-plate capacitor consists of circular plates with a radius of one unit. During the charging process the magnitude of the magnetic field as a function of radius is

A)
B)
C)
D)

Question 9

A charge undergoes an acceleration. The tangential component of the electric field produced during the acceleration is

A) a maximum in the direction of the acceleration.
B) larger than the radial component.
C) decreasing in a manner that is proportional to 1/r² from the source.
D) All of the above answers are correct.
E) None of the above answers is correct.

Question 10

The functional dependence of the transverse component of the radiation field produced by an accelerating charge as a function of distance from the charge is proportional to

A) r.
B) 1/r.
C) r².
D) 1/r².
E) none of the above.

Question 11

The functional dependence of the radial component of the field produced by an accelerating charge as a function of distance from the charge is proportional to

A) r.
B) 1/r.
C) r².
D) 1/r².
E) none of the above.

Question 12

Given a wave pulse that is traveling in the $\hat { i }$ direction while its electric field is in the $- \hat { k }$ direction, the magnetic field is in the

A) $- \hat { j }$ direction.
B) $\hat {j }$

direction.
C) $- \hat { k } + \hat { i }$ direction.
D) $- \hat { k } - \hat { i }$ direction.

Question 13

A wave pulse is traveling in the $- \hat { j }$ direction while its magnetic field is in the $- \hat { k }$ direction. The electric field is in the

A) $- \hat { i }$ direction.
B) $\hat {j }$ direction.
C) $\hat { k }$ direction.
D) $- \hat { k }$ direction.

Question 14

The Maxwell-Ampere Law can be written as $\oint \vec { B } \cdot d \vec { s } = \mu _ { 0 } I + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$ . The term in the equation that does not contribute to the theoretical description of the propagation of an electromagnetic wave pulse is

A) $\oint \vec { B } \cdot d \vec { s }$
B) $\mu _ { 0 } I$
C) $\mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$
D) No term in this equation is related to the propagation of the electromagnetic wave pulse.

Question 15

The frequency of an electromagnetic wave is $2.0 \times 10 ^ { 14 } \mathrm {~Hz}$ . The wavelength of this wave is

A) 150 nm.
B) 67 mm.
C) 1500 nm.
D) 670 nm.

Question 16

A gamma ray has a wavelength of $5.0 \times 10 ^ { - 14 } \mathrm {~m}$ . The frequency of this wave is

A) $6.0 \times 10 ^ { 21 } \mathrm {~Hz}$
B) $6.0 \times 10 ^ { 20 } \mathrm {~Hz}$
C) $3.0 \times 10 ^ { 21 } \mathrm {~Hz}$
D) $15 \times 10 ^ { 21 } \mathrm {~Hz}$

Question 17

The amplitude of the electric field of an electromagnetic wave is 6.0 $\times$ 10 ^-3 V/m. The amplitude of the magnetic field of this wave is

A) 1.8 $\times$
10⁶ T.
B) 1.8 $\times$
10^-11 T.
C) 1.8 $\times$
10^-10 T.
D) 2.0 $\times$
10^-11 T.

Question 18

Unpolarized light with an intensity of I₀ is traveling in the + x direction. The light is incident on a polarizer whose axis is aligned along the y axis. The light that passes through the polarizer has an intensity that is

A) (1/2)I₀ with a polarization along the z axis.
B) (1/2)I₀ with a polarization along the y axis.
C) I₀ with a polarization along the z axis.
D) I₀ with a polarization along the y axis.

Question 19

Initially polarized light is incident on a polarizer. If the intensity of the light after passing through the polarizer is (3/4) of the initial intensity, the angle between the polarizer axis and the original polarization axis of the light is

A) 41.4°.
B) 30°.
C) 48.6°.
D) 60°.

Question 20

Unpolarized light of intensity I₀ is incident upon the first of two polarizers. The second polarizer has its preferential direction at 50° with respect to the first polarizer. The final transmitted intensity is

A) (0.21) I₀.
B) (0.41) I₀.
C) (0.044) I₀.
D) (0.59) I₀.

Question 21

Unpolarized light of intensity I₀ is incident upon the first of two polarizers. The final transmitted intensity is (3/8)I₀. With respect to the first polarizer, the second polarizer has its preferential direction at

A) 52°.
B) 41°.
C) 38°.
D) 30°.

Question 22

The following electromagnetic radiation has a wavelength that is closest to the size of automobile:

A) Radio waves
B) Infrared radiation
C) Visible radiation
D) Ultraviolet radiation

Question 23

The unit associated with an energy flux is

A) joule.
B) watt/meter.
C) watt/meter².
D) joule/meter².

Question 24

At a given point the electric field is 0.25 V/m. The energy flux at this point is

A) 1.7 $\times$
10^-4 W/m².
B) 2.8 $\times$
10^-4 W/m².
C) 8.2 $\times$
10^-4 W/m².
D) 8.2 $\times$
10^-5 W/m².

Question 25

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The direction the wave is traveling in is

A) $\hat { k }$
B) $\hat { j }$
C) - $\hat { j }$

D) $\hat { i }$

Question 26

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The axis of polarization of the wave is

A) $\hat { k }$
B) $\hat { j }$

C) - $\hat { j }$

D) $\hat { i }$

Question 27

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The frequency of the wave is

A) $9.42 \times 10 ^ { 15 } \mathrm {~Hz}$
B) $9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s }$
C) $1.5 \times 10 ^ { 15 } \mathrm {~Hz}$
D) $9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m }$

Question 28

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The wavelength of the wave is

A) $2.0 \times 10 ^ { - 7 } \mathrm {~m}$
B) $2.0 \times 10 ^ { 7 } \mathrm {~m}$
C) $9.99 \times 10 ^ { 6 } \mathrm {~m}$
D) $3.1 \times 10 ^ { 7 } \mathrm {~m}$

Question 29

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The wave number of the magnetic field associated with this wave is

A) $3.1 \times 10 ^ { 7 } \mathrm {~m} ^ { - 1 }$
B) $3.0 \times 10 ^ { - 3 } \mathrm {~m} ^ { - 1 }$
C) $3.0 \times 10 ^ { 5 } \mathrm {~m}$
D) $3.1 \times 10 ^ { 7 } \mathrm {~m}$

Question 30

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The magnitude of the magnetic field associated with this wave is

A) $1.0 \times 10 ^ { - 3 } \mathrm {~T}$
B) $2.0 \times 10 ^ { - 3 } \mathrm {~T}$
C) $3.0 \times 10 ^ { - 3 } \mathrm {~T}$
D) $6.0 \times 10 ^ { - 3 } \mathrm {~T}$

Question 31

An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The direction of the polarization of the magnetic field associated with this wave is

A) $\hat { j }$

B) $\hat { k }$
C) $\hat { i }$
D) Hold on. The wave is not polarized.

Question 32

The speed of radio waves traveling in a vacuum depends on

A) the wavelength of the waves.
B) the frequency of the waves.
C) the polarization of the waves.
D) none of the above.

Question 33

A pressure of $15 \times 10 ^ { - 6 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ is due to sunlight being reflected from a surface of a "solar sail." The energy flux incident on the surface is

A) 1125 W/m².
B) 2250 W/m².
C) 4500 W/m².
D) 9000 W/m².

Question 34

A pressure of $15 \times 10 ^ { - 6 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ is due to sunlight being absorbed by a surface of a "solar sail." The energy flux incident on the surface is

A) 1125 W/m².
B) 2250 W/m².
C) 4500 W/m².
D) 9000 W/m².

Question 35

A wave has double the amplitude of a second wave. The energy density of the second wave is

A) four times that of the first wave.
B) double that of the first wave.
C) equal to that of the first wave.
D) half that of the first wave.
E) one-quarter that of the first wave.

Question 36

An electromagnetic wave with an electric field amplitude of 0.15 V/m has an intensity of

A) $1.0 \times 10 ^ { - 5 } \mathrm {~W} / \mathrm { m } ^ { 2 }$
B) $3.0 \times 10 ^ { - 6 } \mathrm {~W} / \mathrm { m } ^ { 2 }$
C) $1.0 \times 10 ^ { - 5 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ .
D) $3.0 \times 10 ^ { - 5 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ .

Question 37

A spherical wave spreads out from a source, and the total power at a distance of R₀ is P₀. At a distance of 2R₀ the power is

A) P₀/8.
B) P₀/4.
C) P₀/2.
D) P₀.

Question 38

A spherical wave spreads out from a source, and the energy flux at a distance of R₀ is S₀. At a distance of 2R₀ the energy flux is

A) S₀/8.
B) S₀/4.
C) S₀/2.
D) S₀.

Question 39

An electromagnetic wave consists of

A) only an electric field.
B) only a magnetic field.
C) an electric field and a magnetic field oriented parallel to each other.
D) an electric field and a magnetic field oriented perpendicular to each other.

Question 40

The direction of propagation of an electromagnetic wave is given by

A) $\vec { E } \cdot \vec { B }$
B) $- \vec { E } \cdot \vec { B }$
C) $\vec { E } \times \vec { B }$
D) $\vec { B } \times \vec { E }$

Question 41

Stationary charges produce

A) electromagnetic waves.
B) only magnetic fields.
C) only electric fields.
D) both electric and magnetic fields.

Question 42

Accelerating charges produce

A) electromagnetic standing waves.
B) only magnetic fields.
C) only electric fields.
D) both electric and magnetic fields.

Question 43

$\varepsilon _ { 0 }$ is related to the speed of light and the permeability of free space through the relation

A) $\varepsilon _ { 0 } = c ^ { 2 } \mu _ { 0 }$
B) $\varepsilon _ { 0 } = \frac { c ^ { 2 } } { \mu _ { 0 } }$
C) $\varepsilon _ { 0 } = \frac { 1 } { c ^ { 2 } \mu _ { 0 } }$
D) $\varepsilon _ { 0 } = \frac { \mu _ { 0 } } { c ^ { 2 } }$

Question 44

A satellite 300 km above the surface of the Earth emits a radio wave pulse ( $\lambda$ = 25m). The transit time for the wave to reach the surface of the Earth is

A) 1 $\mu$ s.
B) 10 $\mu$ s.
C) 100 $\mu$ s.
D) 1 ms.

Question 45

Consider a 150-W incandescent lightbulb that radiates light in all directions. At a distance of 1.5 m the time-averaged energy flux emitted by the bulb is

A) 7.9 W/m².
B) 5.3 W/m².
C) 100 W/m².
D) 67 W/m².

Question 46

Consider a 150-W incandescent lightbulb that radiates light in all directions. At a distance of 1.5 m the amplitude of the oscillating electric field E₀ is

A) 77 V/m.
B) 63 V/m.
C) 225 V/m.
D) 39 V/m.

Question 47

Consider a 150-W incandescent lightbulb that radiates light in all directions. At a distance of 1.5 m the amplitude of the oscillating magnetic field B₀ is

A) $2.6 \times 10 ^ { - 7 } \mathrm {~T}$
B) $2.1 \times 10 ^ { - 7 } \mathrm {~T}$
C) $7.5 \times 10 ^ { - 7 } \mathrm {~T}$
D) $1.3 \times 10 ^ { - 7 } \mathrm {~T}$

Question 48

The electric field component of an electromagnetic wave is 130 V/m. The electric energy density of the wave is

A) $7.5 \times 10 ^ { - 8 } \mathrm {~J}$
B) $7.5 \times 10 ^ { - 8 } \mathrm {~J} / \mathrm { m }$
C) $7.5 \times 10 ^ { - 8 } \mathrm {~J} / \mathrm { m } ^ { 2 }$
D) $7.5 \times 10 ^ { - 8 } \mathrm {~J} / \mathrm { m } ^ { 3 }$

Question 49

The magnetic field component of an electromagnetic wave is 25 $\mu \mathrm { T }$ . The electric energy density of the wave is

A) $2.5 \times 10 ^ { - 4 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
B) $2.5 \times 10 ^ { - 4 } \mathrm {~J} / \mathrm { m } ^ { 2 }$
C) $2.5 \times 10 ^ { - 2 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
D) $2.5 \times 10 ^ { - 2 } \mathrm {~J} / \mathrm { m } ^ { 2 }$

Question 50

Radiation from a source is striking a surface at a rate of 50 W/m². The peak value of the electric field is

A) 110 V/m.
B) 150 V/m.
C) 190 V/m.
D) 250 V/m.