Obrázky stránek
PDF
ePub

nating current-where the current is continually changing-self-induction plays a very important part. Usually the current in such a circuit cannot be computed by Ohm's law when the voltage and resistance are known.

The interlinkage of a coil is equal to the total number of lines threading through the coil multiplied by the number of turns of wire. If the coil does not contain an iron core,

[blocks in formation]

where L is a constant called the coefficient of self-induction. In any circuit E. M. F. of self-induction = L x rate of change of I.

(82) 1

If the electromotive force is in volts and the current in amperes, L is measured in henries.

The common method of developing electrical energy is by the use of either the direct-current dynamo or the alternating-current dynamo. Both these types utilize induced electromotive forces.

By using alternating currents of more than one phase, rotating magnetic fields can be produced. Any conductor placed in a rotating magnetic field has induced currents in it. There is thus produced a current-magnetic-field force that produces a torque tending to rotate the conductor in the direction in which the magnetic field is rotating. The most common type of alternating-current motor is the induction motor. The armature of this type is placed in a rotating magnetic field, which induces currents in it. Since these currents are in a magnetic field, there are current-magneticfield forces acting which produce rotation of the armature.

PROBLEMS

1. The north-seeking pole of a bar magnet is plunged from above into a coil lying on a table. Is the induced E. M. F. in the coil, as one looks down, clockwise or counterclockwise?

2. The plane of a coil of 200 turns, and 200 sq. cm. in area, is perpendicular to a magnetic field the strength of which is 100 C.G.S. units. Compute the E. M. F. in volts when this field is cut out in one tenth of a second.

3. 50,000 magnetic lines of force are cut out of a coil of 100 turns in 1/100 sec. Compute the mean E. M. F. in volts.

4. A circular coil, of radius 20 cm. and with 200 turns, lying on the floor, is turned over in 0.2 sec. Compute the average E. M. F. in volts if the vertical component of the earth's field is 0.55 C. G. S. unit.

5. A coil (Fig. 315) is rotated continuously about an east-and-west axis. (Assume the earth's field to be horizontal.) (a) In what direction is the induced E. M. F. on the side of the coil that moves downward? (b) At what places in its rotation is the E. M. F. a maximum? (c) a minimum?

6. An east-and-west wire falls to the ground with an average speed of 250 cm./sec. If the horizontal component of the earth's magnetic field is 0.20, find the E. M. F., in volts, induced in 100 m. of the wire.

7. A wire 10 cm. long moves across a uniform magnetic field of 10,000 lines per square centimeter at such a rate that an E.M.F. of 0.5 volt is induced in the wire. Compute the speed of the wire.

East

Up

Down

West

FIG. 315

8. What is the induced E. M.F. in volts in the iron axle of a train traveling northward at 60 mi./hr.? (The length of the axle is 4 ft. 8 in., and the vertical component of the earth's magnetic field is 0.55 C. G.S. unit.)

9. The primary of an induction coil produces 50,000 magnetic lines. If this field disappears in 0.01 sec., how many turns must the secondary winding have to produce 10,000 volts?

10. The secondary of an induction coil has 200,000 turns. In how short a time must 100,000 magnetic lines be removed from this coil to produce 15,000 volts?

11. The north-seeking pole of a magnet is held above an east-and-west wire. (a) If this wire is moved sidewise northward, what will be the direction of the induced E. M. F.? (b) If the wire had a current flowing eastward, what would be the direction of the current-magnetic-field force acting on the wire? (Neglect the effect of the earth's field.)

✔ 12. A coil of 200 turns and an area of 200 sq. cm. is revolving at the rate of 50 revolutions per second about an axis perpendicular to a magnetic field the strength of which is 4000 C.G.S. units. What is the average E.M.F., in volts, when the coil rotates through 180°, starting at a point where the coil has a maximum number of lines passing through it?

13. A metallic door in an east-and-west wall is hinged at the west edge. It is opened southward and swung through 180°. (a) What is the direction of the induced currents in the door? (b) At what point of the motion will the induced E. M. F. be the largest ?

14. How many revolutions per minute must a 40-pole alternating-current generator have, in order to produce a 60-cycle current ?

|

CHAPTER XXXIV

MAGNETIZATION OF IRON

Introduction, 496. Magnetizing force (H), 497. Magnetic induction (B), 498. Curves of magnetization, 499. Magnetic permeability, 500. Diamagnetic substances, 501. Magnetic hysteresis, 502. Magnetic circuits, 503.

496. Introduction. On account of the large number of practical applications of magnetism of iron, a knowledge of the simpler facts of the behavior of iron in magnetic fields is important. Certain concepts are used in practically all the literature pertain

[merged small][graphic][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small]

meaning of these terms can be more clearly understood by describing some experiments with induced electromotive forces.

Let us consider a long solenoid, or helix, AB of Fig. 316, around which is another winding, a secondary, CD. When a current flows through the primary, AB, magnetic lines are produced which run through the solenoid and, at the same time, interlink the secondary coil, CD. Whenever the current in AB is made or broken, the changing magnetic field produces in CD an induced electromotive force, and hence a momentary current in the circuit (not shown in the figure) connected to CD.

It can be proved* that the total quantity of electricity, Q (average current times the time of flow), flowing in the secondary

* A simple proof is given here. is the flux, or the total number of magnetic lines cutting across the secondary coil when the current in the primary is made or circuit when the primary current is made or broken is given by the expression

2

Φ

Q=N2R

2

[blocks in formation]

where R2 is the resistance of the secondary circuit, N2 the number of turns of wire in the secondary, and I the flux, or the total number of magnetic lines running through the primary when the current is flowing in it.

21

It is not difficult to measure by a ballistic galvanometer* the quantity, Q, flowing in the secondary. The number of turns, N. and the resistance, R2, of the secondary circuit can also be found. Hence everything in equation (83) can be measured except Ф. Since it is the only unknown quantity, its value can be easily computed. By a simple transformation of this equation the value of

[merged small][ocr errors][merged small][merged small][merged small]

The reason that equations (83) and (84) have been stated here is to point out that we have available an experimental method for determining flux, or the number of magnetic lines.

Let us suppose that the flux through the helix has been measured in this way. If iron is placed inside the helix, and the experiment

broken. When the primary current is broken, there is induced in the secondary an average electromotive force equal to

Φ N 2t'

2

where N N2 is the number of turns in the secondary coil, and t is the length of time the lines are cutting across the secondary.

Average current in the secondary =

average E. M.F.
R2

Substituting in this the value of the average electromotive force,

[blocks in formation]

Both Q and R, must be measured in C.G.S. electromagnetic units.

2

* A ballistic galvanometer is one where the first "throw" is used-the maxi

mum, not the steady deflection.

repeated, a much larger induced electromotive force is produced in CD, and a larger Q flows. This shows that the magnetic flux is much greater when iron is present. By the aid of equation (84) we can then compute the flux in the iron, or, in other words, determine the magnetic condition of the iron. This is perhaps the simplest method of doing it. In the following sections this experimental method will be made the basis for explaining the meaning of the magnetic terms commonly used.

497. Magnetizing force (H). The strength of the magnetic field at any place is equal to the force acting on a unit north-seeking magnetic pole at the place in question. This definition is, by its nature, limited to a field in air. For example, in the solenoid referred to in the last section, this definition can be directly applied to a point in the field inside the solenoid when there is no iron at that point. It has been pointed out (sect. 365) that in air the number of magnetic lines per square centimeter is always numerically equal to the strength of the field. For example, if one should take the total number of lines running through the primary (as found by the experiment of the last section) and divide it by the sectional area of the core of the primary in square centimeters, he would get the number of lines per square centimeter. If there were no iron in the core, this number would be equal to the strength of the magnetic field in the solenoid. The strength of the field is often called the magnetizing force, and is denoted by the letter H.

Let us now consider the case where iron is placed inside the secondary. The magnetic flux, or the total number of magnetic lines, would be greatly increased; but what we have called the strength or magnetizing force of the field would be the same as before, for it depends on the current, which has not been changed. Hence we may say that the magnetizing force, H, in the iron is equal to the number of magnetic lines per square centimeter which would be present if the iron were absent.*

*This is not accurate for cases where a short piece of iron is used. The ends of all pieces of iron have poles when magnetized, and these poles usually tend to decrease H in the iron. The poles of short pieces of iron have a demagnetizing effect. In cases where the ends are far apart or where there are no ends (and hence no poles, as in transformers) the statement is exact.

« PředchozíPokračovat »