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BELL SYSTEM TECHNICAL JOURNAL 



initely as V increases. Obviously, the effect of V on the current is 

 quite different in the two regions and these two regions require different 

 explanations. 



-8.2 



-8.4 



-8.6 



-9.2 



-9.4 



-6 



-2 



2 4 6 8 



POTENTIAL APPLIED TO ANODE IN VOLTS 



Fig. 3 — Retarding potential curves for parallel plates. 



Retarding Potentials 

 Consider first the retarding potential region in which log i decreases 

 linearly with — Va, the applied potential V. The explanation is to 

 be found in extending the theories which were used to derive the 

 Richardson equation. In that derivation it was implicitly assumed 

 that the only forces which the escaping electron had to overcome were 

 the cathode surface forces, and that any electron which escaped from 

 the cathode would reach the anode. If a retarding potential V* is 

 applied to the anode then only those electrons whose normal com- 

 ponent of velocity u exceeds a value Ua can reach the anode ; where Ua 

 is given by 



mUaVl = {ipc + Vr)e (39) 



in the classical case, or 



7nua''!2 = P,n+ eVr (40) 



in the quantum-mechanical case. Figure 4, curve 1, illustrates the 



* In discussing retarding potentials it is convenient to consider retarding poten- 

 tials as positive even though the anode potential is negative, so that Vr = — V. 



