544 BELL SYSTEM TECHNICAL JOURNAL 



well as in the dielectric between them. In a conductor the total 

 current / passing through the area of the circle is a function of p since 

 the current is distributed throughout the entire cross-section of the 

 conductor. Strictly speaking, the same is true of any circle in the di- 

 electric. There is one important difference, however; the conduction 

 current passing through such circles is the same and the displacement 

 current is usually so small that it can be legitimately neglected. 

 Thus, in the dielectric, we have to an extremely high degree of accuracy 

 unless p is very large 



H,=^, . (36) 



Z7rp 



where / is merely a constant, namely, the total conduction current 

 passing through the area of the circle of radius p. 



That the longitudinal displacement current can be neglected, unless 

 the conductivity of the conductors is small, has been already indicated 

 in the opening paragraph. The following comparison is an aid to the 

 mathematical argument. The density of the longitudinal conduction 

 current is gE and that of the displacement current is ioieE. Near the 

 boundary, E is substantially the same iil the conductor and in the di- 

 electric. In copper, g = (1/1.724)10« and in air e = (l/367r)10-ii. 

 Thus, even at very high frequencies, the density of the displacement 

 current is very small compared to that of the conduction current. 

 On the other hand, the conduction current is ordinarily distributed 

 over a small area while the displacement current may flow across a 

 large area. The latter area would have to be very large, however, 

 before it could even begin to compensate for the extremely low current 

 density. 



Electromotive Intensities in Dielectrics 



With the aid of equations (12) and (36), we can now calculate the 

 electromotive intensities in the dielectric between two conductors. 

 Thus, the transverse intensity is 



Substituting this in the second equation of the set (12), we obtain 

 the following differential equation for the longitudinal intensity: 



dE, 

 dp 



ICjOfJ, ~ 



2^' (^^) 



Zirp 



g + ioje 

 where m is the permeability of the dielectric. Integrating with respect 



