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The series motor. The moving coil, or armature, of a motor is not placed between the poles of a permanent magnet but between those of an electromagnet which is magnetized by a current from the same source of supply that gives the current to the rotating coil. The advantage is obvious, for an electromagnet gives a much stronger magnetic field. There are several ways of connecting the rotating coil and the magnet coils. The simplest of these is shown diagrammatically in Fig. 291. The magnet coils A and B, called the field windings, are in series with the revolving coil C, or armature. This

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the current flows in on one wire to one brush. There it divides, part going through the armature C, the other part going through the field coils. These two currents unite again at the other brush. In this type of motor the field magnets are wound with many turns of fine wire.

The compound motor. The compound motor is a combination of the series and shunt motors. There are two windings on each pole. One of these is of fine wire in many turns, and is connected like that of the shunt motor. The other winding consists of a few turns of large wire which is connected in series.

Each of these types of motor has its own special advantages. The series motor will run at a high speed when it has a light load and at a low speed with a heavy load. The shunt motor has a fairly constant speed for different loads. A full account of the advantages and disadvantages is obviously beyond the scope of this book.

471. Summary. If the current is flowing in a circular coil of radius r and N turns, the strength of field H at the center is given by equation (74),

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where the current, i, is measured in C. G. S. electromagnetic units.

If the current is measured in amperes and denoted by I, then (equa

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At a distance r from a long straight wire carrying a current i, measured

in C.G. S. electromagnetic units (equation (75)),

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or, when current is measured in amperes (equation (75 a)),

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H =

10 r

At the center of a long solenoid (equation (76)),

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where i is the current in C. G. S. electromagnetic units, N the total number of turns, and I the length of the solenoid.

The C.G.S. electromagnetic unit of current is defined in terms of the strength of the magnetic field it will produce. In the text, equation (74) is chosen for defining this unit.

Because a current flowing in a wire produces a magnetic field, it will exert mechanical forces on magnets close by. Since the current exerts a force on the magnet, the latter must react with a force which shows itself as a force on the wire which carries the current. Hence it follows that there will be forces acting on current-carrying conductors which are placed in magnetic fields. These forces are called current-magnetic-field forces.

The current-magnetic-field force is always in a direction perpendicular to the wire and also perpendicular to the magnetic field in which the wire is placed. Two methods are suggested in the text for finding the direction of this force.

When a straight wire carrying a current, i, measured in C.G.S. electromagnetic units, is placed in and at right angles to a uniform magnetic field, the current-magnetic-field force on the wire is (equation (77))

F = Hil,

where H is the strength of the field, and I is the length of the wire.

When two parallel wires are near each other, each wire produces a magnetic field near the other wire, so that each wire is in a magnetic field. These fields will be perpendicular to the wires, and a force, given by equation (77), will act on each wire. If the currents are flowing in the same direction, there is attraction; if they are flowing in opposite directions, there is repulsion.

A coil of wire carrying a current and placed in a magnetic field tends to set itself in such a position that the maximum number of magnetic lines thread through the coil.

Explanations of moving-coil galvanometers, direct-current ammeters, and voltmeters are given in this chapter.

Electric motors apply the forces developed when wires carrying currents are placed in strong fields.

ix

PROBLEMS

1. A magnetic pole of strength 40 C. G. S. units is placed at the center of a circular coil which has a radius of 30 cm. and 10 turns of wire. Find the force on the pole when the current is 5 amperes.

2. A magnetic pole of 20 C. G. S. units is placed 5 cm. away from a long straight wire. What will be the force on this pole when the current in the wire is 20 amperes?

3. A straight wire carrying a current of 20 amperes runs perpendicularly through a magnetic field the strength of which is 5000 C.G.S. units. How much force is acting on each centimeter of length of the wire ?

4. A north-seeking pole is placed just below an east-and-west wire carrying a current eastward. What is (a) the direction of the current-magneticfield force on the wire? (b) the force on the pole? (Neglect the effect of the earth's magnetic field.)

5. An east-and-west wire carries a current of 10 amperes westward. (a) If the strength of the earth's field is 0.6 C. G. S. unit, what is the currentmagnetic-field force on 1 m. of this wire? (b) If the angle of dip is 70°, what is the direction of this force?

6. A rectangular coil, 10 by 20 cm., of 15 turns, is hung in the earth's magnetic field with the plane of the coil parallel to the earth's field and in a vertical position. The current, 5 amperes, flows down on the north side of the coil and up on the south side. The horizontal component of the earth's field is 0.18 C.G.S. unit. (a) What is the direction of the current-magnetic-field force on the north edge of the coil? (b) Compute the torque acting about a vertical axis on the coil.

7. A long vertical wire carries a current of 25 amperes directed upward. A north-seeking pole of strength 120 C.G.S. units is placed 5 cm. north of the wire. (a) What will be the direction of the current-magnetic-field force? (Neglect the effects of the earth's field.) (b) What will be the magnitude of the force on the wire? (Find the magnitude of the force on the pole, as in Problem 2.)

8. An ammeter has a moving coil which, including connecting wires, has a resistance of 8.0 ohms. A current of 0.01 ampere through this coil will give a full-scale deflection. What must be the resistance of a shunt in order that a full-scale deflection may be produced by a total current of 10 amperes?

9. If the moving coil has a resistance of 5 ohms and gives a full-scale deflection for 0.011 ampere, how much resistance must be placed in series with it to make a voltmeter which will give a full-scale deflection with 3 volts?

10. What must be the value of the series resistance in order to make the instrument of Problem 9 a voltmeter which gives a full-scale deflection with 100 volts?

11. A voltmeter having a range of 0-5 volts has a total resistance of 450 ohms. What must be done to make the range 0-50 volts?

12. Two accurate voltmeters which have resistances of 10,000 and 15,000 ohms respectively are connected in series across a direct-current power circuit of 100 volts. What will the two instruments read?

CHAPTER XXXIII

INDUCED ELECTROMOTIVE FORCES

Introduction, 472. Faraday's experiment, 473. Other experiments, 474. General case, 475. A quantitative law of induced electromotive forces, 476. Induced electromotive forces produced by means of alternating currents, 477. The transformer, 478. A wire cutting magnetic lines, 479. Rules for the direction of the induced electromotive force, 480. Lenz's law, 481. Relationship between the current-magnetic-field force and the direction of the induced electromotive force, 482. The Arago experiment, 483. The induction coil, 484. The telephone transmitter, 485. A simple telephone circuit, 486. Self-induction, 487. Inductance, or coefficient of selfinduction (L), 488. Energy in a magnetic field, 489. Dynamos, 490. The counter electromotive force of a motor, 491. The alternating-current dynamo, 492. Rotating magnetic fields: the induction motor, 493. Longdistance transmission of energy, 494. Summary, 495.

472. Introduction. The discovery of the voltaic cell opened a new era in electricity, for before that time only electric currents of insignificant magnitude could be produced. But even the voltaic cell is not suited for developing large amounts of electrical energy. The discoveries of Faraday and Henry opened up better methods for the production of electrical energy in great quantities. In fact, tremendous industrial applications of electricity today are possible only because of the discoveries of these men.

This chapter explains the principles involved in these discoveries, and their applications in such things as the dynamo, the transformer, and the telephone.

473. Faraday's experiment. Faraday wound two coils on an iron ring (see Fig. 293). These two windings were insulated from each other so that the current from one coil could not flow over into the other. Faraday found that when a current was starting in the coil connected to the battery, there was a momentary deflection of the galvanometer, G. He found also that when the current was

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