SPACE CHARGE BETWEEN PARALLEL PLANE ELECTRODES 51 



right of a plane at a potential Fi.^^ From Child's equation the current 

 in amperes per square centimeter is given by 



I = 2.33 X 10~^ ^ „ = — ^To— (amps, per sq. cm.) (1) 



oo »->o 



or solving for 5o 



So = 1.527 X 10~*-n7r — 7-1/2 (centimeters). (2) 



Accordingly, whenever the conditions at the first plane are represented 



V=0 Vi tpV] 



I 



SPACE CHARGE \ 

 LIMITED CURRENTJ 



-So- 



OSq 



I 



FIRST SECOND 



PLANE PLANE 



Fig. 1 — Hypothetical conditions to assist in visualizing the unit of distance So. 



by / and Vi, distance from the first plane may be measured in units 

 of ^o. The distance in centimeters is then 



5 = aSo. (3) 



Similarly a natural unit of potential is Vi and the potential of any 

 plane at a distance S is then given by 



V=^V,. (4) 



Potential Distributions 



All possible potential distributions to the right of the first plane 

 can now be expressed in terms of ^ as a function of a. The mathe- 

 matical derivation is straightforward and is given in the appendix. 



^^ This analogy is useful in getting a physical picture of the units but it must 

 not be carried too far as will be evident when the problem of reflected currents is 

 considered. 



