TRANSVERSE MOTION OF ELECTRONS 



619 



Thus, the same factor $ relates the actual charge to the "effective charge" 

 acting on the circuit and the actual circuit voltage to the voltage produced 

 at the location of the charge. 



We will not consider in this section the "space charge" voltage produced 

 by the charge itself (the voltage at point a in Fig. 13.4). 



The circuit voltage V we consider as varying as exp(— F^) in the direction 

 of propagation. The voltage in the vicinity of the circuit is given by 



V(x, y) = W (13.3) 



ELECTRODE 



Fig. 13.3 — The situation of Fig. 13.2 results in the same charge flow as if the charge 

 were put on terminal a of the circuit shown, which consists of two capacitors of capaci- 

 tances Ci and C2 . 



02 



$ya 



Fig. 13.4 — A voltage V inserted in the ground lead divides across the condensers so 

 that Va = *F, where * is the same factor which relates the charge flowing in the ground 

 lead to the charge Q applied at a in Figs. 13.2 and 13.3. 



Here x and y refer to coordinates normal to z and <l> is a function of x and y. 

 We will choose x and y so 



d^/dx =0 (13.4) 



Then 



Ey = -Vd^/dy = -^'V (13.5) 



$' = d^/dy (13.6) 



In (13.3), <l> will vary somewhat with T, but, as we are concerned with a 

 small range only in F, we will consider $ a function of y only. 

 From Chapter II we have 



TViKi 



V = 



and 



(r' - fD 



(2.10) 



(2.18) 



