Deck 31: Electromagnetic Fields and Waves

Question 1

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.724 W/m². What is the maximum value of the magnetic field in the wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 77.9 nT
B) 55.1 nT
C) 38.9 nT
D) 108 nT
E) 156 nT

Answer 1

77.9 nT

Question 2

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) . What is the Poynting vector at the point P at that instant? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 18 µW/m²
B) -18 µW/m²
C) 9.0 µW/m²
D) -9.0 µW/m²
E) -18 µW/m²

Answer 2

18 µW/m²

Question 3

The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 μT. What is the magnitude of the electric field for that wave at P? (c = 3.0 × 10⁸ m/s)

A) 636 N/C
B) 745 N/C
C) 5.23 µN/C
D) 6.36 µN/C
E) 7.45 µN/C

Answer 3

636 N/C

Question 4

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C. What is the magnitude of the magnetic field for that wave at P? (c = 3.0 × 10⁸ m/s)

A) 2.91 µT
B) 1.90 µT
C) 1.10 µT
D) 1.41 µT
E) 2.41 µT

Question 5

A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) . What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 × 10⁸ m/s)

A) 0.27 nT
B) -0.27 nT
C) 0.27 nT
D) 6.8 nT
E) -6.8 nT

Question 6

In an electromagnetic wave, the electric and magnetic fields are oriented such that they are

A) parallel to one another and perpendicular to the direction of wave propagation.
B) parallel to one another and parallel to the direction of wave propagation.
C) perpendicular to one another and perpendicular to the direction of wave propagation.
D) perpendicular to one another and parallel to the direction of wave propagation.

Question 7

An electromagnetic wave propagates along the +y direction as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

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

Question 8

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. The direction of the electric field vector of this wave is

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 9

A capacitor is hooked up to a resistor and an AC voltage source as shown in the figure. The output of the source is given by V(t) = V₀ sin ωt. The plates of the capacitor are disks of radius R. Point P is directly between the two plates, equidistant from them and a distance R/2 from the center axis. At point P

A) there is no magnetic field because there is no charge moving between the plates.
B) there is a constant magnetic field.
C) there is a time-varying magnetic field.

Question 10

The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m². The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 170 J
B) 210 J
C) 250 J
D) 300 J
E) 340 J

Question 11

The energy per unit volume in an electromagnetic wave is

A) equally divided between the electric and magnetic fields.
B) mostly in the electric field.
C) mostly in the magnetic field.
D) all in the electric field.
E) all in the magnetic field.

Question 12

If the z-component of the magnetic field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation B_z(x, t) = (1.25 μT) cos[(3800 m^-1)x - (1.14 × 10-¹² rad/s)t], what is the largest that the y component of the electric field can be? (c = 3.0 × 10⁸ m/s)

A) 375 N/C
B) 4.17 × 10^-15 N/C
C) 3.75 × 10⁸ N/C
D) 4.17 × 10^-9 N/C
E) 1.25 × 10⁶ N/C

Question 13

If the electric field and magnetic field of an electromagnetic wave are given by E = E₀ sin(kx - ωt) and B = B₀ sin(kx - ωt), and if the value of E₀ is 51 µV/m, what is the value of B₀? (c = 3.0 × 10⁸ m/s)

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 14

Given that the wavelengths of visible light range from 400 nm to 700 nm, what is the highest frequency of visible light? (c = 3.0 × 10⁸ m/s)

A) 3.1 × 10⁸ Hz
B) 7.5 × 10¹⁴ Hz
C) 2.3 × 10²⁰ Hz
D) 4.3 × 10¹⁴ Hz
E) 5.0 × 10⁸ Hz

Question 15

When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface?

A) 4F
B) 2F
C) F
D) F/2
E) F/4

Question 16

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

A) xy-plane.
B) +z-direction.
C) -z-direction.
D) -x-direction.
E) -y-direction.

Question 17

The y-component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s)t].
(c = 3.0 × 10⁸ m/s)
(a) What is the largest that the x-component of the wave can be?
(b) What is the largest that the z-component of the wave can be?

Question 18

The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation E_y = (375 N/C) cos[kx - (2.20 × 10¹⁴ rad/s)t]. What is the wavelength of this electromagnetic wave? (c = 3.0 × 10⁸ m/s)

A) 0.272 µm
B) 1.36 µm
C) 2.72 µm
D) 8.57 µm
E) 17.1 µm

Question 19

The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T. What is the intensity of the wave? (c = 3.0 × 10⁸ m/s, c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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 20

If an electromagnetic wave has components E_y = E₀ sin(kx - ωt) and B_z = B₀ sin(kx - ωt), in what direction is it traveling?

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

Question 21

A radiometer has two square vanes (each measuring 1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the electromagnetic power absorbed by the blackened vane? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 0.030 W
B) 0.040 W
C) 0.050 W
D) 0.060 W
E) 0.090 W

Question 22

A 7.5 × 10¹⁴ Hz laser emits a 7.7-μs pulse, 5.0 mm in diameter, with a beam energy density of 0.51 J/m³. What is the amplitude of the electric field of the emitted waves? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 340 kV/m
B) 480 kV/m
C) 240 kV/m
D) 150 kV/m
E) 120 kV/m

Question 23

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What is the amplitude of the electric field? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 1600 V/m
B) 1900 V/m
C) 2200 V/m
D) 2500 V/m
E) 2800 V/m

Question 24

An 800-kHz radio signal is detected at a point 8.5 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.90 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the average electromagnetic energy density at that point? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 3.6 pJ/m³
B) 5.1 pJ/m³
C) 7.2 pJ/m³
D) 10 pJ/m³
E) 14 pJ/m³

Question 25

An 800-kHz radio signal is detected at a point 2.7 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.36 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the intensity of the radio signal at that point? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 170 µW/m²
B) 240 µW/m²
C) 340 µW/m²
D) 120 µW/m²
E) 86 µW/m²

Question 26

An 800-kHz radio signal is detected at a point 4.5 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.63 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the magnetic field amplitude of the signal at that point? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 2.1 nT
B) 1.7 nT
C) 1.3 nT
D) 2.5 nT
E) 2.9 nT

Question 27

The total electromagnetic power emitted by the sun is 3.8 × 10²⁶ W. What is the radiation pressure on a totally absorbing satellite at the orbit of Mercury, which has an orbital radius of 5.8 × 10¹⁰ m? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 30 µPa
B) 0.30 µPa
C) 0.030 µPa
D) 300 µPa
E) 3.0 µPa

Question 28

An electromagnetic wave has a peak electric field of 3.0 kV/m. What is the intensity of the wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 24 kW/m²
B) 12 kW/m²
C) 8.0 kW/m²
D) 4.0 kW/m²

Question 29

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What is the intensity of the microwave beam? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 5.2 kW/m²
B) 5.7 kW/m²
C) 6.2 kW/m²
D) 6.7 kW/m²
E) 7.2 kW/m²

Question 30

If a beam of electromagnetic radiation has an intensity of 120 W/m², what is the maximum value of the electric field? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 1.5 kV/m
B) 1.0 µT
C) 1.0 µV/m
D) 0.30 kV/m
E) 0.0032 V/m

Question 31

If the intensity of an electromagnetic wave is 80 MW/m², what is the amplitude of the magnetic field of this wave? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 0.82 mT
B) 0.33 µT
C) 10 T
D) 14 T
E) 0.58 mT

Question 32

The intensity of solar radiation near the earth is 1.4 kW/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? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 14 kN
B) 94 µN
C) 140 µN
D) 23 µN
E) 47 µN

Question 33

Near the earth the intensity of radiation from the sun is 1.35 kW/m². What volume of space in this region contains 1.0 J of electromagnetic energy? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 4.5 × 10^-6 m³
B) 3300 m³
C) 7.4 × 10^-4 m³
D) 1400 m³
E) 220,000 m³

Question 34

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? (c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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

Question 35

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What is the power output of the oven? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 0.50 kW
B) 0.55 kW
C) 0.60 kW
D) 0.65 kW
E) 0.70 kW

Question 36

A very small source of light that radiates uniformly in all directions produces an electric field amplitude of 2.96 V/m at a point 33.0 m from the source. What is the power output from the source? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Question 37

A sinusoidal electromagnetic wave in vacuum delivers energy at an average rate of
5.00 µW/m². What are the amplitudes of the electric and magnetic fields of this wave?
(c = 3.0 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Question 38

An 800-kHz radio signal is detected at a point 9.1 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.440 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the average total power radiated by the transmitter? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 0.27 MW
B) 0.32 MW
C) 0.38 MW
D) 0.45 MW
E) 0.50 MW

Question 39

The average intensity of the sunlight in Miami, Florida, is 1.04 kW/m². For surfaces on which the light is all absorbed, what is the average value of the radiation pressure due to this sunlight in Miami? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 2.28 µPa
B) 1.73 µPa
C) 6.93 µPa
D) 3.47 µPa
E) 9.78 µPa

Question 40

28) A sinusoidal electromagnetic wave is propagating in vacuum. At a given point P and at a particular time, the electric field is in the +x direction and the magnetic field is in the -y direction.
(a) What is the direction of propagation of the wave?
(b) If the intensity of the wave at point P is what is the electric field amplitude at that point? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Question 41

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 µJ. What magnitude force does the microwave beam exert on the base of the oven? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 1.6 µN
B) 2.0 µN
C) 2.5 µN
D) 3.0 µN
E) 3.5 µN

Question 42

Unpolarized light passes through three polarizing filters. The first one is oriented with a horizontal transmission axis, the second filter has its transmission axis 25.7° from the horizontal, and the third one has a vertical transmission axis. What percent of the light gets through this combination of filters?

A) 7.6%
B) 92.4%
C) 50.0%
D) 0.00%

Question 43

Polarized light passes through a polarizer. If the electric vector of the polarized light is horizontal what, in terms of the initial intensity I₀, is the intensity of the light that passes through a polarizer if the polarizer is tilted 22.5° from the horizontal?

A) 0.854I₀
B) 0.147I₀
C) 0.191I₀
D) 0.011I₀

Question 44

The following are positioned in sequence: A source of a beam of natural light of intensity I₀; three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity is zero at the observer. Which of the following pairs of angles are possible axis angle settings of polarizer B?

A) 40° and 90°
B) 40° and 130°
C) 40° and 140°
D) 90° and 130°
E) 90° and 140°

Question 45

In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of 1000 W/m². What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°, θ₂ = 30° and θ₃ =60°?

A) 141 W/m²
B) 316 W/m²
C) 433 W/m²
D) 563 W/m²
E) 188 W/m²

Question 46

A totally absorbing surface having an area of 7.7 cm² faces a small source of sinusoidal electromagnetic radiation that is 2.4 m away. At the surface, the electric field amplitude of the radiation is 84 V/m. (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)
(a) What is the radiation pressure exerted on the surface?
(b) What is the total power output of the source, if it is assumed to radiate uniformly in all directions?

Question 47

A laser beam has a wavelength of 633 nm and a power of 0.500 mW spread uniformly over a circle 1.20 mm in diameter. This beam falls perpendicularly on a perfectly reflecting piece of paper having twice the diameter of the laser beam and a mass of 1.50 mg. (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)
(a) What are the amplitudes of the electric and magnetic fields in this laser beam?
(b) What acceleration does the laser beam give to the paper?

Question 48

A 22.0-kg mirror with a surface area of 1.0 m² and a reflectivity is bombarded by light of average intensity at an angle of to the normal of its surface. If the light has a duration of how much does the velocity of the mirror change during that time? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 120 nm/s
B) 4.2 nm/s
C) 3.6 nm/s
D) 2.1 nm/s

Question 49

A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the torque due to radiation pressure on the vane assembly about the vertical axis? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 2.4 × 10^-12 N ∙ m
B) 6.0 × 10^-12 N ∙ m
C) 1.2 × 10^-11 N ∙ m
D) 1.8 × 10^-11 N ∙ m
E) 2.4 × 10^-11 N ∙ m

Question 50

Light of intensity I₀ and polarized horizontally passes through three polarizes. The first and third polarizing axes are horizontal, but the second one is oriented 20.0° to the horizontal. In terms of I₀, what is the intensity of the light that passes through the set of polarizers?

A) 0.780I₀
B) 0.180I₀
C) 0.442I₀
D) 0.883I₀

Question 51

Unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned. If of the light passes through this combination of filters, what is the angle between the transmission axes of the filters?

A) 53°
B) 73°
C) 85°
D) 80°

Question 52

A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m² is incident normally upon the vanes. What is the radiation pressure on the blackened vane? (c = 3.00 × 10⁸ m/s, μ₀ = 4π × 10^-7 T ∙ m/A, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 1.0 × 10^-10 Pa
B) 1.0 × 10^-9 Pa
C) 1.0 × 10^-8 Pa
D) 1.0 × 10^-7 Pa
E) 1.0 × 10^-6 Pa