618 BELL SYSTEM TECHNICAL JOURNAL 



imposed in the presence of a transverse field component, this gain is some- 

 what reduced. 



13.1 Circuit Equation 



Consider a tubular electrode connected to ground through a wire, shown 

 in Fig. 13.1. Suppose we bring a charge Q into the tube from oo . A charge Q 

 will flow to ground through the wire. This is the situation assumed in the 

 analysis of Chapter II. In Fig. 2.3 it is assumed that all the lines of force 

 from the charge in the electron beam terminate on the circuit, so that the 

 whole charge may be considered as impressed on the circuit. 



ELECTRODE 



(^ 



Q 

 "WTTTT^TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTy 



Fig. 13.1— When a charge Q approaches a grounded conductor from infinity and in the 

 end all the lines of force from the charge end on the conductor, a charge Q flows in the 

 grounding lead. 



ELECTRODE 



V7777777777777777777777777777777777777777777777. 



Fig. 13.2 — If a charge Q approaches a conductor from infinity but in the end only part 

 of the Unes of force from the charge end on the conductor, a charge <I>Q flows in the ground- 

 ing lead, where <J> < 1. 



Now consider another case, shown in Fig. 13.2, in which a charge Q is 

 brought from oo to the vicinity of a grounded electrode. In this case, not all 

 of the lines of force from the charge terminate on the electrode, and a charge 

 $() which is smaller than Q flows through the wire to ground. 



We can represent the situation of Fig. 13.2 by the circuit shown in Fig. 

 13.3. HereC2 is the capacitance between the charge and the electrode and 

 C\ is the capacitance between the charge and ground. We see that the charge 

 4>() which flows to ground when a charge () is brought to a is 



*<2 = <2C2/(Ci + Co) (13.1) 



Now suppose we take the charge Q away and hold the electrode at a 

 potential V with respect to ground, as shown in Fig. 13.4. What is the po- 

 tential Va at fl? We see that it is 



F. = [C2/(Ci-|-C2)]r = <i.F (13.2) 



