MAGNETISM AND ELECTROMAGNETICS 47 



(cm.) 3 of air is taken as the unit of reluctance since unit m.m.f. 

 produces unit flux through it. 



When unit m.m.f. is applied across a (cm.) 3 of a magnetic 

 material of permeability /*, the flux produced is n lines, or the 

 induction density is n lines per square centimeter. The reluc- 



tance of the path is therefore - units. 



M 



If the length of the path is increased to I cm. the m.m.f. per 

 centimeter and the magnetizing force are reduced in the ratio 

 1 : I. The flux density is therefore reduced in the same ratio 

 and becomes 



an M /*,. 



9 = -y n = j lines per square centimeter. 



If now the section of the path is increased to A sq. cm. the m.m.f. 

 per centimeter and the magnetizing force are not changed, and 

 thus the induction density remains the same, but the flux through 

 the path is increased in proportion to the area; it is 



M Ml m.m.f. 



~rnA = = = 

 I I I reluctance 



Thus the reluctance of a path of uniform section is 



and is directly proportional to its length and inversely propor- 

 tional to its sectional area and to the permeability of the material 

 forming it. 



The equation connecting the m.m.f. acting on a path, the re- 

 luctance of the path and the flux through the path can be written 

 in three ways: 



CD * = !- ........ (74) 



the flux is equal to the m.m.f. divided by the reluctance; 



(2) M = $31, ........ (75) 



the m.m.f. is equal to the flux multiplied by the reluctance; 



(3) 31= f, ........ (76) 



the reluctance is equal to the m.m.f. divided by the flux. 



