270 ELEMENTARY LESSONS ON [CHAP. v. 



a maximum is reached shows that the coefficient of 

 magnetisation k is not constant, but that it is less 

 at higher degrees of magnetisation than at lower. A 

 piece of nickel placed in a field of small intensity is 

 magnetised about five times as strongly as a piece of 

 iron of the same size would be, but in a strong field the 

 iron would be the more strongly magnetised. Exact 

 measurements of the different values of k in fields of 

 different intensity are yet wanting. 



314. Potential due to a (Solenoidal) Magnet. 

 A long thin uniformly magnetised magnet exhibits 

 free magnetism only at the two ends, and acts on 

 external objects just as if there were two equal quantities 

 of opposite kinds of magnetism collected at these two 

 points. Such a magnet is sometimes called a solenoid 

 to distinguish it from a magnetic shell (Art. 107). 

 Ordinary straight and horse-shoe shaped magnets are 

 imperfect solenoids. The magnetic potential due to a 

 solenoid, and all its magnetic effects, depend only on 

 the position of its two poles, and on their strength, and 

 not on the form of the bar between them, whether straight 

 or curved. In Art. 310 (c) was given the rule for finding 

 the potential due to a system of poles. Suppose the 

 two poles of a solenoid have strengths + m and m 

 (taking S. -seeking pole as of negative value), and that 

 the respective distances of these poles from an external 

 point P, are r and r 2 : then the potential at P will be, 



n 



Suppose a magnet curled round until its N. and S. 

 poles touch one another : it will not act as a magnet 

 on an external object, and will have no " field " (Art. 

 105) ; for if the two poles are in contact, their distances 

 r^ and r 2 to an external point P will be equal, and 



/ -- - J W i\\ fog __ Q 



V r r 2 / 



315. Potential due to a Magnetic Shell. It 

 can be demonstrated that the potential dtie to a magnetic 



