Multilayer Coils with Square and Circular Section. 977 



Coil with a Square Section. 



The coil with a square section can also be studied by the 

 same method. The side of the square is denoted by 2a. 

 The origin of co-ordinates is placed at the centre of the 

 square. The layers are supposed to be arranged parallel to 

 one of the sides. One of the coordinate axes is drawn 

 parallel to that side and the other perpendicular to it. The 

 first is called OX and the second OY. (See fig. 9.) 



Fig. 9. — Diagram of coil with square cross section. 





l 



) 



7 



c 



1 









aa 





















«.. 



A 







a 



— X 



In this case, if the coil is ungrounded, V at is zero. 

 Hence Y at (x, y) is 



A, (19) 



4a 



dt 



1L 



2a 1J dt> 



because the e.m.f. induced between two layers is proportional 



to the area of the cross-section subtended by the layers, since 



the diameter of the coil was assumed to be large in comparison 



with the dimensions of its cross-section. 



d 2 V 

 It is clear that -v-2 = 0. Therefore p = 0. It remains to 



compute a. It is seen from (2) that a is made up of two parts. 

 The first of these contains /c as a factor, and the second 

 similarly involves K e . It is clear that at BC and AD (fig. 9) 



~— = 0. Hence [see equations (1), (2)] the only contri- 



butions to the term involving K e are given bv AB and CD, 



' dY dV 

 i.e. by the end layers of the coil. At CD, ^ — ~JT anc * 



Phil Mag. S. 6. Yol. 43. No. 257. May 1922. 3 R 



