MAGNETIC DKSIGX OK HKLAYS 



43 



.1 ir Gap Between Parallel Planes 



For magnetic paths in which the flux is uniform, it was shown above 

 that the rehietance is gi\en by (17). This apphes to the case of an air 

 gap between parallel planes of area .4, as shown in Fig. 9, where the 

 length of the path is the separation x. The reluctance of such a gap may 

 therefore be written as: 



« = !• 



In this, as in subsequent expressions for air gap reluctance, the multi- 

 plier 1/na , which is the reciprocal of the permeability of air, is omitted 

 for convenience. In CGS units, fXa — ^■ 



Special Gap Shapes 



The simple relation just given provides a basis for the calculation of 

 more complex shapes. For example, the reluctance of the wedge shaped 

 gap of Fig. 10 may be found by assuming tubes of flux in parallel through- 

 out the gap. Then the permeance of an elementary path is A(P = bAr/rd 

 and the total permeance of the gap is the sum of these elementary paths, 

 or: 



(P 





- dr b , r2 

 — = - In — 

 r 6 ri 



D= 1/tt -- 



Fig. 8 — Field of a uniformly wound toroidal core. 



