CHAP. I] FLUX AND MAGNETOMOTIVE FORCE 19 



are in parallel and should be added; hence, integrating the foregoing 

 expression between the limits }Z), and $D, we get: (P - (//A/2*) Ln( /),/!),). 

 Prob. 26. Show that, when the radial thickness & of a ring is small as 

 compared to its mean diameter D, the exact expression for permeance, 

 obtained in the preceding problem, differs but little from the approxi- 

 mate value, //A&/7rZ), used before. Solution: Using the expansion, 

 *Ln[(l +z)/(l -x)]=x + $x*+l3*+ ... and putting 



we get (P = (,Afc/*D)[l +$(b/Dy + l(b/Dy+ . . . ]. When the ratio of 

 6 to D is small, all the terms within the brackets except the first one, 

 can be neglected. 



Prob. 27. Show that the answer to prob. 11 is 2.1 per cent high on 

 account of the density being assumed there as uniform throughout the 

 cross-section of the ring. 



