Dielectric Strength in High Frequency Fields. 243 



-cycles a second *. In air the change is less, the breakdown 

 voltages at 60 and at 40,000 cycles a second being respec- 

 tively 22*5 and 19*5 kilovoltsf. The effect is not to be 

 accounted for by temperature change, for during the test 

 this does not rise appreciably. An explanation % has been 

 given in general terms based on the fact that on the appli- 

 cation of the field there is polarization at <.the velocity of 

 electric waves in the medium, followed by a further polariza- 

 tion caused by the interattraction of the separated molecular 

 charges. This secondary polarization is not instantaneous, 

 and the breakdown conditions are determined by the super- 

 position of the two fields, the elastic restoring force being, as 

 always in dielectrics, proportional to the displacement. 



2. Let F be the intensity of the applied field, and x the 

 electrical displacement. When, as in paraffin-wax, inter- 

 attraction is negligibly small, bx = F. When present it has 

 been shown § to be approximately proportional to x 2 , so that, 

 when fully established, 



bx = ~F + cx 2 (1) 



During the growth of the internal field || we may write, when 

 F is unidirectional, 



bx = F + cx 2 (l- e-**), (2) 



where a is constant and small relative to the time of test, or 

 to the periodic time when the field is alternating. From this 



{b-2cx(l-e--j}^-«cx> 



.... (3) 



' = 



J J at 



ov dx ctcx 2 e~ at 



dt b-2cx(l-e- at )' ' * " 



This is infinite, and the material breaks down, when 



b 



■Zc(L — e- at ) 



w 



* 'Dielectric Phenomena in High Voltage Engineering,' F. W. 

 Peek, Jr., McGraw-Hill, N.Y., p. 165. 



t Peek, loc. cit. p. 107. 



% " The Electric Strength of Solid Dielectrics," Phil. Mag. vol. xxx. 

 July 1915, p. 133. 



§ " The Electric Strength of Solid Dielectrics," loc. cit. p. 130. 



|| See " The Polarization of Dielectrics in a Steadv Field of Force," 

 Phil. Mag. March 1910, p. 401. 



K2 





