Physics For Scientists And Engineers 6E - part 272
Problems
1085
does it take for light to reach you from a lightning stroke
10.0 km away?
3. The speed of an electromagnetic wave traveling in a trans-
parent nonmagnetic substance is
, where 0 is
the dielectric constant of the substance. Determine the
speed of light in water, which has a dielectric constant at
optical frequencies of 1.78.
4. An electromagnetic wave in vacuum has an electric field
amplitude of 220 V/m. Calculate the amplitude of the
corresponding magnetic field.
Figure 34.3 shows a plane electromagnetic sinu-
soidal wave propagating in the x direction. Suppose that
the wavelength is 50.0 m, and the electric field vibrates
in the xy plane with an amplitude of 22.0 V/m. Calculate
(a) the frequency of the wave and (b) the magnitude
and direction of
B when the electric field has its maxi-
mum value in the negative y direction. (c) Write an
expression for
B with the correct unit vector, with
numerical values for B
max
, k, and %, and with its magni-
tude in the form
6. Write down expressions for the electric and magnetic
fields of a sinusoidal plane electromagnetic wave having a
frequency of 3.00 GHz and traveling in the positive x direc-
tion. The amplitude of the electric field is 300 V/m.
In SI units, the electric field in an electromagnetic wave is
described by
Find (a) the amplitude of the corresponding magnetic
field oscillations, (b) the wavelength *, and (c) the fre-
quency f.
8.
Verify by substitution that the following equations are solu-
tions to Equations 34.8 and 34.9, respectively:
9. Review problem. A standing-wave interference pattern is
set up by radio waves between two metal sheets 2.00 m
apart. This is the shortest distance between the plates that
will produce a standing-wave pattern. What is the funda-
mental frequency?
10.
A microwave oven is powered by an electron tube called a
magnetron, which generates electromagnetic waves of fre-
quency 2.45 GHz. The microwaves enter the oven and are
reflected by the walls. The standing-wave pattern produced
in the oven can cook food unevenly, with hot spots in the
food at antinodes and cool spots at nodes, so a turntable is
often used to rotate the food and distribute the energy. If a
microwave oven intended for use with a turntable is
instead used with a cooking dish in a fixed position, the
antinodes can appear as burn marks on foods such as
carrot strips or cheese. The separation distance between
the burns is measured to be 6 cm 1 5%. From these data,
calculate the speed of the microwaves.
B " B
max
cos(kx ) %t)
E " E
max
cos(kx ) %t)
E
y
"
100 sin(1.00 $ 10
7
x ) %t)
7.
B " B
max
cos(kx ) %t)
5.
v " 1/
√
0&
0
#
0
Section 34.3 Energy Carried by Electromagnetic Waves
11. How much electromagnetic energy per cubic meter is con-
tained in sunlight, if the intensity of sunlight at the Earth’s
surface under a fairly clear sky is 1 000 W/m
2
?
12.
An AM radio station broadcasts isotropically (equally in all
directions) with an average power of 4.00 kW. A dipole
receiving antenna 65.0 cm long is at a location 4.00 miles
from the transmitter. Compute the amplitude of the emf
that is induced by this signal between the ends of the
receiving antenna.
What is the average magnitude of the Poynting vector
5.00 miles from a radio transmitter broadcasting
isotropically with an average power of 250 kW?
14.
A monochromatic light source emits 100 W of electromag-
netic power uniformly in all directions. (a) Calculate the
average electric-field energy density 1.00 m from the
source. (b) Calculate the average magnetic-field energy
density at the same distance from the source. (c) Find the
wave intensity at this location.
A community plans to build a facility to convert solar
radiation to electrical power. They require 1.00 MW of
power, and the system to be installed has an efficiency of
30.0% (that is, 30.0% of the solar energy incident on the
surface is converted to useful energy that can power the
community). What must be the effective area of a perfectly
absorbing surface used in such an installation, assuming
sunlight has a constant intensity of 1 000 W/m
2
?
16.
Assuming that the antenna of a 10.0-kW radio station radi-
ates spherical electromagnetic waves, compute the maxi-
mum value of the magnetic field 5.00 km from the
antenna, and compare this value with the surface magnetic
field of the Earth.
The filament of an incandescent lamp has a 150-2
resistance and carries a direct current of 1.00 A. The fila-
ment is 8.00 cm long and 0.900 mm in radius. (a) Calcu-
late the Poynting vector at the surface of the filament,
associated with the static electric field producing the
current and the current’s static magnetic field. (b) Find
the magnitude of the static electric and magnetic fields at
the surface of the filament.
18. One of the weapons being considered for the “Star Wars”
antimissile system is a laser that could destroy ballistic
missiles. When a high-power laser is used in the Earth’s
atmosphere, the electric field can ionize the air, turning it
into a conducting plasma that reflects the laser light. In
dry air at 0°C and 1 atm, electric breakdown occurs for
fields with amplitudes above about 3.00 MV/m. (a) What
laser beam intensity will produce such a field? (b) At this
maximum intensity, what power can be delivered in a
cylindrical beam of diameter 5.00 mm?
19. In a region of free space the electric field at an instant
of time is
E " (80.0iˆ ' 32.0 jˆ ) 64.0kˆ) N/C and the
magnetic field is
B " (0.200iˆ ' 0.080 0jˆ ' 0.290kˆ) &T.
(a) Show that the two fields are perpendicular to each
other. (b) Determine the Poynting vector for these fields.
20. Let us model the electromagnetic wave in a microwave
oven as a plane traveling wave moving to the left, with an
intensity of 25.0 kW/m
2
. An oven contains two cubical
17.
15.
13.