INDUCED MAGNETISATION 245 



S is very near 90. That is, the lines of force enter the sphere 

 very nearly normally when //, is large except near the equatorial 

 plane. 



If we use K instead of /x we obtain 



A == 7; 



Long straight wire placed in a field in air uniform 

 before its introduction. Experiment shows that with a long 

 straight wire placed in a uniform field the polarity is developed chiefly 

 near the ends.* Let us suppose that the induced poles are w, 

 that the radius of the wire is r, and that its length is /. Let us as an 

 admittedly rough approximation suppose that m are at the ends 

 If the original field is H, the field at the centre within the wire i 



H - 2ro/ = H - 8m// 2 . 

 v*/ 



If the magnetic susceptibility is K the intensity of magneti- 

 on is 



sation is 



8m 



and the total polarity on a section imagined to be made through 

 the centre will be 



The assumption that the poles are at the ends gives 



Sm 



2 TJ 



m = 7rr\ H - 



or m = 



1 + 



If /cr 2 // 2 is so small that we may put the denominator = 1 5 

 that is, if we may neglect the effect of the ends in calculating the 

 induction in the middle parts of the wire : 



2 H. 



This is nearly true if / is greater than 800r. 



Circular iron wire in a circular field. If a solenoid be 

 bent round into a circle, the intensity H of the field within it, at a 



* Ewing, Magnetic Induction, chap, ii ; Searle and Bedford, Phil. Trans., 

 A, 198, p. 98. 



