Deck 34: Electromagnetic Waves

Question 1

What should be the height of a dipole antenna (of dimensions 1/4 wavelength) if it is to transmit 1200 kHz radiowaves?

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

Answer 1

62.5 m

Question 2

How much electromagnetic energy is contained in each cubic meter near the Earth's surface if the intensity of sunlight under clear skies is 1000 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

Answer 2

3.3 × 10−⁶ J

Question 3

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

Answer 3

67 kW

Question 4

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 5

Find the force exerted by reflecting sunlight off a reflecting aluminum sheet in space if the area normal to the sunlight is 10000 m² and the solar intensity is 1350 W/m².

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

Question 6

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by 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 7

If the radiant energy from the sun comes in as a plane EM wave of intensity 1340 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

Question 8

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by 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 9

The Earth is 1.49 × 10¹¹ meters from the sun. If the solar radiation at the top of the Earth's atmosphere is 1340 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

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 11

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by 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 12

What is the maximum radiation pressure exerted by sunlight in space (S = 1350 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 13

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by 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 14

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by 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 15

What is the maximum radiation pressure exerted by sunlight in space (S = 1350 W/m²) on a flat black surface?

A) 2.25 × 10−⁵ Pa
B) 0.06 Pa
C) 7 × 10−⁴ Pa
D) 4.5 × 10−⁶ Pa
E) 9.0 × 10−⁶ Pa

Question 16

What is the average value of the magnitude of the Poynting vector 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 17

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 × 10−⁵ W/m²

Question 18

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

Question 19

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 20

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 21

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 22

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 23

The speed of light is given by the value of

A) ε₀μ₀.
B)
.
C)
.
D)
.
E)
.

Question 24

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 25

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 6000 kg were placed into orbit and turned toward the sun, what would be the force exerted on the sail? (Assume a solar intensity of 1380 W/m².)

Question 26

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

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

Question 27

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 28

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 29

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 30

An open circuit consists of a 12 μF parallel plate capacitor charged to 200 V and a 10 Ω 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 μA.
B) 2.4 × 10−⁴ A.
C) 2.4 mA.
D) 10 A.
E) 20 A.

Question 31

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 32

Near the surface of the planet, the Earth's magnetic field is about 0.50 × 10−⁴ T. How much energy is stored in 1.0 m³ of the atmosphere because of this field?

Question 33

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 34

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)
.
B)
.
C) ε₀E².
D)
.
E)
.

Question 35

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 36

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? ( is the velocity of the light wave.)

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

Question 37

High frequency alternating current is passed through a solenoid that contains a solid copper core insulated from the coils of the solenoid. Which statement is correct?

A) A copper core remains cool no matter what the frequency of the current in the solenoid is.
B) The copper core remains cool because the induced emf is parallel to the solenoid axis and fluctuates rapidly.
C) The copper core heats up because an emf parallel to the solenoid axis is induced in the core.
D) The copper core heats up because circular currents around its axis are induced in the core.
E) The copper core heats up because the electric field induced in the copper is parallel to the magnetic field produced by the solenoid.

Question 38

Since ε₀ = 8.85 × 10−¹² C² / N ⋅ m², the units of ε₀E² can be reduced to

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

Question 39

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

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

Question 40

A spherical particle of density and 2.00 mm radius is located at the same distance from the Sun as the Earth. R_SE = 1.5 × 10¹¹ m. . 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.