Download Exercises – Chapter 13

Exercises – Chapter 13
1. If you pull a permanent magnet rapidly away from a tank circuit, what is likely to happen in that circuit?
E.1
Charge will oscillate in the tank’s capacitor and inductor.
2. Will the speed with which you pull the magnet away from the tank circuit (Exercise 1) affect the period of its
charge oscillation?
E.2
No.
E.2
The tank circuit is a type of harmonic oscillator, so its period of oscillation is independent of the amplitude
of that oscillation. Moving the magnet faster may induce a larger amplitude oscillation, but the period of
that oscillation will be unchanged.
3. A tank circuit consists of an inductor and a capacitor. Give a simple explanation for why the magnetic field in the
inductor is strongest at the moment the separated charge in the capacitor reaches zero.
E.3
The inductor’s magnetic field contains energy and it peaks when the capacitor’s energy is zero.
4. The metal wires from which most tank circuits are made have electrical resistances. Why do these resistances
prevent charge from oscillating forever in a tank circuit, and what happens to the tank circuit’s energy as time passes?
E.4
The wires waste the tank circuit's energy as thermal energy, gradually reducing the amount of charge
sloshing in the tank until the sloshing stops altogether.
5. To add energy to the charge oscillation in a tank circuit with an antenna, at which time during the oscillation cycle
should you bring a positively charged wand close to the antenna?
E.5
Each time the antenna reaches its peak positive charge, push the positive wand close to it. You’ll then be
doing work on the oscillating charge.
6. Two identical tank circuits with antennae are next to one another. Explain why charge oscillating in one tank circuit
can continue to do work on charge oscillating in the other tank circuit.
E.6
Charge oscillations in the two tank circuits have the same period so that the two tank circuits can exchange
energy via sympathetic vibration. The fluctuating electromagnetic fields from the first antenna push on
charges in the second antenna in perfect synchrony with the charge fluctuations in that second antenna.
7. The ignition system of an automobile produces sparks to ignite the fuel in the engine. During each spark process,
charges suddenly accelerate through a spark plug wire and across a spark plug’s narrow gap. Sometimes this process
introduces noise into your radio reception. Why?
E.7
As charges accelerate in the wires, they emit radio waves.
8. To diminish the radio noise in a car (see Exercise 7), the ignition system uses wires that are poor conductors of
electricity. These wires prevent charges from accelerating rapidly. Why does this change improve your radio reception?
E.8
Since accelerating electric charge is what produces radio waves, limiting that acceleration reduces the
intensity of radiated electromagnetic waves.
9. The electronic components inside a computer transfer charge to and from wires, often in synchrony with the
computer’s internal clock. Without packaging to block electromagnetic waves, the computer will act as a radio
transmitter. Why?
E.9
As charges accelerate in the computer, they emit radio waves.
10. To save power in a computer, its thousands of wires usually avoid sharp bends. Why do sharp bends in currentcarrying wires waste power?
E.10 Since accelerating electric charge is what produces radio waves, the sudden accelerations experienced by
currents as they flow around sharp bends lead to intense and wasteful electromagnetic radiation.
11. The sun emits a stream of energetic electrons and protons called the solar wind. These particles frequently get
caught up in the earth’s magnetic field, traveling in spiral paths that take them toward the north or south magnetic
poles. When they head northward and collide with atoms in the earth’s upper atmosphere, those atoms emit light we
know as the aurora borealis, or northern lights. These particles also interfere with radio reception. Why do they emit
radio waves?
E.11 The spiraling charges are accelerating and thus emit electromagnetic waves.
12. When a radio signal travels through a coaxial cable, charge moves back and forth on both the central wire and the
surrounding tube. Show that both electric and magnetic fields are present in the coaxial cable.
E.12 Whenever the charges on the central wire and surrounding tube are different, there are electric fields
pointing from positive to negative charges. And whenever charge moves on either of the two conductors,
that moving charge produces magnetic fields.
13. If you wave a positively charged wand up and down vertically, the electromagnetic wave it emits has which
polarization?
E.13 Vertical polarization.
14. If you set a magnetic compass on the table and spin its magnetic needle horizontally, its accelerating poles will
emit an electromagnetic wave with which polarization?
E.14 Vertical polarization.
15. While a particular AM radio station claims to transmit 50,000 W of music power, that’s actually its average power.
There are times when it transmits more power than that and times when it transmits less. Explain.
E.15 The AM station changes the power of its transmission in order to represent air pressure fluctuations with
the radio wave.
16. When your receiver is too far from an AM radio station, you can only hear the loud parts of the transmission. When
it’s too far from an FM station, you lose the whole sound all at once. Explain the reasons for this difference.
E.16 In an AM transmission, the radio wave is strongest during the loudest portions of the broadcast. But in an
FM transmission, the radio wave intensity is constant.
17. When an AM radio station announces that it’s transmitting at 950 kHz, that statement isn’t quite accurate. Explain
why it may also be transmitting at 948 kHz and 954 kHz.
E.17 Amplitude modulation introduces additional frequencies that extend as much as 5 kHz above and below
the carrier wave.
18. The Empire State Building has several FM antennas on top, added in part to increase its overall height. These
antennas aren’t very tall. Why do short antennas, located high in the air, do such a good job of transmitting FM radio?
E.18 Television transmission involves high-frequency, short-wavelength radio waves. Since a good antenna is
one-quarter wavelength long, television transmission requires relatively short antennas.
19. Porous, unglazed ceramics can absorb water and moisture. Why are they unsuitable for use in a microwave oven?
E.19 Water trapped in the ceramic would absorb microwaves, and the ceramic would become extremely hot. It
might even shatter.
20. Why are most microwave TV dinners packaged in plastic rather than aluminum trays?
E.20 Aluminum trays would reflect the microwaves and make it difficult to cook the food properly.
21. Why is it so important that a microwave oven turn off when you open the door?
E.21 Releasing the microwaves into the room wouldn’t be healthy.
22. Compare how a potato cooks in a microwave oven with how it cooks in an ordinary oven.
E.22 In a microwave oven, the potato’s water absorbs microwaves. The microwave energy becomes thermal
energy and the potato’s temperature rises relatively uniformly. In an ordinary oven, heat flows gradually
into the potato through its surface and its temperature rises nonuniformly. The middle of the potato cooks
last.
23. When you’re listening to FM radio near buildings, reflections of the radio wave can make the reception particularly
bad in certain locations. Compare this effect to the problem of uneven cooking in a microwave oven.
E.23 Both involve destructive interference in electromagnetic waves.
24. Dish-shaped reflectors are used to steer microwaves in order to establish communications links between nearby
buildings. Those reflectors are often made from metal mesh. Why don’t they have to be made from solid metal sheets?
E.24 Microwaves cannot respond to holes in the metal that are significantly smaller than their wavelengths. The
metal mesh is equivalent to solid metal as far as the microwaves are concerned.
25. Why is the thin metal handle of a Chinese food container dangerous when placed in a microwave oven?
E.25 It is thin enough to be heated by the resulting currents and its sharp ends may spark.
26. Is a thick, smooth-edged stainless steel bowl dangerous in a microwave oven?
E.26 No (although it may alter the rate at which the food nearby cooks).
27. A cyclotron is a particle accelerator invented in 1929 by American physicist Ernest O. Lawrence. It uses electric
fields to do work on charged particles as they follow circular paths in a strong magnetic field. Lawrence’s great insight
was that all the particles take the same amount of time to complete one circle, regardless of their speed or energy. That
fact allows the cyclotron to do work on all the particles at once as they circle together. How can a faster moving
electron take the same time to circle as a slower moving electron?
E.27 The path of a faster moving electron bends more gradually, so it travels in a larger circle. It returns to its
starting point at the same time the slower moving electron returns to its starting point.
28. An extremely fast-moving charged particle traveling in a magnetic field can radiate X-rays, a phenomenon known
as synchrotron radiation. Why is the magnetic field essential to this emission?
E.28 Without the magnetic field, the charged particle would travel at constant velocity (at constant speed along
a straight path) and would not radiate electromagnetic waves.