Sec. 4-4] ELECTRICAL TRANSDUCERS 227 



4-4. Surface Charges and Surface Potentials 



4-41. Wilson Plate 



A simple system for the measurement of surface charges which are 

 induced by relatively large electric fields is shown in Fig. (4-4)1. The 

 system 1 uses an insulated electrode P which, for practical measure- 

 ments of atmospheric electricity, is flush with the ground but insu- 

 lated from it. In other applications it may be surrounded by a guard 

 ring. 



For the measurement in d-c fields, the plate is first shielded by a 

 grounded cover S and momentarily discharged. The shield S is then 



F 



ir w >f y 



=i= F 



7 



-* — x — * 



Fig. (4-4)1. Wilson plate Fig. (4-4)2. Equi- 



as a transducer for sur- valent circuit of 



face charges. the Wilson plate. 



withdrawn and the plate P is exposed to the electric field. The field 

 causes a surface-charge density 



CE 



a = 



a 



where C is the capacitance of the plate to ground (including that of 

 the electrometer connected to the output terminals), E the voltage, 

 and a the surface area. 



For the measurement of time-varying surface charges or of time- 

 varying electric field causing surface charges, a simple electrode, 

 such as the uncovered Wilson plate, is usually sufficient ( "field variom- 

 eter"). The equivalent circuit for a collector electrode or a Wilson 

 plate at variational field strength is shown in Fig. (4-4)2. 



A number of mechanical systems ("field mills") have been described which, 

 in effect, cause a continuously repeating shielding and exposure of the plate; 

 see J. A. Chalmers, "Atmospheric Electricity," chap. IV, par. 73, p. 63, 

 Oxford University Press, New York, 1949; R. Gunn, Phys. Rev., 71, 181 (1947); 

 see also X. Russelvedt, Jahrb. Met. Inst. (Oslo), 1925 (1926). 



1 C. T. R.Wilson, Phil. Mag., 17, 634 (1909), Phil. Trans. Roy.Soc. (London), 

 (A) 92, 555 (1916), and (A) 221, 73 (1920). 



