46 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



Leakage Reluctances 



An accurate estimate of the reluctance between magnetic members 

 requires a detailed knowledge of the flux paths. Since these are only 

 knoAvn accurately in cases for which solutions of the field equations are 

 available, approximations are obtained by assuming geometrical paths 

 such as straight lines, arcs of circles, ellipses, and so forth. From these 

 assumed paths the reluctance is calculated by means of the expression 

 {/na. The choice of suitable approximations depends largely upon a 

 knowledge of the flux paths in certain simple cases which can be analyzed 

 rigorously, and upon the experimental exploration of more complicated 

 fields. 



The method is satisfactory provided the separation between the mag- 

 netic members is small. It has been used to derive the relations given in 

 Figs. 10 and 11. A further application of this method gives the reluctance 

 between the side surfaces of coaxial cylinders, as shown in Fig. 13. This 

 is useful in estimating the leakage reluctance shunting an air gap. 



Where the separation between magnetic members is large, it is difficult 

 to estimate the configuration of the flux paths. It is then necessary to 

 employ the relations applying to the most nearly similar configuration 

 for which a rigorous solution is known. Two such solutions are applicable 

 to a number of problems. The first is the case of two infinitely long, 

 parallel, equipotential, circular cylinders, shown in Fig. 14. The second 

 is the case of two equipotential spheres of equal size, shown in Fig. 15. 



h- — 



Fig. 12 — Effective pole face area referred to gap x at f. 



