MAGNETIC METHODS 73 



Hence there must be Atv lines of force coming from pole m to provide one 

 line for each of the An square centimeters of the surface of said unit 

 sphere. 



A magnetic pole of strength m would originate m • A-n- lines of force. 

 It would create a magnetic field of strength m at a distance of 1 centimeter. 

 The above discussion introduces implicitly the concept of fractional parts of 

 a line of force. In fact, the unit magnetic pole considered would generate 

 12.5664 lines of force, or Air lines, using tt as equal to 3.1416. 



Another characteristic of magnetic fields that relates also to lines of 

 force and their number per unit section is expressed in Equation 1. This 

 equation indicates that magnetic force varies inversely as the square of the 

 distance. Referring to the unit magnetic pole of Figure 10, if a sphere of 

 2 cm. radius were inscribed around it, the surface area of the sphere would 



\\ 





'/.'^-.f • 







y ,;■ 







Fig. 11. — Examples of magnetic fields and lines of force. 

 Note: The arrows indicate the direction in which a free + pole would move. 



be 167r (i.e. 47r-4), or four times as great as in the case of the unit sphere. 

 With only A-n lines of force coming from the unit magnetic pole at the 

 surface of the sphere of 2 cm. radius, there would be 0.25 of a line per 

 square cm. A field of 0.25 line per square cm. is obviously only 34 as 

 strong as a field with 1 line per unit of section. 



Using the relation of Equation 1 : that F = \^ , in its application to 



the problem, Wi and m^ are unit poles. With Wi fixed, and m^ positioned 

 first at a distance r = 1 cm., (or on the unit sphere) and second at a distance 

 r — 2 cm. (or on the larger sphere) : 



For the first case : _ mi - m^ _ 1 • 1 _ 1 _ ^r _ 1 



(r=lcm.) ^- r^ - —^ - l - H - I 



