96 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



4 PULL RELATIONS 



As shown in Section 2, the pull F ran be determined from the field 

 energy U by means of equation (2) . If the gap reluctance varies linearly 

 with X, this equation reduces to: 



as shown in the companion article. Equation (12) is Maxwell's law for 

 the pull between parallel plane surfaces of area A . As used here, 1/A has 

 the more general sense of the coefficient of x in a linear expression for 

 the gap reluctance. This equation is therefore applicable to all the cases 

 previously discussed, with A, of course, taken as A 2 or A3 for the rela- 

 tions applying to Figs. 5 and 6. As with the magnetization relations, it is 

 convenient to give separate consideration to the pull at low densities 

 and that at high densities. 



Pull for Linear Magnetizatio7i 



At low densities, where the magnetization relations are approximately 

 linear, the reluctance conforms to the eciuivalent magnetic circuit of 

 Fig. 4. In this case, (pa is given by J?/((Ro + x/A), and equation (12) be- 

 comes: 



F = - ^ 



2 ' 

 SttA' 



((Ro + I)' 



which may be written in the more familiar form : 



2ir{NIY 



F = 



A(«. + |V- (13) 



For conformity with (13) the pull for a gi\'en value of x should vary 

 as (AU) , giving a linear plot with a slope of two when plotted against 

 xV7 on logarithmic paper. Fig. 1 1 shows pull measurements of the relay 

 of Fig. 2 plotted in this way. The dashed lines tangent to the curves 

 have a slope of two, and conform in this respect to (13). It is convenient 

 to denote the pull indicated by these dashed lines as F'. Near and below 

 the point of tengency the actual pull /'' differs little from F'. The pull, 

 like the magnetization, is measured under the condition of initial de- 

 magnetization, which gives lower magnetization, and hence less pull, 

 than normally applies in actual use when the magnet has been previously 



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