490 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



should not be confused with the electrode area used in previous sec- 

 tions.) We assume 



and 



e^z = for all (r, 9, z) 

 eee = for r — a 

 Trr —P for r = h 



(20) 

 (21) 

 (22) 



Manipulation of (15) through (22) allows the evaluation of the con- 

 stants A and B as 



and 



Thus 



Also 



A = - 



«^,+ (l-2.) 



B = 



b'^d - 2a) P 

 5,+ (1-2.) 



1 dp err + eee + Cz 



pdP P 



1 ap ^ 2(1 + (r)k b' 

 pdP 3 



yields 

 1 



"^-,+ (1-2.) 



1 36 _ err|r=6 _ k{l + o) 



bdP P 3 



1-^-. 



2-1 



a^ 



r, + (1 - 2cr) 



a~ 



Combining (2), (14), (23), and (24) we obtain 



I 



(23) 



(24) 



k (25) 



^. r/ie Case a = ^ 



The equations derived above reduce to the expressions one would 

 obtain if the dielectric were considered to be a compressible fluid when 

 a is set equal to ^. 



