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**Unformatted text preview: **Problem Set Displacement Current 29.42 - A parallel-plate, air-filled capacitor is being charged as
in Fig. 29.23. The circular plates have radius 4.00 cm, and at a
particular instant the conduction current in the wires is 0.520 A.
(a) What is the displacement current density jD in the air space
between the plates? (b) What is the rate at which the electric field
between the plates is changing? (c) What is the induced magnetic
ﬁeld between the plates at a distance of 2.00 cm from the axis?
(d) At 1.00 cm from the axis? Waves 32. 2- Consider each of the electric- and magnetic—field orienta-
tions given next. In each case, what is the direction of propaga-
tion of the wave? (a) E m the +x—direction, B in the +y- di-rcction;
(b) E in the —y—direction, B in the +x—direction; (c) E in the
+z—direction, Bin the ~x—direction; (d) E 1n the +y-direction, B
in the —z—directior1. 32.10 - The electric field of a sinusoidal electromagnetic wave
obeys the equation E: (375 V/m) cos[(l 99 X 107 rad/m)x +
(5. 97 X 1015 rad/sh}. (a) What 13 the speed of the wave? (1)) What
are the amplitudes of the electric and magnetic fields of this wave?
(c) What are the frequency, wavelength, and period of the wave? Is
this light visible to humans? 32.18 -- A sinusoidal electromagnetic wave from a radio sta«
tion passes perpendicularly through an open window that has
area 0.500 m2. At the window, the electric field of the wave has
rms value 0.0400 V/rn. How much energy does this wave carry
through the Window during a 30.0-s commercial? 32.21 - The intensity ofa cylindrical laser beam is 0.300 W/rnz.
The cross-sectional area of the beam is 3.0 X It?4 n12 and the
intensity is uniform across the cross section of the beam. (a) What
is the average power output of the laser? (b) What is the rms value
of the electric field in the beam? 32.22 - A sinusoidal electromagnetic wave emitted by a cellular
phone has a. Wavelength of 35.4 cm and an electric—field amph-
tude of 5.40 X 10—2 V/m at a distance of 250 in from the phone.
Calculate (a) the frequency of the wave; (b) the magnetic—field
amplitude; (c) the intensity of the wave. 32.24 - Television Broadcasting. Public television station
KQED in San Francisco broadcasts a sinusoidal radio signal at a
power of 777 kW. Assume that the wave spreads out uniformly
into a hemisphere above the ground. At a home 5.00 km away
from the antenna, (a) what average pressure does this wave exert
on a totally reﬂecting surface, (13) what are the amplitudes of the
electric and magnetic fields of the wave and (c) what' IS the aver—
age density of the energy this wave carries? ((1) For the energy
density' in part (c), what percentage is due to the electric field and
what percentage' 15 due to the magnetic field? 32.29 - Laboratory Lasers. He—Ne lasers are often used in
physics demonstrations. They produce light of wavelength 633 um
and a power of 0500 mW spread (Net a cylindrical beam 1.00 mm in diameter (although these quantities can Vary). (a) What is the
intensity of this laser beam? (b) What are the maximum values of
the electric and magnetic fields? (c) What is the average energy
density in the laser beam? ' 32.42 " CF A circular wire loop has aradius of 7.50 cm. A sinu-
soidal electromagnetic plane wave traveling in air passes through
the loop, with the direction of the magnetic field of the wave per-
pendicular to the plane of the loop. The intensity of the wave at
the location of the loop is 0.0275 W/lnz, and the wavelength of the
wave is 6.90 in. What is the maximum emf induced in the loop? 32.45 “ CP Global Positioning System (GPS). The GPS
network consists of 24 satellites, each of which makes two orbits
around the earth per day. Each satellite transmits a 50.0—W (or
even less) sinusoidal electromagnetic signal at two frequencies,
one of which is 1575.42 MHz. Assume that a satellite transmits
half of its power at each frequency and that the waves travel uni-
formly in a downward hemisphere. (a) What average intensity
does a GPS receiver on the ground, directly below the satellite,
receive? (Hint: First use Newton’s laws to find the altitude of the
satellite.) (b) What are the amplitudes of the electric and magnetic
fields at the GPS receiver in part (a), and how long does it take the
signal to reach the receiver? (0) If the receiver is a square panel
1.50 cm on a side that absorbs all of the beam, what average pres—
sure does the signal exert on it? (d) What wavelength must the
receiver be tuned to? Interference 35.4 - Radio Interference. Two radio antennas A and B radiate
in phase. Antenna B is 120 In to the right of antenna A. Consider
pdint Q along the extension of the line connecting the antennas,
a horizontal distance of 40 In to the right of antenna B. The fre—
quency, and hence the wavelength, of the emitted waves can be
varied. (a) What is the longest wavelength for which there will be
destructive interference at point Q? (b) What is the longest wave-
length for which there will be constructive interference at point Q? 35.7 - Young’s experiment is performed with light from excited
helium atoms (A 2 502 nrn). Fringes are measured carefully on
a screen 1.20 m away from the double slit, and the center of the
20th fringe (not counting the central bright fringe) is found to
be 10.6 mm from the center of the central bright fringe. What is
the separation of the two slits? 35.8 " Coherent light with wavelength 450 nm falls on a pair of
slits. On a screen 1.80 In away, the distance betWeen dark fringes
is 3.90 mm. What is the slit separation? 35.19 - Coherent light with wavelength 500 nm passes through
narrow slits separated by 0.340 m. At a distance from the slits
large compared to their separation, what is the phase difference
(in radians) in the light from the two slits at an angle of 23.0” from
the centerline? 35.22 -- Two slits spaced 0.0720 mm apart are 0.800 m from
a screen. Coherent light of wavelength A passes through the two
slits. In their interference pattern on the screen, the distance
from the center of the central maximum to the first minimum is
3.00 m. If the intensity at the peak of the central maximum is
0.0600 W/mz, what is the intensity at points on 'the screen that
are (a) 2.00 mm and (b) 1.50 mm from the center of the central
maximum? ...

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