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BELL SYSTEM TECHNICAL JOURNAL 



helix which has been slit along a helical line normal to the wire of which the 

 helix is wound. The clashed slanting lines again connect points which were 

 the same point before the helix was slit and developed. Again we assume a 

 height of a half wavelength. Thus, if the polarities are maximum +,—,+, 

 — etc. as shown at the bottom, they will be maximum —,+,—,+,—,+ 

 etc. as shown at the top, and zero half-way up. In this case the field is a 

 standing wave along any horizontal line, and no other component can be 

 introduced to make it a traveHiig wave. Half of the field strength can be re- 

 garded as constituting a component traveling to the right and half as a 

 component traveling to the left. 



TOP 





Fig. 3.11 — Voltages on a developed heli.x for two turns per wavelength. 



The equipotentials used to represent the field about the wires of Fig. 3.9, 

 Case I and Fig. 3.10 belong to the field 



V -f j^p = In tan (s + jx) (3.31) 



Here V is potential and i/' is a stream function. There are negative equi- 

 potentials about z — X = and positive equipotentials about .v = 0, s = 

 ±t/2. For an equipotential coinciding with the surface of a wire of c-diam- 

 eter, 2 Swire , d/p is thus 



at X = 0, c < 7r/4 

 ats = 



d/p = '-^ 

 7r/4 



F = hi tan c 

 V — In tanh .v 



(3.32) 



(3.34) 



Hence, for an equipotential on the wire with an z-diameter 2z, the .v-diani- 

 eter 2.x- can be obtained from (3.33) and (3.34) as 



2.V = 2 tanh-i tan z (3.35) 



Of course, the ratio of the x-diameter di to the pitch is given by 



di/p = 



x/4 



(3.36) 



where x is obtained from (3.35). 



