Multilayer Coils with Square and Circular Section. 971 



The potential of the upper end of the section is higher than 

 the potential at the lower end by 



-L 



di 



Je 



where the current i is reckoned positive when entering the 

 coil through a turn at the lower end of the section and 

 leaving through a turn in the upper. Hence the potential 

 at P exceeds the potential at by 



dt 



\ a a V Mi 



Fig. 7. — Diagram showing co-ordinates used in the ease of a eoil with 

 circular cross section. 



Ungrounded Coil. — Consider the case when the coil is 

 insulated. Then by symmetry the potential at . does 

 not vary. Discarding any constant potential, it is therefore 

 legitimate to state that the potential of is zero. Therefore 

 the average potential at (#, y) is 



V = 



di 



It 



Gin 



y 



a 



V 



a V 



(3) 



From this expression p can be found by means of equa- 

 tion (1). In order to find cr, V must be found. 



In order to find V it is convenient to introduce polar 

 coordinates (r, 0), OX being chosen as the polar axis. The 



