SPACE CHARGE BETWEEN PARALLEL PLANE ELECTRODES 51 



right of a plane at a potential Vi}^ From Child's equation the current 

 in amperes per square centimeter is given by 



I = 2.33 X lO^^-^r^- = — e^— (amps, per sq. cm.) (1) 



or solving for ^o 



5o = 1.527 X 10-'-^ = ^^jjT^ (centimeters). (2) 



Accordingly, whenever the conditions at the first plane are represented 



V=0 Vi ^Vi 



^ SPACE CHARGE \ 

 ^LIMITED CURRENT/ 



-So- 



■OSq- 



FIRST 

 PLANE 



SECOND 

 PLANE 



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



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

 of S{i. The distance in centimeters is then 



6" = (tSq. 



(3) 



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

 plane at a distance 5 is then given by 



V = ipVi. 



(4) 



Potential Distributions 



All possible potential distributions to the right of the first plane 

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

 matical derivation is straightforward and is given in the appendix. 



i^ 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. 



