636 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Figure 2.1 will help to make this clear. Here the impressed current I flows 

 to the right and back through the circuit of impedance Z. The voltage will 

 increase to the right and hence the field will be directed to the left. 

 In general, for an impressed current / we will write the field produced as 



£ = -Z(co, 3)1 (2.10) 



Here Z(co, jS) is a circuit impedance per unit length, which is usually a 

 function of a> and j8. In terms of an admittance, the relation connecting 

 impressed current and field is 



7=-7(<o,^)£ (2.11) 



Wv 



rr^ 



o+V 



Fig. 2.1 — ^The voltage and field produced by a current impressed on an impedance Z. 



This can also be made clearer by means of an illustration. Suppose that 

 the impressed current density in a very broad beam is i and the "circuit" 

 is merely free space. Then 



(a 

 and from Poisson's equation 



_ = —j^h = - = - - 

 dz e 0) € 



i = —j(i)eE 



But, the admittance of a unit cube is just ^'coc, and the current through 

 this admittance is ^'cotE. 



Thus, when we have calculated the field caused by an impressed con- 

 vection current, the admittance is the negative of the field divided by the 

 convection current. 



In (2.5), t, or rather, cri, where a is the area of the beam, may be re- 

 garded as the impressed current. If F(a), 0) is the circuit admittance, one 

 way of writing the condition for a natural mode of propagation of stream 

 and circuit is 



(rt= -F(a>,i3)JE: (2.12) 



