Download Electromagnetic Waves Practice Test

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) A 2.12 × 1014 Hz electromagnetic wave propagates in carbon tetrachloride with a speed of
2.05 × 108 m/s. The wavelength of the wave in carbon tetrachloride is closest to:
A) 1070 nm
B) 1290 nm
C) 1200 nm
D) 967 nm
E) 1420 nm
2) A 6.53 × 1014 Hz electromagnetic wave propagates in carbon tetrachloride with a speed of
2.05 × 108 m/s. The wavelength of the wave in vacuum is closest to:
A) 413 nm
B) 368 nm
C) 505 nm
D) 459 nm
2)
E) 314 nm
3) A 8.38 × 1014 Hz electromagnetic wave propagates in carbon tetrachloride with a speed of
2.05 × 108 m/s. The relative magnetic permeability of carbon tetrachloride is 1.00. The dielectric
constant of carbon tetrachloride at a frequency of 8.38 × 1014 Hz is closest to:
A) 2.52
B) 1.38
C) 1.76
D) 2.14
1)
3)
E) 1
4) A planar electromagnetic wave is propagating in the positive x-direction. At a certain point P
and at a given instant, the electric field of the wave is given by E = -j 82 mV/m. The magnetic
vector of the wave, at the point P at that instant is closest to:
A) (-2.7 × 10 -10 T) k
4)
B) (+2.7 × 10 -10 T) k
C) (+2.7 × 10 -10 T) j
D) (-6.8 × 10 -9 T) j
E) (+6.8 × 10 -9 T) k
5) A planar electromagnetic wave is propagating in the positive x-direction. At a certain point P
and at a given instant, the electric field of the wave is given by E = -j 12 mV/m. The Poynting
vector at the point P at that instant is closest to:
A) (+3.8 × 10 -7 W/m2) i
B) (+1.9 × 10 -7 W/m2) i
C) (-1.9 × 10 -7 W/m2) k
D) (-3.8 × 10 -7 W/m2) i
E) (-1.9 × 10 -7 W/m2) i
1
5)
6) The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of
724 mW/m2. The maximum value of the magnetic field in the wave is closest to:
6)
A) 7.79 × 10 -8 T
B) 1.56 × 10 -7 T
C) 5.51 × 10 -8 T
D) 1.08 × 10 -7 T
E) 3.89 × 10 -8 T
7) The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of
939 mW/m2. The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. The
total energy that traverses the area in a time interval of one minute is closest to:
A) 210 J
B) 340 J
C) 300 J
D) 170 J
7)
E) 250 J
8) 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 630 mV/m. Assume that the signal power is
radiated uniformly in all directions and that radio waves incident upon the ground are
completely absorbed. The magnetic field amplitude of the signal at that point, in nT, is closest to:
A) 2.5
B) 2.1
C) 1.7
D) 1.3
E) 2.9
8)
9) 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 900 mV/m. Assume that the signal power is
radiated uniformly in all directions and that radio waves incident upon the ground are
completely absorbed. The average electromagnetic energy density at that point is closest to:
A) 1.4 × 10 -11 J/m3
9)
B) 5.1 × 10 -12 J/m3
C) 3.6 × 10 -12 J/m3
D) 7.2 × 10 -12 J/m3
E) 1.0 × 10 -11 J/m3
10) 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 360 mV/m. Assume that the signal power is
radiated uniformly in all directions and that radio waves incident upon the ground are
completely absorbed. The intensity of the radio signal at that point is closest to:
A) 1.7 × 10 -4 W/m2
B) 3.4 × 10 -4 W/m2
C) 1.2 × 10 -4 W/m2
D) 8.6 × 10 -5 W/m2
E) 2.4 × 10 -4 W/m2
2
10)
11) 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 440 mV/m. Assume that the signal power is
radiated uniformly in all directions and that radio waves incident upon the ground are
completely absorbed. The average total power radiated by the transmitter is closest to:
A) 3.8 × 10 5 W
11)
B) 2.7 × 10 5 W
C) 4.5 × 10 5 W
D) 3.2 × 10 5 W
E) 5.0 × 10 5 W
Figure 32.1
A radiometer has two square vanes (1 cm by 1 cm), attached to a light horizontal cross arm, and pivoted about a vertical
axis through the center. The center of each vane is 6 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. Radiant energy, which has
an intensity of 300 W/m2, is incident normally upon the vanes.
12) In Fig. 32.1, the radiant power absorbed by the blackened vane is closest to:
A) 0.03 W
B) 0.06 W
C) 0.05 W
D) 0.04 W
13) In Fig. 32.1, the radiation pressure on the blackened vane is closest to:
A) 1 × 10-10 Pa
12)
E) 0.09 W
13)
B) 1 × 10-6 Pa
C) 1 × 10-7 Pa
D) 1 × 10-9 Pa
E) 1 × 10-8 Pa
14) In Fig. 32.1, the torque on the vane assembly, about the vertical axis, is closest to:
A) zero
B) 6 × 10-12 N ∙ m
C) 1.8 × 10-11 N ∙ m
D) 1.2 × 10-11 N ∙ m
E) 2.4 × 10-11 N ∙ m
3
14)
15) The wavelength of visible light ranges from 400 nm to 700 nm. The highest frequency of visible
light is closest to:
A) 7.5 × 1014 Hz
15)
B) 5.5 × 1014 Hz
C) 15 × 1014 Hz
D) 4.3 × 1014 Hz
E) 8.3 × 1014 Hz
16) If the z-component of the magnetic field of an electromagnetic wave traveling in the x-direction
through vacuum obeys the equation
B z = (1.25 µT) cos[(3800 m-1)x - (1.14 × 1012 rad/s)t],
16)
then the largest that the y-component of the electric field can be is closest to:
A) 375 N/C
B) 1.25 × 106 N/C
C) 4.17 × 10-9 N/C
D) 4.17 × 10-15 N/C
E) 3.75 × 108 N/C
Situation 32.1
A microwave oven operates 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 mJ.
17) In Situation 32.1, the power output of the microwave oven is closest to:
A) 700 W
B) 550 W
C) 600 W
D) 650 W
18) In Situation 32.1, the intensity of the microwave beam is closest to:
A) 5200 W/m2
17)
E) 500 W
18)
B) 7200 W/m2
C) 6200 W/m2
D) 6700 W/m2
E) 5700 W/m2
19) In Situation 32.1, the electric field amplitude is closest to:
A) 1600 V/m
B) 2500 V/m
C) 1900 V/m
D) 2200 V/m
E) 2800 V/m
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19)
20) In Situation 32.1, the force on the base due to the radiation is closest to:
A) 2.0 × 10-6 N
20)
B) 3.0 × 10-6 N
C) 2.5 × 10-6 N
D) 3.5 × 10-6 N
E) 1.5 × 10-6 N
21) A 7.8 × 1014 Hz laser emits a 8.7-µs pulse, 5.0 mm in diameter, with a beam energy density of
0.21 J/m3. The number of wavelengths in the length of the beam is closest to:
21)
A) 6.8 × 10 10
B) 2.0 × 10 9
C) 2.0 × 10 11
D) 2.0 × 10 10
E) 6.8 × 10 9
22) A 2.7 × 1014 Hz laser emits a 2.0-µs pulse, 5.0 mm in diameter, with a beam energy density of
0.75 J/m3. The power emitted by the laser is closest to:
A) 4.4 kW
B) 13 kW
C) 22 kW
D) 8.9 kW
22)
E) 18 kW
23) 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. The amplitude of the electric field of the emitted waves is closest to:
23)
A) 1.2 × 10 5 V/m
B) 4.8 × 10 5 V/m
C) 2.4 × 10 5 V/m
D) 1.5 × 10 5 V/m
E) 3.4 × 10 5 V/m
24) A 8.6 x 1014 Hz laser emits a 9.7 µs pulse, 5.0 mm in diameter, with a beam energy density of
0.85 J/m3. The average Poynting vector magnitude of the beam is closest to:
A) 6.4 × 10 7 W/m2
B) 9.0 × 10 7 W/m2
C) 2.6 × 10 8 W/m2
D) 1.8 × 10 8 W/m2
E) 1.3 × 10 8 W/m2
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24)
Situation 32.2
A standing planar electromagnetic wave is established in a resonant cavity formed by two parallel conducting plates that
are 12 cm apart. The number of electric field antinoidal planes, including the cavity walls, in the standing wave is three.
25) In Situation 32.2, the frequency of the electromagnetic wave in GHz (G = giga = 109), is closest
to:
A) 5.00
B) 3.75
C) 6.25
D) 2.50
E) 1.25
25)
26) In Situation 32.2, the number of antinoidal planes for the magnetic field is:
A) 4
B) 3
C) 5
D) 6
26)
E) 2
27) In Situation 32.2, the smallest distance between an electric field antinoidal plane and a magnetic
field antinoidal plane, in cm, is closest to:
A) zero
B) 2.0
C) 1.0
D) 3.0
E) 4.0
27)
28) A certain glass has an index of refraction of 1.44 at a wavelength of 560 nm in vacuum. What is
the effective dielectric constant at the corresponding frequency?
A) 2.07
B) 1.44
C) 3.66
D) 1.98
E) 1.20
28)
29) Electromagnetic standing waves are set up in a conducting cavity resonator in the form of a
hollow metal box. The waves bounce back and forth between two parallel surfaces separated by
0.80 cm. What is the minimum resonant frequency for such a resonator?
A) 15.5 GHz
B) 4.42 GHz
C) 18.8 GHz
D) 12.4 GHz
E) 3.30 GHz
29)
Situation 32.3
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[ks - (2.20 × 1014 rad/s)t].
30) In Situation 32.3, the wavelength of the electromagnetic wave is closest to:
A) 2.72 µm
B) 1.36 µm
C) 8.57 µm
D) 17.1 µm
30)
E) 0.272 µm
31) In Situation 32.3, the largest that the x-component of the magnetic field of the wave can be is
closest to:
A) 1.36 µT
B) 1.25 µT
C) 1.13 × 1011 T
31)
D) 1.70 × 10-12 T
E) 0.00 µT
32) In Situation 32.3, the largest that the z-component of the magnetic field of the wave can be is
closest to:
A) 1.70 × 10-12 T
B) 1.25 µT
C) 0.00 µT
D) 1.36 µT
E) 1.13 × 1011 T
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32)
33) 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, the force that the same
wave would exert on the surface is:
A) 4F
B) F/2
C) F/4
D) 2F
E) F
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
34) A sinusoidal electromagnetic wave is propagating in vacuum.
(a) At a given point and at a particular time the electric field is in the +x-direction and
the magnetic field is in the -y-direction. What is the direction of propagation of the
wave?
(b) At the above point the intensity of the wave is 0.86 W ∙ m-2. What is the electric field
34)
amplitude at this point? (Note: µo = 4π × 10-7 T ∙ m/A and c = 3.00 × 108 m/s)
35) An electromagnetic wave has a wavelength of 2.90 × 10-5 m in air and a wavelength of
35)
1.74 × 10-5 m in a certain dielectric material. Find the dielectric constant for the material.
36) A source of light produces an electric field amplitude of 9.10 V/m 44.0 m from the
source. What is the power output from the source?
36)
37) A totally absorbing surface of area A = 7.7 cm2 faces a small source of sinusoidal
electromagnetic radiation that is 2.4 m away. At the surface A the electric field
amplitude of the radiation is 84 V/m. (Note: µ0 = 4π × 10-7 T ∙ m/A and
37)
c = 3.00 × 108 m/s.)
(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?
38) An electromagnetic standing wave is resonating in a cavity with n = 1. The nodal plane
of the E field and the closest nodal plane of the B field are separated by 0.87 m.
(a) Find the length of the resonating cavity.
(b) Find the frequency of the electromagnetic wave.
38)
39) 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.
(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?
39)
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33)
Answer Key
Testname: UNTITLED4
1) D
2) D
3) D
4) A
5) A
6) A
7) D
8) B
9) C
10) A
11) B
12) A
13) B
14) B
15) A
16) A
17) C
18) D
19) D
20) A
21) E
22) A
23) E
24) C
25) B
26) A
27) B
28) A
29) C
30) C
31) E
32) B
33) A
34) (a) -z-direction (b) 25 V/m
35) 2.78
36) 2670 W
37) (a) 3.1 × 10 -8 Pa
(b) 6.8 × 10 2 watts
38) (a) 1.74 m
(b) 8.6 × 107 Hz
39) (a) E max = 577 N/C, B max = 1.92 µT
(b) 2.22 × 10-6 m/s2
8