All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.
2. 0.15 V
8. (a) counterclockwise, (b) clockwise, (c) zero, (d) counterclockwise
14.(a) 0.43 V, (b) 16 mA, (c) 3.5 mN
22. 0.925 revolutions per second
34. (a) 6.0 V, (b) step-down
36. (a) step-down, (b) 3.3 A, (c) 0.33 A, (d) 3.6 W
40. Using the transformers saves 33.4 kW.
46. L = 2.2 mH, N2 = 32 turns.
54 29 J
The rest of the Chapter 21 answers can be found in the AC Circuits page.
2. Magnetic flux is the average perpendicular component of the magnetic field times the area of the surface it is pointing through. The magnetic flux depends not just on the magnetic field, but also on the surface, its shape, and which way it is oriented in the field.
3. First question: Yes, there is a changing negative flux as the south pole approaches. The current created by the emf must generate a positive flux to compensate. This means there is a counterclockwise current, looking from the direction the magnet approached from.
Second question: No, because the flux is constant, so no emf is generated.
Third question: Yes, in the opposite direction from the first question, since the flux change is reversed. The current is then clockwise.
4. Since the flux is decreasing, a counterclockwise current is needed to generate a magnetic field out of the paper to compensate.
5. The loop on the left has a constant flux, so no current is generated. The loop on the right has a decreasing flux into the paper. The current must flow to increase the flux into the paper. Therefore, it flows clockwise.
6. The shield prevents external magnetic fields from inducing an emf in the cable, distorting the signal.
7. Placing two wires carrying equal and opposite current next to each other reduces the magnetic field created by the currents, and therefore, reduces interference with other circuits. It also reduces the effect of magnetic flux on the wire, since the effect cancels in the two conductors.
8. The starter motor would turn the engine when a battery applied current to it. Once the engine was running, it would turn the motor, which would then generate an emf in the motor wiring, which could be used to charge the battery. A motor is basically a generator run "backwards".
9. When a refrigerator starts, a motor starts to run. After it is running smoothly, it creates a back-emf which limits the flow of the current. However, when it first starts, the motor is not yet producing a back-emf, and current is limited only by the resistance of the motor, which is much smaller than its inductive reactance when it is running. When an electric heater is turned on, it draws a constant current as long as it is on, because the current is going through a resistance rather than an inductor.
10. While a motor is running, it is producing a "back-emf" opposing the turning of its coils in the magnetic field. This is the same type of emf produced by a generator. Similarly, a generator requires force to turn, so it is like a motor opposing the direction in which it is being turned.
11. This is a do-it-yourself question. Consider the direction of the force created on the currents in the coils as they turn between the poles of the magnet. You may find figure 21-13 more useful than 21-12.
12. Yes, it requires only a conductor, so it can create a current in the conductor.
13. See figure 21-19. As the metallic trash passes over the magnets, eddy currents could be created in it, which would tend to slow down its motion, possibly allowing it to be sorted from non-metallic trash.
14. Consider a loop drawn inside the pivoted bar, so that it is on the left side inside the field. As the bar drops, the flux through this loop decreases into the paper, so a clockwise current would be generated around this loop to compensate. As the bar falls, part of the work would go into maintaining this current (which heats the bar as it flows), so the current slows down the falling of the bar. A bar with slots would impede the flow of the current, so much less power would go into into producing the current, and the bar would fall faster.
15. Currents would be generated in the aluminum as it is pulled out of the magnet, just as in the examples with a current loop confined to a wire. Creating this current would require work, which would be supplied by the force of pulling the aluminum out of the magnet.
16. Consider a ring drawn around the metal tube, with the magnet approaching from above. As the magnet approaches, the flux through the ring increases, so a current is generated around the ring to oppose that flux. This current produces a magnetic field opposite to the field of the falling magnet, and tends to force it back upward. Moreover, the induced current is proportional to the speed at which the magnet falls, since it is proportional to the rate of change of the flux. This means that the retarding force on the magnet is proportional to its velocity. The velocity will increase until these forces are balanced, at which time it reaches its terminal velocity.
17. The explanation, again, is the current which is created in the bar as it passes through the magnetic field. The current acts in a direction such that it opposes the movement of the bar, and thus damps out the motion.
18.
You could decide which lead is paired with another by testing with an ohm-meter
to see which pairs of wires have little resistance between them. The ratio
of turns can be determined by passing an AC current through one connected pair,
and measuring the voltages on each side. Using the tranformer equation gives
19. Higher-voltage lines probably are not used because they would be more dangerous. The electric fields around them are higher, which can lead to induced currents in nearby metallic items as well (leakage currents).
20. Yes, a loudspeaker can function as a microphone, because the sound makes the coils move between the poles of the magnet, which induces an emf in them. With a microphone, you want a small vibration to make a large emf, but for a speaker, it is better to produce a larger vibration with a small emf.
21. The current that flows depends on how much power is being sent through the transformer. The resistance is just a minor factor in determining this. The current would only be 24,000 A if it were direct current, not AC. Normally, the inductive impedence is the limiting factor.
22. The low resistance of the primary coil means that a large DC current flows through it. When used as intended, in an AC circuit, the current is limited by the inductive impedence, which is much greater.
23. (a) The mutual inductance is greatest when all the flux from one coil goes through the other. Placing them on top of each other in parallel would accomplish this. (b) The mutual inductance is least when none of the flux from one goes through the other. This can be set up by orienting one coil to be perpendicular to the other, so that the normal component of the magnetic field produced by one is zero in the plane of the other loop.
24. The wire should be coiled all on top of itself to maximize
the inductance. For a solenoid, the inductance is proportional to
N2A/l, where l is the length of the solenoid.
If the wire has fixed length d, and the solenoid has radius r,
then
The self-inductance can be minimized by making a coil of wire, then winding another back along itself in the opposite direction, canceling out the magnetic fields inside.
The rest of the Chapter 21 answers can be found in the AC Circuits page.
| Physics 222 | Department of Physics | University of Tennessee |