MAGNETIC METHODS 69 



U > 2m dt 



|n s|Jn Sp m- m+l^ 



2d* 



Fig. 7. — Two magnetic particles end to end, or side by side, have a moment M — 2 mds. 



If we place n similar magnetic particles end to end, the effect pro- 

 duced will be the same as a line magnet of length nds and M = mnds. 



By experiment it has been found possible to produce two complete 

 magnets by cutting any magnet between the poles ; no matter where the 

 cutting takes place, two magnets are produced. Furthermore, their relative 

 strengths are proportional to their lengths. 



+ 



^ 



SMN s In s n 



(b) 



-f- - -f - 



Fig. 8. — (a) « magnetic particles end to end produce a line magnet of length nds. 

 (b) Cutting a magnet between its poles makes two magnets. 



Thus we see that a magnet must be considered as consisting of small 

 magnetic particles. It is not necessary for mathematical analysis to con- 

 sider these particles as molecules or even smaller than molecules. Any 

 particle so small that the space occupied by it is infinitesimal may be con- 

 sidered as a magnetic particle. 



Bar Magnet. — For most practical purposes, a bar magnet may be con- 

 sidered as a straight line magnet, with its magnetic poles located at points 

 situated at a distance of 1/12 of the length of magnet from each end. These 

 relationships are illustrated in Figure 9. 



The longer a bar magnet is in comparison to its thickness, the nearer 

 the poles are to its ends. Theoretically an infinitely thin magnet would 

 show no magnetic effects at any place along it other than at the ends where 

 the poles would be situated. Such a magnet is called a simple magnet. 



Referring to Figure 9, if the physical length of the bar magnet L is 

 12 cm., the dimension (I), or one-half the distance separating the poles, 

 would be 5 cm. The figure shows also that the two poles would be, in this 



