Deck 24: Electromagnetic Waves

Question 1

If the radiant energy from the sun comes in as a plane EM wave of intensity 1 340 W/m²,calculate the peak values of E and B.

A)300 V/m,10 ^{- 4} T
B)1 000 V/m,3.35*10 ^{- 6} T
C)225 V/m,1.60*10 ^{- 3} T
D)111 V/m,3.00* 10 ^{- 5} T
E)711 V/m,2.37 *10 ^{- 6} T

Answer 1

1 000 V/m,3.35*10 ^{- 6} T

Question 2

The speed of light is given by the value of

A) $\varepsilon$ ₀ $\mu$ ₀.
B) $\sqrt { \varepsilon _ { 0 } \mu _ { 0 } }$ .
C) $\frac { 1 } { \sqrt { \varepsilon _ { 0 } \mu _ { 0 } } }$ .
D) $\frac { 1 } { \varepsilon _ { 0 } \mu _ { 0 } }$ .
E) $\sqrt { \frac { \varepsilon _ { 0 } } { \mu _ { 0 } } }$ .

Answer 2

$\frac { 1 } { \sqrt { \varepsilon _ { 0 } \mu _ { 0 } } }$ .

Question 3

If the maximum E-component of an electromagnetic wave is 600 V/m,what is the maximum B-component?

A)1.4 T
B)1.8 *10 ^{- 5} T
C)2.0 / 10 ^{* 6} T
D)1.0 *10 ^{- 3} T
E)1.6 *10 ^{- 10} T

Answer 3

2.0 / 10 ^{* 6} T

Question 4

Magnetic fields are produced by

A)constant electric currents.
B)electric currents that vary sinusoidally with time.
C)time-varying electric fields.
D)all of the above.
E)only (a)and (b)above.

Question 5

At every instant the ratio of the magnitude of the electric to the magnetic field in an electromagnetic wave in vacuum is equal to

A)the speed of radio waves.
B)the speed of light.
C)the speed of gamma rays.
D)all of the above.
E)only (a)and (b)above.

Question 6

A plane parallel plate capacitor has plates of 10 cm² area that are 1.0 mm apart.At an instant when charge is being accumulated on the plates at a rate of 12 nC/s,the displacement current between the plates is

A)1.06* 10 ^{- 16} A.
B)1.2 *10 ^{- 8} A.
C)8.85 * 10 ^{- 9} A.
D)1.00 A.
E)1.36 A.

Question 7

A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain.What is the intensity of the signal at a distance of 10 km?

A)8*10 ^{- 5} W/m²
B)8 *10 ^{- 6} W/m²
C)3 *10 ^{- 3} W/m²
D)0.8 W/m²
E)2.5 *10 1^{- 5} W/m²

Question 8

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by
$B = 1.2 \times 10 ^ { - 6 } \sin \left[ 2 \pi \left( \frac { z } { 240 } - \frac { t \times 10 ^ { 7 } } { 8 } \right) \right]$
in SI units.What is the frequency of the wave?

A)500 MHz
B)250 kHz
C)1.25 MHz
D)10 mHz
E)300 MHz

Question 9

The Earth is 1.49* 10¹¹ meters from the sun.If the solar radiation at the top of the Earth's atmosphere is 1 340 W/m²,what is the total power output of the sun?

A)7.10 * 10²⁷ W
B)2.20 * 10³⁰ W
C)6.62 * 10²⁶ W
D)3.74 * 10²⁶ W
E)2.98 * 10²⁵ W

Question 10

At a distance of 10 km from a radio transmitter,the amplitude of the E-field is 0.20 volts/meter.What is the total power emitted by the radio transmitter?

A)10 kW
B)67 kW
C)140 kW
D)245 kW
E)21 kW

Question 11

An open circuit consists of a 12 $\mu$ F parallel plate capacitor charged to 200 V and a 10 $\Omega$ resistor.At the instant when a switch closes the circuit (with no battery in it)the displacement current between the plates of the capacitor is

A)1.2 $\mu$ A.
B)2.4 *10 ^{- 4} A.
C)2.4 mA.
D)10 A.
E)20 A.

Question 12

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by
$B = 1.2 \times 10 ^ { - 6 } \sin \left[ 2 \pi \left( \frac { z } { 240 } - \frac { t \times 10 ^ { 7 } } { 8 } \right) \right]$
in SI units.What is the speed of the EM wave?

A)3* 10⁸ m/s
B)100 m/s
C)10⁶ m/s
D)2 * 10⁷ m/s
E)2 * 10⁸ m/s

Question 13

Since $\varepsilon$ ₀ = 8.85 *10 ^{- 12} C² / N . m²,the units of $\varepsilon$ ₀E² can be reduced to

A) $\frac { \mathrm { J } } { \mathrm { s } \cdot \mathrm { m } ^ { 3 } }$
B) $$\frac { \mathrm { N } } { \mathrm { s } \cdot \mathrm { m } ^ { 3 } }$$ .
C) $$\frac { \mathrm { J } } { \mathrm { m } ^ { 3 } }$$
D) $\frac { \mathrm { N } } { \mathrm { m } ^ { 3 } }$
E) $\frac { w } { m ^ { 3 } }$

Question 14

The correct form of Ampere's law for circuits with gaps in them is

A) $\oint \mathrm { B } \cdot d \mathbf { s } = 0$ .
B) $\oint \mathbf { B } \cdot d \mathbf { s } = I _ { \text {enciosed } }$ .
C) $\oint \mathbf { B } \cdot d \mathbf { s } = \mu _ { 0 } I _ { \text {enclosed } }$ .
D) $\oint \mathbf { B } \cdot d \mathbf { s } = \mu _ { 0 } I _ { \text {enclosed } } + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { E } } { d t }$ .
E) $\oint \mathbf { B } \cdot d \mathbf { s } = \mu _ { 0 } I _ { \text {enclosed } } + \mu _ { 0 } \varepsilon _ { 0 } \frac { d \Phi _ { I } } { d t } - \frac { \varepsilon _ { 0 } } { \left( \mu _ { 0 } \right) ^ { 2 } } \frac { d \Phi _ { B } } { d t }$ .

Question 15

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by
$B = 1.2 \times 10 ^ { - 6 } \sin \left[ 2 \pi \left( \frac { z } { 240 } - \frac { t \times 10 ^ { 7 } } { 8 } \right) \right]$
in SI units.What is the maximum E-field?

A)1000 V/m
B)180 V/m
C)81 V/m
D)360 V/m
E)0.40 V/m

Question 16

The magnetic field amplitude in an electromagnetic wave in vacuum is related to the electric field amplitude by B =

A) $\frac { E } { c }$
B) $$\frac { E } { \sqrt { c } }$$
C)E
D) $E \sqrt { c }$
E)cE

Question 17

What is the average value of the magnitude of the Poynting vector $\vec { S }$ at 1 meter from a 100-watt lightbulb radiating in all directions?

A)1 W/m²
B)4 W/m²
C)2 W/m²
D)8 W/m²
E)12 W/m²

Question 18

In an electromagnetic wave,1)how are the electric and magnetic field directions related and 2)how is the direction of travel determined from their directions? ( $\overrightarrow { \mathbf { c } }$ is the velocity of the light wave. )

A) $\overrightarrow { \mathbf { E } } \| \overrightarrow { \mathbf { B } } ; \frac { \overrightarrow { \mathbf { c } } } { c } = \frac { \overrightarrow { \mathbf { E } } \times \overrightarrow { \mathbf { B } } } { | \overrightarrow { \mathbf { E } } \times \overrightarrow { \mathbf { B } } | }$ .
B) $\overrightarrow { \mathbf { E } } \| \overrightarrow { \mathbf { B } } ; \frac { \overrightarrow { \mathbf { c } } } { c } = \frac { \overrightarrow { \mathbf { B } } \times \overrightarrow { \mathbf { E } } } { | \overrightarrow { \mathbf { B } } \times \overrightarrow { \mathbf { E } } | }$ .
C) $\overrightarrow { \mathbf { E } } \perp \overrightarrow { \mathbf { B } } ; \frac { \overrightarrow { \mathbf { c } } } { c } = \frac { \overrightarrow { \mathbf { E } } \times \overrightarrow { \mathbf { B } } } { | \overrightarrow { \mathbf { E } } \times \overrightarrow { \mathbf { B } } | }$ .
D) $\overrightarrow { \mathbf { E } } \perp \overrightarrow { \mathbf { B } } ; \frac { \overrightarrow { \mathbf { c } } } { c } = \frac { \overrightarrow { \mathbf { B } } \times \overrightarrow { \mathbf { E } } } { | \overrightarrow { \mathbf { B } } \times \overrightarrow { \mathbf { E } } | }$ .
E) $\overrightarrow { \mathbf { E } } = \overrightarrow { \mathbf { B } } / c ; \frac { \overrightarrow { \mathbf { c } } } { c } = \frac { \overrightarrow { \mathbf { B } } \overrightarrow { \times } \mathbf { E } } { | \overrightarrow { \mathbf { B } } \times \overrightarrow { \mathbf { E } } | }$ .

Question 19

How much electromagnetic energy is contained in each cubic meter near the Earth's surface if the intensity of sunlight under clear skies is 1 000 W/m²?

A)3.3 *10 ^{- 6} J
B)3.3 J
C)0.003 J
D)10 ^{- 4} J
E)3.0 * 10⁵ J

Question 20

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by
$B = 1.2 \times 10 ^ { - 6 } \sin \left[ 2 \pi \left( \frac { z } { 240 } - \frac { t \times 10 ^ { 7 } } { 8 } \right) \right]$
in SI units.What is the wavelength of the EM wave?

A)120 m
B)240 m
C)60 m
D)100 m
E)360 m

Question 21

Find the frequency of X-rays of wavelength 1 Å = 10^-10 m.

A)3 * 10¹⁸ Hz
B)3 * 10¹⁰ MHz
C)6 * 10⁹ Hz
D)3 * 10⁸ Hz
E)3 *10²⁰ Hz

Question 22

A spherical particle of density $\rho = 5.00 \frac { \mathrm { g } } { \mathrm { cm } ^ { 2 } }$ and 2.00 mm radius is located at the same distance from the Sun as the Earth. R_SE = 1.5* 10¹¹ m, $G = 6.67 \times 10 ^ { - 11 } \frac { \mathrm { Nm } ^ { 2 } } { \mathrm {~kg} ^ { 2 } } , S = 1365 \frac { \mathrm { W } } { \mathrm { m } ^ { 2 } } , M _ { S } = 1.99 \times 10 ^ { 30 } \mathrm {~kg}$ .
If the particle absorbs 100 percent of the sunlight reaching it,the ratio of the force exerted by the solar radiation to the force of gravity exerted on the particle by the Sun is

A)5.8 *10 ^{- 5}.
B)0.58.
C)1.0.
D)1.7.
E)1.7*10⁴.

Question 23

Polarized light is to have its polarization plane rotated by 90 $\degree$ .In which of the following cases does the final beam have the greatest intensity?

A)3 polarizing filters,each rotate beam by 30 $\degree$ .
B)2 polarizing filters,both rotate beam by 45 $\degree$ .
C)1 polarizing filter,rotating beam by 90 $\degree$ .
D)None of the above,polarized light can't be rotated.

Question 24

What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m²)on a highly polished silver surface?

A)1.4 *10 ^{- 2} Pa
B)0.12 Pa
C)9.0 *10 ^{- 6} Pa
D)4.5 *10 ^{- 5} Pa
E)2.3 * 10 ^{- 6} Pa

Question 25

Near the surface of the planet,the Earth's magnetic field is about 0.50 *10 1^{- 4} T.How much energy is stored in 1.0 m³ of the atmosphere because of this field?

Question 26

The intensity of radiation reaching the earth from the sun is 1 350 W/m².The earth's radius is 6.4 * 10⁶ m.How big a force does this radiation exert on the earth? (Assume it is all absorbed. )

A)5.8 * 10⁸ N
B)1.2 * 10⁹ N
C)2.3 * 10⁹ N
D)4.6 *10⁹ N
E)1.7 *10¹⁷ N

Question 27

When E and B are the amplitudes of the electric and magnetic fields in an electromagnetic wave in vacuum,the total average energy density in the wave is

A) $\frac { 1 } { 4 } \varepsilon _ { 0 } E ^ { 2 }$ .
B) $\frac { 1 } { 2 } \varepsilon _ { 0 } E ^ { 2 }$ .
C) $\varepsilon$ ₀E².
D) $\frac { B ^ { 2 } } { \mu _ { 0 } }$ .
E) $\frac { E B } { \mu _ { 0 } }$ .

Question 28

An FM radio station broadcasts at 98.6 MHz.What is the wavelength of the radiowaves?

A)60.8 m
B)6.08 m
C)3.04 m
D)0.314 m
E)0.33 cm

Question 29

Scattered light in the atmosphere is often partially polarized.The best way to determine whether or not light from a particular direction in the sky shows polarization is to

A)diffract the light through a single slit.
B)squint while looking in that direction.
C)rotate a piece of polaroid film about an axis parallel to the ray while looking through it in that sky direction.
D)rotate a piece of polaroid film about an axis perpendicular to the ray while looking through it in that sky direction.
E)reflect the rays from that direction on a shiny metal surface.

Question 30

Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1)and 2R (sphere 2)from the sun respectively.The ratio of the pressure of solar radiation on sphere 2 to that on sphere 1 is

A)0.25.
B)0.50.
C)1.0.
D)2.0.
E)4.0.

Question 31

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by
$$B = 1.2 \times 10 ^ { - 6 } \sin \left[ 2 \pi \left( \frac { z } { 240 } - \frac { t \times 10 ^ { 7 } } { 8 } \right) \right]$$
in SI units.Find the average power per square meter carried by the EM wave.

A)720 W
B)172 W
C)500 W
D)2 * 10⁷ W
E)86 W

Question 32

Green light has a wavelength of 5.4 *10^-7 m.What is the frequency of this EM-wave in air?

A)5.55 * 10¹⁴ Hz
B)6.00 *10¹¹ Hz
C)9.00* 10⁸ Hz
D)3.00 * 10¹⁰ MHz
E)1.80* 10¹⁵ Hz

Question 33

Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1)and 2R (sphere 2)from the sun respectively.The ratio of the gravitational force exerted by the sun on sphere 1 to the pressure of solar radiation on sphere 1 is T₁;the ratio for sphere 2 is T₂.The ratio of T₂ to T₁ is

A)0.25.
B)0.50.
C)1.0.
D)2.0.
E)4.0.

Question 34

The sun radiates energy at a rate of 3.86 *10²⁶ W.Its radius is 7.0 * 10⁸ m.If the distance from the Earth to the sun is 1.5 * 10¹¹ m,what is the intensity of solar radiation at the top of the Earth's atmosphere?

Question 35

In the atmosphere,the shortest wavelength electromagnetic waves are called

A)microwaves.
B)infrared waves.
C)ultraviolet waves.
D)X-rays.
E)gamma rays.

Question 36

A solar cell has a light-gathering area of 10 cm² and produces 0.2 A at 0.8 V (DC)when illuminated with S = 1 000 W/m² sunlight.What is the efficiency of the solar cell?

A)16%
B)7%
C)23%
D)4%
E)32%

Question 37

You can raise the temperature of an object with

A)microwaves.
B)infrared waves.
C)ultraviolet rays.
D)all of the above.
E)only (a)and (b)above.

Question 38

What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m²)on a flat black surface?

A)2.25 *10 1^{- 5} Pa
B)0.06 Pa
C)7 *10 ^{- 4} Pa
D)4.5 *10 ^{- 6} Pa
E)9.0 *10 ^{- 6} Pa

Question 39

What should be the height of a dipole antenna (of dimensions 1/4 wavelength)if it is to transmit 1 200 kHz radiowaves?

A)11.4 m
B)60 cm
C)1.12 m
D)62.5 m
E)250 m

Question 40

Find the force exerted by reflecting sunlight off a reflecting aluminum sheet in space if the area normal to the sunlight is 10 000 m² and the solar intensity is 1 350 W/m².

A)0.72 N
B)0.09 N
C)9 N
D)45 N
E)0.18 N

Question 41

A possible means of spaceflight is to place a perfectly reflecting aluminized sheet into Earth orbit and use the light from the sun to push this solar sail.If a huge sail of area 6.00 *10⁵ m² and mass 6 000 kg were placed into orbit and turned toward the sun,what would be the force exerted on the sail? (Assume a solar intensity of 1 380 W/m². )