Solutions to Homework #5 for Physics
104, Summer 2003
1. As charges accelerate, they emit EM waves at a broad range of frequencies,
that can interfere with radio reception.
5. When there is no charge in the capacitor, the current is maximum
through the inductor, which makes its magnetic field maximum at
that point .
6. If there is an inductor in any circuit, any attempt to change the
current doesn't happen instantaneously but at a slower rate determined
by the inductance. This happens because of Lenz's law; there is a
resistance to changing magnetic fields resulting from the imposed change
in current. The resulting induced current is superimposed on the same
circuit and opposes the original change.
12. AM signal transmission relies on the modulation of the amplitude,
which weakens as you move away from the station's antenna. If you are
far away from the station, you can thus hear only the large amplitude
(loud parts) of the transmission. FM signal transmission relies on
the modulation of frequency, which is undetectable if there is no
amplitude from different parts of the signal.
15. Ambient signals from people's microwaves operating at 2.45 Ghz
will interfere with communications signals at the same frequency.
1. Since (wavelength)(frequency) = c(speed of light), then
wavelength = (3x10^8 m/s)/(900 x 10^6 hz) = 33 cm.
4. Using the same relation in (1), the corresponding frequencies for
160-m, 15-m and 2-m wavelengths are 1.875Mhz, 20Mhz and 150Mhz,
a. Liqueur gets hot because it has a water component to hit,
which can be polarized and heated with the microwaves. The merengue
is frozen so it cannot be easily polarized.
b. Cooking an egg using microwaves heats the interior liquid egg white
which expands to form a gas, causing the explosion out of the shell.
Similarly, moisture inside the corn kernel expands into a gas suddenly
when heated by a microwave, thus causing the popping.
c. A thin metallic sheet, in contrast to a thick metallic sheet,
has a higher resistance (just as a thin cable wire has a higher
resistance than a thick cable). Higher resistance means more resistive
heating (Ohm's Law: P=(I^2)R), for the same current.
d. A wire-mesh cage shields the food from all electric fields, including
microwave waves, since we have learned that all electric charges reside
on the surface of a metal conductor(the cage in this example).
a. The wavelengths of waves of frequencies 825.03Mhz and 870.03Mhz are
36.4 cm and 34.5 cm, respectively, using the equation in Problem 1 above.
b. The proper length of an antenna, to be resonant at the radiowave frequency
it is transmitting is a quarter-wavelength. For (a), these are 9.1cm
and 8.6cm, respectively.
c. The 900 people will encounter interference between each other's
signal if their handsets operated at these frequencies.
d. These unfortunate people will be standing along the axis of the antenna,
along which no EM wave propagation occurs.
e. EM waves travel transverse to the direction of the antenna. The polarization
of the E-field is then along the vertical, which induces charge motion along
a receiver antenna, if it were oriented vertically.
f. A metal building provides an EM shield, inside of which no charges
can stay. No charges means no charges to accelerate in any antenna.
h. Transmission of the weak signal will allow an overlap of communication
between the phone and different bases, so that no calls will be 'dropped'.
1. For efficient transmission/emission, the antenna length must
be (1/4) of the wavelength. Red light's wavelngth is
6. The UV light is scattered more via Raleigh Scattering since
its wavelength is closer to the small size of the scattering
particles in the atmosphere, as compared to the longer wavelengths
8. On the moon, there is no atmosphere that provides Raleigh scattering,
as compared to the earth. On the earth, even if the sun is overhead,
light reflected from other sources still get scattered and the blue
color washes out the faint light from the distant stars.
12. Whenever there is a change of medium, EM waves like light are
reflected back.If the surface is not calm, the water will still reflect
your image back but at various angles and you lose a good image.
15. Granulated sugar has many surfaces that reflect white light in various
directions, without being absorbed. These randomly directed waves make the sugar
1. Each particle of light carries energy proportional to its frequency,according
to E = (Planck's constant)(frequency) = hf = (6.626 x 10^-34 J/s)(5.08 x 10^14Hz)
= 3.37 x 10^-19 J.
a. Water droplets are relatively large, so that they can absorb all the
different colors of white light, and re-emit them.
b. Blue light is still reflected more than red light, by atmospheric particles.
So we see a blue sky. But if there is less dust of particles in this example,
the blue is mixed with the dark sky you expect to see when the scattering
is less, and you see black space.
c. On an airless moon, there is no atmosphere that would otherwise be
responsible for Raleigh scattering. Thus, the sky would look black
since outer space is mostly black.
d. Water is still polarizable, not as strongly as metals. Thus, some
light will cause polarization and thus, reflection. THis is what happens
when you have a change of interface.
e. Light bends from cold to warm air, since its speed in air of various temperatures
changes, causing a change of index of refraction.