# 1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field.

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1 Chapter 25 EXERCISE key 1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field. 2. Magnetic induction will not occur in nylon, since it has no magnetic domains. That s why electric guitars use steel strings. 3. The magnetic domains that become aligned in the iron core contribute to the overall magnetic field of the coil and therefore increase its magnetic induction. 4. The magnetic field of the iron core adds to the magnetic field of the coil, as stated in the answer to the previous exercise. Greater magnetic field means greater torque on the armature. 5. Work must be done to move a current-carrying conductor in a magnetic field. This is true whether or not the current is externally produced or produced as a result of the induction that accompanies the motion of the wire in the field. It s also a matter of energy conservation. There has to be more energy input if there is more energy output. 6. While the armature of a motor spins, converting electrical energy to mechanical energy, electric current (in the opposite direction) is induced. When this occurs a motor acts as a generator. 7. A cyclist will coast farther if the lamp is disconnected from the generator. The energy that goes into lighting the lamp is taken from the bike s kinetic energy, so the bike slows down. The work saved by not lighting the lamp will be the extra force distance that lets the bike coast farther. 8. Part of the Earth s magnetic field is enclosed in the wide loop of wire imbedded in the road. If this enclosed field is somehow changed, then in accord with the law of electromagnetic induction, a pulse of current will be produced in the loop. Such a change is produced when the iron parts of a car pass over it, momentarily increasing the strength of the field. A practical application is triggering automobile traffic lights. (When small ac voltages are used in such loops, small eddy currents are induced in metal of any kind that passes over the loop. The magnetic fields so induced are then detected by the circuit.) 9. As in the previous answer, tiny currents induced in the metal change the magnetic field, which in turn changes the ac current in the coils and sets off an alarm. 10. The changing magnetic field of the moving tape induces a voltage in the coil. A practical application is a tape recorder. 11. Copper wires were not insulated in Henry s time. A coil of non-insulated wires touching one another would comprise a short circuit. Silk was used to insulate the wires so current would flow along the wires in the coil rather than across the loops touching one another. 12. When the ground shakes, inertia of the suspended massive magnet tends to resist such shaking. But the coils of wire are fixed to the Earth and shake relative to the magnet. Motion of the magnet within conducting loops induces a current, which depends on the strength of the earthquake. So the law of inertia and the law of electromagnetic induction underlie the operation of this device. 13. In both cases the direction of the magnetic force is perpendicular to the magnetic field and the motion of charges but with different results. In the motor effect, the magnetic force pushes the wire upward. In the generator effect, the wire is pushed downward and the magnetic force pushes electrons in a direction along the wire to produce a current. 14. Voltage is induced. 15. Agree with your friend. Any coil of wire spinning in a magnetic field that cuts through magnetic field lines is a generator. 16. In accord with Faraday s law of induction, the greater the rate of change of magnetic field in a coil or armature, the greater the induced voltage. So voltage output increases when the generator spins faster. 17. In accord with electromagnetic induction, if the magnetic field alternates in the hole of the ring, an alternating voltage will be induced in the ring. Because the ring is metal, its relatively low resistance will result in a correspondingly high alternating current. This current is evident in the heating of the ring.

2 18. Two things occur in the windings of the electric motor driving a saw. Current input causes them to turn and you have a motor. But motion of windings in the magnetic field of the motor also makes them a generator. The net current in the motor is the input current minus the generated output current, which is opposite in direction to the input current. You pay the power company for the net current. When the motor jams, the net current is increased because of the absence of generated current. This can burn the windings of the saw! 19. The changing magnetic field produced when the current starts to flow induces a current in the aluminum ring. This current, in turn, generates a magnetic field that opposes the field produced by the magnet under the table. The aluminum ring becomes, momentarily, a magnet that is repelled by the hidden magnet. It is repelled just as the aluminum ring levitates in the photo opener with Jean Curtis. 20. The electromagnet is ac, which means a continually changing magnetic field in the copper ring. This induces a current in the ring, which then becomes its own electromagnet, which is continually repelled by the large electromagnet. The force of repulsion equals the weight of the ring, producing mechanical equilibrium. 21. If the light bulb is connected to a wire loop that intercepts changing magnetic field lines from an electromagnet, voltage will be induced which can illuminate the bulb. Change is the key, so to stay lit the electromagnet should be powered with ac. 22. Since all the electric resistance in this case is merely that of the wire itself (no other external load), twice the wire length means twice the resistance. So although twice the number of loops means twice the voltage, twice-as-much resistance results in the same current. 23. Induction occurs only for a change in the intercepted magnetic field. (a) The galvanometer will display a pulse when the switch in the first circuit is closed and current in the coil increases from zero.

3 (b) When the current in the first coil is steady, no current is induced in the secondary and the galvanometer reads zero. (c) The galvanometer needle will swing in the opposite direction when the switch is opened and current falls to zero. 24. The iron core increases the magnetic field of the primary coil. The greater field means a greater magnetic field change in the primary, and a greater voltage induced in the secondary. Furthermore, the core guides more magnetic field lines from the primary to the secondary. The effect of an iron core in the coils is the induction of appreciably more voltage in the secondary. 25. A transformer requires alternating voltage because the magnetic field in the primary winding must change if it is to induce voltage in the secondary. No change, no induction. 26. When the secondary voltage is twice the primary voltage and the secondary acts as a source of voltage for a resistive load, the secondary current is half the value of current in the primary. This is in accord with energy conservation, or since the time intervals for each are the same, power conservation. Power input = power output; or (current voltage) primary = (current voltage) secondary: with numerical values, (1 V) primary = ( 1 2 2V) secondary. (The simple rule power = current voltage is strictly valid only for dc circuits and ac circuits where current and voltage oscillate in phase. When voltage and current are out of phase, which can occur in a transformer, the net power is less than the product current voltage. Voltage and current are then not working together. When the secondary of a transformer is open, for example, connected to nothing, current and voltage in both the primary and the secondary are completely out of phase that is, one is maximum when the other is zero and no net power is delivered even though neither voltage nor current is zero.) 27. A transformer is analogous to a mechanical lever in that work is transferred from one part to another. What is multiplied in a mechanical lever is force, and in an electrical lever, voltage. In both cases, energy and power are conserved. Multiplied energy is a conservation of energy no-no! 28. A step-up transformer multiplies voltage in the secondary; a step-down transformer does the opposite decreases voltage in the secondary. 29. The hum heard when a transformer is operating on a 60 hertz ac line is a 60 hertz forced vibration of the iron slabs in the transformer core as their magnetic polarities alternate. The hum is greater if any other mechanical parts are set into vibration. 30. The name of the game with E&M is change. No change, no induction. Alternating current changes direction, normally at 60 Hz. 31. High efficiency requires that the maximum number of magnetic field lines produced in the primary are intercepted by the secondary. The core guides the lines from the primary through the secondary. Otherwise some of the magnetic field generated by the primary would go into heating metal parts of the transformer instead of powering the secondary circuit. 32. A physical space is between the two. They are linked, however, by changing magnetic fields the same in each coil. 33. The voltage impressed across the lamp is 120 V and the current through it is 0.1 A. We see that the first transformer steps the voltage down to 12 V and the second one steps it back up to 120 V. The current in the secondary of the second transformer, which is the same as the current in the bulb, is one tenth of the current in the primary or 0.1 A. 34. Oops! This is a dc circuit. Unless there is a changing current in the primary, no induction takes place. No voltage and no current are induced in the meter. 35. By symmetry, the voltage and current for both primary and secondary are the same. So 12 V is impressed on the meter, with a current of 1 A ac. 36. In a power line, the high voltage is between one wire and another, not from one end of a given wire to the other end. The voltage difference between one end of the wire and the other is actually small, corresponding to the small current in the wire. The voltage difference between the wires multiplied by the current gives the power transmitted to the load. The voltage difference between one end of a wire and the other multiplied by the current gives the (much smaller) power dissipated in the wire. So, in applying Ohm s law, it s important that the voltage and current are applied to the same part of the circuit.

4 37. No, no, no, a thousand times no! No device can step up energy. This principle is at the heart of physics. Energy cannot be created or destroyed. 38. The moving magnet will induce a current in the loop. This current produces a field that tends to repel the magnet as it approaches and attract it as it leaves, slowing it in its flight. From an energy point of view, the energy that the coil transfers to the resistor is equal to the loss of kinetic energy of the magnet. 39. As the magnet falls, it induces current that circles in the conducting pipe and is accompanied by its own magnetic field. The moving magnet is slowed by interaction with this induced field. 40. Slowness of fall is due to interaction of the magnetic field of the falling magnet with the field induced in the conducting tube. No conduction, as with a cardboard tube, means no induced field and no slowness of fall. 41. Motion of conducting sheets through a magnetic field induces swirling currents (eddy currents) with fields that interact with the magnet and slow motion. Such doesn t occur in non-conducting cardboard. 42. Induced currents in the bar are accompanied by their own magnetic fields, which interact with the magnet and slow motion. 43. A voltage difference is induced across the wings of a moving airplane. This produces a momentary current and charge builds up on the wing tips to create a voltage difference that counteracts the induced voltage difference. So charge is pulled equally in both directions and doesn t move. 44. Such a scheme violates both the 1st and 2nd laws of thermodynamics. Because of inherent inefficiencies, the generator will produce less electricity than is used by the adjoining motor to power the generator. A transformer will step up voltage at the expense of current, or current at the expense of voltage, but it will not step up both simultaneously that is, a transformer cannot step up energy or power. Like all practical systems, more energy is put in than is supplied for useful purposes.

5 45. The source of an electromagnetic wave is an oscillating electric charge. 46. Waving it changes the flux of the Earth s magnetic field in the coil, which induces voltage and hence current. You can think of the flux as the number of field lines that thread through the coil. This depends on the orientation of the coil, even in a constant field. 47. The incident radio wave causes conduction electrons in the antenna to oscillate. This oscillating charge (an oscillating current) provides the signal that feeds the radio. 48. The frequencies are the same. 49. Agree with your friend, for light is electromagnetic radiation having a frequency that matches the frequency to which our eyes are sensitive. 50. Electromagnetic waves depend on mutual field regeneration. If the induced electric fields did not in turn induce magnetic fields and pass energy to them, the energy would be localized rather than waved into space. Electromagnetic waves would not exist.

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