566 BELL SYSTEM TECHNICAL JOURNAL 



In the dielectric between the coaxial conductors, the longitudinal 

 displacement current density is very small; in fact, it would be zero 

 if the conductors were perfect. This current density is continuous 

 across the surface of the disk and, therefore, gE^ is exceedingly small. 

 Hence, the second of the above equations becomes approximately 



(97) 



so that 



P 



(98) 



where P is independent of p but may be a function of z. Under these 

 conditions, the remaining two equations are 



^ = - i.^H,, ^= - gE,. (99) 



From the form of these equations and from (98), we conclude that 

 the general expressions for the intensities in the disk are 



^ Ae- + Be- ^ o{_Be^" - Ae-q 



P gP 



where a = Vgco/^i. 



On the outside flat surface of the disk (given by z = ^ where h is 

 the thickness of the plate), the magnetomotive intensity is very nearly 

 zero; ^^ therefore, 



Ae''^ + Be-"'' = 0. (101) 



From this we obtain 



A = - Ce-''\ B = Ce''\ (102) 



where C is some constant. Thus equations (100) can be written as 

 follows : 



C sinh a{h — z) 



P 

 P _ oC cosh aiji — z) 

 gP 



(103) 



and at the boundary between the disk and the dielectric of the trans- 

 mission line {z = 0), we have 



^=-coth<jh. (104) 



J^v g 

 ^" On account of the negligibly small longitudinal current in the disk. 



