Multilayer Coils with Square and Circular Section. 969 



prism of unit height is built on EFGH as a base, 



tf o O V o Tfi-c-r 

 4-7T ~dn 



is the flux o£ the electric displacement out through the face 

 of the prism having FE for its trace. 



Since FG, EH are negligible in comparison with FE, the 

 flux through them may be neglected. It remains to find 

 the flux through GH. 



For this purpose, prolong HE and drop a perpendicular 

 to HE from G. Call Gi the base of this perpendicular. 

 Now Gauss's theorem may be applied to the triangular 

 prism having unit height and GGiH for base. The point G 

 can always be so chosen as to have the lins GG} exactly in 

 between the wires of each layer. Then there is no flux 

 across GG^ Hence the flux out through GH plus the 

 flux out through GiH is equal to the charge in the volume 

 GGiH. It must now be remembered that the flux out 

 through GH for the prism GG X H is the flux into the 

 prism EFGH through the same face. Hence the flux 

 into the prism EFGH is 



Hence 



4-7T ~dn 4-7T ~d?i ' 

 Sometimes an additional consideration is necessary. 

 This happens whenever the line GH of fig. 5 cannot 

 be drawn without cutting the wires. This, for example, 

 would be the case if the wires in each layer were close 

 together, as is seen from fig. 6, where the wires are 



Fig. 6.— Possible inside structure of multilayer coil wound with 

 rectangular wires. 



WMMiiMms^mMmA 



mmmwmmmwm 



represented by the small shaded rectangles. However, 

 in this case the zigzag path ABODE can replace GH 



<PY 



so that (2) still holds, where GiH-r-y- has been left out 



