10 



BELL SYSTEM TECHNICAL JOURNAL 



ments with the model showed a variety of other phenomena including 

 rotational hysteresis loss and its reduction to zero in high fields, the 

 effect of strain on magnetization, the existence of hysteresis in the 

 strain vs. magnetization diagram, the effect of vibration and the 

 existence of time lag and accommodation with repeated cycling of 

 the field. 



Ewing's general method may be illustrated by calculating the 

 magnetization curve and hysteresis loop for an infinite line of parallel 



MAGNETIC FIELD-STRENGTH 



Fig. 6 — A magnetization curve and hysteresis loops of a Ewing model 

 of 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 



IJ.A 



pm - 



(1) 



Here r is the distance between the centers of the magnets and the 

 P{d)'s are Legendre functions of the angle, 9, between the direction 

 of 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 of 

 magnets can easily be obtained by summing W for all pairs. 



Wi^ - 



2ixj 



[1.2OP2(0) + \MP,{9){llry 



^G. Mahajani, Phil. Trans. Roy. Soc, 228A, 63-114 (1929). 



(2) 



