CHAP. IJ FLUX AND MAGNETOMOTIVE FORCE 13 



In a similar way, the magnetomotive force of a magnetic circuit 

 is used up bit by bit in the consecutive parts of the circuit. One " 

 can speak not only of the total magnetomotive force of a closed 

 circuit, but also of the magnetomotive force acting upon a certain 

 part of the circuit, and "of magnetomotive force per unit length of 

 the lines of force. Thus, for instance, if 1000 ampere-turns is con- 

 sumed in a uniform magnetic circuit 1 cm. long, the magnetomo- 

 t ive force per unit length of path is 250 ampere-turns. 



The magnetomotive force per unit length of path is called the mag- 

 intensity at a point, or the m.m.f. gradient, and is denoted by 

 //. Thus, if the circuit is uniform, the magnetic intensity at any 

 point is 



H-M/l, ....... (7) 



whore M is the magnetomotive force acting upon the length / of 

 the circuit. If the magnetic circuit is non-uniform, for instai 

 t he cross-section of the ring is different at different places, or if the 

 permeability is different at some parts of the circuit due to the 

 presence of iron, the m.m.f. gradient is different at different point s. 

 and at each point it is expressed by the equation 



H=dM/dl, ....... (8) 



where dM is the m.m.f. necessary for establishing the flux in the 

 length dl of the circuit. If M is in ampere-turns, and / is in centi- 

 meters, H is in ampere-turns per centimeter. 

 Eqs. (7) and (8) can be also written in the form 



M = Hl, ......... (9) 



and 



C h 11,11. 

 Ji\ 



(10) 



These formulae, expressed in words, simply mean that t he 

 n n t ive force acting upon a certain part of a magnetic circuit is the 

 line integral of the mapne tic intensity along the path, ,.r the sum nf 

 .m. f.s. used up in the elementary parts of the pat h. The rein 

 tion between M and // will become clearer to the student in the 

 various applications that follow. 



Prob. 14. What Is the magnet i<- intmsity it. pro!.. 



AllS. About TJ.~ ainpcre-t urns p.-i , m. of path. 



