﻿Capacity of a Pancake Coil. 737 



Computation of the Function «(#). 

 As stated in the introduction, the differential of charge is 

 di f . 



The independent variable here chosen is r. As r varies 

 from to a, and as varies from to 2tt, the whole coil is 

 traversed by the point (•?*, 9). The differential of area 

 is 2irrdr, and the differential of charge is then -Lii-a-rdr, 

 where a is given by (17) becau-e expression (17) gives the 

 surface density only on one side of the coil. 



By (3), on the coil r becomes acosv; so that 



a = *J 1 — cos 2 v = 



v a 



Substituting this in (3), and expressing the fact that 



Anrardr 



it is found that 

 . . 2 K rh ( 



7T v a- — 



11© 



It now remains to substitute (18), (19) into (1). If the 

 ungrounded condenser terminal is connected to the centre, 

 Xi is to be taken as and x 2 is to be taken as a. If, 

 however, it is connected to the periphery, x x is to be taken 

 ns a and a? 2 as 0. 



The first of these gives 



C = — iT + g t iil 



77 I 10 b L dJ 



and the second 



(20) 



V 



c -^[Hl|i <«» 



If, now, the coil should be used with the centre grounded, 

 and the ungrounded terminal of the condenser should be 

 connected to the periphery, formula (21) applies, and in 

 that formula V o =0. This gives 



C'o = ~ (22) 



This is the effective capacity if the centre is grounded. 

 Phil Mag. S. 6. Vol. 4-1. No. 262. Oct. 1922. 3 B 



