Sec. 4-3] 



ELECTRICAL TRANSDUCERS 



223 



equal to the electron concentration n~. Errors are likely to arise from 

 surface contamination of the probe. 



For theoretical consideration and alterations of the theory due to probe 

 geometry (cylindrical and spherical probes), see A. Von Engel, "Ionized Gases," 

 pp. 262ff., Oxford University Press, London, 1955, and G. Francis, "The Glow 

 Discharge at Low Pressures," in S. Fliigge (ed.), "Encyclopedia of Physics," 

 vol. 22, pp. 62ff., Springer Verlag, Berlin, 1956. 



4-3. Space Potential 



A space potential is the potential at a given point in an electric 

 field. It is usually expressed as the potential difference between this 

 point and a fixed electrode (e.g., ground). 



The space potential in an electric gas discharge with a high ion 

 concentration can be measured with the Langmuir probe (4-2). For 

 the measurement of space potentials in the earth's atmosphere, 

 special probes ("collectors") have been developed; they are de- 

 scribed in 4- 3 1 . The space potentials in electron optical arrangements 

 can be measured with a system described in 4-32. The application of 

 this system is limited to special cases; more frequently the space 

 potential is found from model experiments in the electrolytic trough 

 (4-33). 



4-31. Potential Probes, Collectors 



A space-potential probe as used for atmospheric-electricity studies 

 generally consists of a metallic electrode S, well insulated by a rod A 



n '03^ 



*-A 



S 

 Rq — AW — r — • — t 

 R e 



E s R, 



U\ 



rfr 



c-^ 



Fig. (4-3)1. Potential 

 probe, collector: S, 

 metal electrode; A, 

 insulated rod. 



Fig. (4-3)2. Equivalent 

 circuit of the potential 

 probe illustrated in Fig. 

 (4-3)1. 



from ground (or from the reference electrode), as shown in Fig. (4-3)1. 

 The electrode S should be small compared to the dimensions of the 

 field, so that the field is practically homogeneous in the vicinity of the 

 probe. When exposed to an electric field, the electrode S will gradu- 

 ally assume the local potential E s by exchange of charges with the 



