Solutions to Homework #5 for Physics 104, Summer 2003

## Chapter 11

Exercises 1,5,6,12,15

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.

## Problems

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, respectively.

## Case 1,4

1.

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).

4.

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'.

## Chapter 12

Exercises 1,6,8,12,15,22

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 of IR.

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 appear white.

## Problem 1

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.

## Case 1

1.

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.