In fig. 15 (J. A. Fleming, Magnets and Electric Currents, p. 193) are shown three very different types of hysteresis curves, characteristic of the special qualities of the metals from which they were respectively obtained. The distinguishing feature of the first is the steepness of its outlines; this indicates that the induction increases rapidly in relation to the magnetic force, and hence the metal is well suited for the construction of dynamo magnets. The second has a very small area, showing that the work done in reversing the magnetization is small; the metal is therefore adapted for use in alternating current transformers. On the other hand, the form of the third curve, with its large intercepts on the axes of H and B, denotes that the specimen to which it relates possesses both retentiveness and coercive force in a high degree; such a metal would be chosen for making good permanent magnets.
Several arrangements have been devised for determining hysteresis more easily and expeditiously than is possible by the ballistic method. The best known is J. A. Ewing’s hysteresis-tester,[22] which is specially intended for testing the sheet iron used in transformers. The sample, arranged as a bundle of rectangular strips, is caused to rotate about a central horizontal axis between the poles of an upright C-shaped magnet, which is supported near its middle upon knife-edges in such a manner that it can oscillate about an axis in a line with that about which the specimen rotates; the lower side of the magnet is weighted, to give it some stability. When the specimen rotates, the magnet is deflected from its upright position by an amount which depends upon the work done in a single complete rotation, and therefore upon the hysteresis. The deflection is indicated by a pointer upon a graduated scale, the readings being interpreted by comparison with two standard specimens supplied with the instrument. G. F. Searle and T. G. Bedford[23] have introduced the method of measuring hysteresis by means of an electro-dynamometer used ballistically. The fixed and suspended coils of the dynamometer are respectively connected in series with the magnetizing solenoid and with a secondary wound upon the specimen. When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre. For specimens of large sectional area it is necessary to apply corrections in respect of the energy dissipated by eddy currents and in heating the secondary circuit. The method has been employed by the authors themselves in studying the effects of tension, torsion and circular magnetization, while R. L. Wills[24] has made successful use of it in a research on the effects of temperature, a matter of great industrial importance.
C. P. Steinmetz (Electrician, 1891, 26, p. 261; 1892, 28, pp. 384, 408, 425) has called attention to a simple relation which appears to exist between the amount of energy dissipated in carrying a piece of iron or steel through a magnetic cycle and the limiting value of the induction reached in the cycle. Denoting by W the work in ergs done upon a cubic centimetre of the metal (= 1/4π ∫ H dB or ∫ H dI), he finds W = ηB1.6 approximately, where η is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction. The value of the constant η ranges in different metals from about 0.001 to 0.04; in soft iron and steel it is said to be generally not far from 0.002. Steinmetz’s formula may be tested by taking a series of hysteresis curves between different limits of B, measuring their areas by a planimeter, and plotting the logarithms of these divided by 4π as ordinates against logarithms of the corresponding maximum values of B as abscissae. The curve thus constructed should be a straight line inclined to the horizontal axis at an angle θ, the tangent of which is 1.6. Ewing and H. G. Klaassen (Phil. Trans., 1893, 184, 1017) have in this manner examined how nearly and within what range a formula of the type W = ηBε may be taken to represent the facts. The results of an example which they quote in detail may be briefly summarized as follows:—
| Limits of B. | Hysteretic Constant. η | Index. ε (= tan θ) | Degrees. θ |
| 200 to 500 | ... | 1.9 | 62.25 |
| 500 to 1,000 | ... | 1.68 | 59.25 |
| 1,000 to 2,000 | ... | 1.55 | 57.25 |
| 2,000 to 8,000 | 0.01 | 1.475 | 55.75 |
| 8,000 to 14,000 | 0.00134 | 1.70 | 59.50 |
It is remarked by the experimenters that the value of the index ε is by no means constant, but changes in correspondence with the successive well-marked stages in the process of magnetization. But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index ε = 1.6, and assigning a suitable value to η, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small. Alexander Siemens (Journ. Inst. Eng., 1894, 23, 229) states that in the hundreds of comparisons of test pieces which have been made at the works of his firm, Steinmetz’s law has been found to be practically correct.[25] An interesting collection of W-B curves embodying the results of actual experiments by Ewing and Klaassen on different specimens of metal is given in fig. 16. It has been shown by Kennelly (Electrician, 1892, 28, 666) that Steinmetz’s formula gives approximately correct results in the case of nickel. Working with two different specimens, he found that the hysteresis loss in ergs per cubic centimetre (W) was fairly represented by 0.00125B1.6 and 0.00101B1.6 respectively, the maximum induction ranging from about 300 to 3000. The applicability of the law to cobalt has been investigated by Fleming (Phil. Mag., 1899, 48, 271), who used a ring of cast cobalt containing about 96% of the pure metal. The logarithmic curves which accompany his paper demonstrate that within wide ranges of maximum induction W = 0.01B1.6 = 0.527I1.62 very nearly. Fleming rightly regards it as not a little curious that for materials differing so much as this cast cobalt and soft annealed iron the hysteretic exponent should in both cases be so near to 1.6. After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal of a crowd of small compass needles (representative of magnetic molecules) is proportional to the 1.6th power of the aggregate maximum magnetic moment before or after completion of the cycle.
| Fig. 16. |
| a, Fine steel wire 0.257 mm. diam. b, Fine iron wire 0.34 mm. diam. c, Fine iron wire 0.2475 mm. diam. d, Thin sheet iron 0.47 mm. thick. e, Iron wire 0.602 mm. diam. f, Iron wire 0.975 mm. diam. g, Sheet iron 1.95 mm. thick. h, Thin sheet iron 0.367 mm. thick. i. Very soft iron wire. |
The experiments of K. Honda and S. Shimizu[26] indicate that Steinmetz’s formula holds for nickel and annealed cobalt up to B = 3000, for cast cobalt and tungsten steel up to B = 8000, and for Swedish iron up to B = 18,000, the range being in all cases extended at the temperature of liquid air.
| Fig. 17. |
The diagram, fig. 17, contains examples of ascending induction curves characteristic of wrought iron, cast iron, cobalt and nickel. These are to be regarded merely as typical specimens, for the details of a curve depend largely upon the physical condition and purity of the material; but they show at a glance how far the several metals differ from and resemble one another as regards their magnetic properties. Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H + 4πI, and 4πI (except in extreme fields) greatly exceeds H in numerical value, we may generally, without serious error, put I = B/4π, and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred. A scale for the approximate transformation for the curves in fig. 12 is given at the right-hand side of the diagram, the greatest error introduced by neglecting H/4π not exceeding 0.6%. A study of such curves as these reveals the fact that there are three distinct stages in the process of magnetization. During the first stage, when the magnetizing force is small, the magnetization (or the induction) increases rather slowly with increasing force; this is well shown by the nickel curve in the diagram, but the effect would be no less conspicuous in the iron curve if the abscissae were plotted to a larger scale. During the second stage small increments of magnetizing force are attended by relatively large increments of magnetization, as is indicated by the steep ascent of the curve. Then the curve bends over, forming what is often called a “knee,” and a third stage is entered upon, during which a considerable increase of magnetizing force has little further effect upon the magnetization. When in this condition the metal is popularly said to be “saturated.” Under increasing magnetizing forces, greatly exceeding those comprised within the limits of the diagram, the magnetization does practically reach a limit, the maximum value being attained with a magnetizing force of less than 2000 for wrought iron and nickel, and less than 4000 for cast iron and cobalt. The induction, however, continues to increase indefinitely, though very slowly. These observations have an important bearing upon the molecular theory of magnetism, which will be referred to later.