34 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



comprising the drop ^^(R^ through the iron part of this path in series 

 with that across the two parallel paths followed by (Pla and <pa ■ 



Obviously, this pattern can be elaborated and made more exact by 

 more detailed consideration, particularly with respect to the leakage 

 field across the coil, which is not wholly confined to that between its 

 ends. In general, the field may be divided to any desired degree of refine- 

 ment into tubes of induction, which may then be treated as a network. 

 Thus, in principle, magnetic circuit representation may be used to 

 evaluate the magnetization relations to any desired degree of accuracy. 



Determination of the magnetization relations is thus reduced to the 

 evaluation of the reluctances appearing in the magnetic circuit. These 

 include both the reluctances of the iron parts for the major tubes of in- 

 duction directed along the axes of these parts, and the reluctances of the 

 air gaps and leakage paths. To evaluate these reluctances there are 

 needed (1) values of the permeability of magnetic materials, as related 

 to the flux density within them, and (2) expressions for the reluctances 

 of gaps and leakage paths. These two topics are discussed in the sections 

 following. While much of the material in these two sections is familiar, 

 it is reviewed here with emphasis on the analytical formulation of the 

 relations involved. 



4 MAGNETIZATION CHARACTERISTICS OF MATERIALS 



Magnetic properties are expressed either in terms of the relation be- 

 tween the permeability n and the induction 5, or of that between B and 

 the potential gradient //, from which the fx — B relation is derived. The 

 experimental determination of this relation is most commonly made 

 with a uniformly wound ring sample, in whic h B and H are uniform 

 throughout. 



For increasing magnetization, as in relay operation, the pertinent 

 B — H relation is that obtained with an initially demagnetized specimen, 

 shown as the solid line in the first cjuadrant in Fig. 4. This is the normal 

 magnetization curve. It is nearly coincident with the locus of the terminal 

 points (such as 1 and 2) of hysteresis loops obtained by cyclic magnetiza- 

 tion and demagnetization. 



The normal magnetization curv^e for magnetic iron is shown in Fig. 5 

 together with the corresponding ju — 5 curve. The permeability increases 

 from its initial value ^lo to a maximum value n' at a density B' cor- 

 responding to the "knee" of the B — H curve. (The single prime super- 

 script is used throughout this paper to designate values of the various 

 magnetic constants at maximum permeability.) Thereafter ju declines. 



