04 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



magnetic pull on two parallel planes with a field of luiiform densitj^ ^pa 

 between them. It can be directly derived from the fact that the gap 

 energy is J(/?G/(87r), with 3^ = XipGl Ai . The change in this energy for a 

 differential change dr of the gap equals F dx, so that F is given by equa- 

 tion (27). Derived in this way, it is apparent that (27) depends only on 

 the field in the gap, and is quite independent of the density in the mag- 

 netic material. 



Pull in Terms of Applied mmf 



In the low density region, where (R is substantially a function of x 

 only and the magnetization curves are linear, W — U, and hence the 

 expression for F given by equation (8) becomes: 



dx\6\/ 



This expression for the pull in the linear region is known as the equation 

 of Perrot and Picou.^ As NI = (R^/(4x), it is identical with (26). 



For the magnetic circuit of Fig. 23, substitution in (28) of the ex- 

 pression for (R given by (24) gives the following expression for the pull : 



^^, ^ 27r(iV/)' 



a(^(R, -f ^) 



X y ' (29) 



In the low density region, the reluctance can always be expressed in 

 terms of the equivalent values of Fig. 25. Using the equivalent values of 

 closed gap reluctance (Ro and of pole face area .4, the pull is given by 

 equation (29). This expression is therefore of general application in the 

 low density region, and is the most convenient equation to use for this 

 purpose. 



High Density Pidl 



It was shown above that equation (27) can be derived directly from 

 the expression for the field energy associated with the gap. This expres- 

 sion is quite independent of the reluctance in the rest of the magnetic 

 circuit, and is therefore eciually applicable in the low and high density 

 regions. This essentially physical argument shows that (20) and (27) 

 are applicable through the full range of magnetization. 



The same result can be obtained from equation (7) by substituting in 

 it the expression for U given by (3), and substituting al^/(47r) for NI. 



