. The Bell System technical journal . r such a group of magnetsresemble in general form the actual curves of iron : they show a perme-ability first increasing then decreasing, and saturation and hysteresis. A magnetization curve and a hysteresis loop obtained ^ with a model of 130 magnets in square array, are shown in Fig. 6. Experi- J. A. Ewing summarized in Magnetic Induction in Iron and Other Metals,The Electrician, London, 3d ed. (1900). 3 J. A. Ewing and H. G. Klaassen, Phil. Trans. Roy. Soc, 184A, 985-1039 (1893). 10 BELL SYSTEM TECHNICAL JOURNAL ments with the model showed a variety of
. The Bell System technical journal . r such a group of magnetsresemble in general form the actual curves of iron : they show a perme-ability first increasing then decreasing, and saturation and hysteresis. A magnetization curve and a hysteresis loop obtained ^ with a model of 130 magnets in square array, are shown in Fig. 6. Experi- J. A. Ewing summarized in Magnetic Induction in Iron and Other Metals,The Electrician, London, 3d ed. (1900). 3 J. A. Ewing and H. G. Klaassen, Phil. Trans. Roy. Soc, 184A, 985-1039 (1893). 10 BELL SYSTEM TECHNICAL JOURNAL ments with the model showed a variety of other phenomena includingrotational hysteresis loss and its reduction to zero in high fields, theeffect of strain on magnetization, the existence of hysteresis in thestrain vs. magnetization diagram, the effect of vibration and theexistence of time lag and accommodation with repeated cycling ofthe field. Ewings general method may be illustrated by calculating themagnetization curve and hysteresis loop for an infinite line of parallel. MAGNETIC FIELD-STRENGTH Fig. 6—A magnetization curve and hysteresis loops of a Ewing modelof 130 pivoted magnets in square array. equally spaced magnets (Fig. 7a). It is done most simply by con-sidering first the magnetic potential energy * of a magnet of moment/i^and length I, in the field of a similar magnet: W = IJiA pm a ,2/2 pm - (1) Here r is the distance between the centers of the magnets and theP{d)s are Legendre functions of the angle, 9, between the directionof the moment of the magnet and the line joining the magnet centers. p^(e) = (1 + 2 cos 20)/4,p,(d) = (9 + 20 cos 26 + 35 cos 40)/64,, p^(e) = (50 + 105 cos 2d + 126 cos 49 + 231 cos 60)/512. The potential energy per magnet, Wi, for an infinite straight row ofmagnets can easily be obtained by summing W for all pairs. Wi^ - 2ixj [(0) + \MP,{9){llry ^G. Mahajani, Phil. Trans. Roy. Soc, 228A, 63-114 (1929). (2) THE PHYSICAL BASIS OF FERROMAGNETISM 11 The behavior of the lin
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