﻿Capacity of a Pancake Coil, 



735 



where the symbol Q 2 «( t /.0) stands for the limit of 

 Q 2)i (/.8) as 8 approaches zero taking only real and 

 positive values. 



SinCen ° W l-^StPoW-W], 



all a-2n but « , a 2 vanish, and a , a 2 are determined by the 

 relations 



aoQoO'.0)=V -fLj 



rt 2 Q 2 (,y .0) = |L 



. . . (14) 



Thuj 



3 dt ^ . . \ . or <^ Q 2 (y .sinh m)^ , . 



. . . (15) 



The surface density of charge in coulombs is obtained as 



10- 11 J£ BV 

 a 8-989 4tt dn' 



where K is the dielectric constant of the medium, and =r — 



on 



is the directional derivative of V with respect to the normal 



drawn away from the surface. The same may be written as 



4-7T on' 



where 



10 



-ii 



K = 



8*989 



K, 



• (16) 



Now at the disk the normal is parallel to OZ. Hence 



on-\ z 

 Hence by (3J 



V /3V\ . p „ , 



V- = j ^— I it z > and 



On Vo~/2=o 



(fL/"<°- 



on a I sin v \^u J u ._ 



and by (15), (16) 



A7ra \ 



"hU ° * U dt) QoO-.O) 



+ *yt 0,(5.0) n(/A) j 



