CHAP. I] FLUX AND MAGNETOMOTIVE FOR E 15 



The last expression, according to eqs. (7) and (11), can be written 

 simply as 



H = Bv, (15) 



or, since v=*l/p t 



B=fjtH (16) 



Eqs. (15) and (16) state Ohm's law for a unit magnetic path, for 

 instance, a path one centimeter long and one square centimeter in 

 cross-section. H is the magnetomotive force between the oppo- 

 site faces of the cube, fi is the permeance of the cube, and B is the 

 flux passing through it. The reader will remember similar equa- 

 tions U=?F and D = *F for the unit electrical conductor and the 

 unit prism of a dielectric respectively. 



Instead of beginning the theory of the magnetic circuit with 

 eq. (1) and developing it into eq. (16), it is possible to begin it with 

 eq. (16). Namely, the known magnetic phenomena show that 

 at each point in the medium there is a magnetic intensity H which 

 is the cause of the magnetic state, and that the effect is measured 

 by the flux density B; p is the physical constant which shov, 

 proportionality between H and B. The magnetic circuit is then 

 assumed to be built up of infinitesimal tubes of flux in series and 

 in parallel, and finally eq. (1) is obtained. 



Prob. 15. What is the flux density in prob. 1J ' 



A us. 534 maxwells per square centimeter (.534 gaussi 



Prob. 16. How many ampere-turns per pole are required to establish 

 a flux -if 7 kilolines ; PQ centimeter in the air-pap of a 



machi l>eing 3 mm.? Solution: Ac.-urding to 



//- 7000/1. 25 -5600 ampere-turns per centimeter of length. Hen.e the 



dred nunX U 5600X0.3 -1680 ampen-tu; 



9. Reluctances and Permeances in Series and in Parallel. In 

 practin>. <>nc lias to deal mostly with magnetic circuits of irregular 

 form, f>r instance, those nf electric machines (Vii:. -I) in which 

 the flux is established partly in air and partly in iron, each of vary- 

 ing cross-sect ion. The circuit consists in this case of several reluc- 

 tances in series. One may say, tor instance, that the total 



:otive force required in this machine, per in: jcuit. 



is 80(X) ampere-turns, of which 6000 are used in the air-gap, 1500 



in the tit-Id frame, and 500 in the armature. I I ii- is analogous to 



n'n- between the total e.m.f. of an elec; : ,1 . and the 



voltage drop in the various parts of tin circuit. 



