Electric Strength of Solid Dielectrics. 133 



This very simple relation may be otherwise derived from 

 the consideration that failure must occur when the total 

 displacement reaches some definite limit depending on the 

 atomic structure. Let this be X, let q =ma the quantity 



Fin". 4. 



which appears at once on the application of the field, and 

 that slowly developed qi = mcc l . The magnitude of the first 

 polarization is such that the second is a minimum, the total 

 displacement at breakdown being fixed. The external energy 

 which must be supplied to the medium in order to produce 

 the second displacement is ?y 2 =m(X — x )v, v being constant. 

 But in the first stage sSq/v is constant, =a say; thus 



m 



and this is a minimum when .r = X/2, or iVi=£ Q , 



5. Influence of Frequency of Field. 



Electric breakdown occurs more easily at high frequency. 

 In the case of glass the effect of raising- the latter from 50 

 to 8500 is to lower the disruptive voltage in a ratio 2*5 *. 

 From equation (3) it is seen that the work of breakdown 

 must be less at higher frequencies, in order that at a given 

 voltage the breakdown thickness should be greater. AC in 

 fig. 3 must then be less for a given value of <r , that is a 

 smaller voltage will cause failure. 



The reason why breakdown occurs at a particular dis- 

 placement peculiar to each frequency is not to be found in 

 the system of force external to the atom. To account for it 

 the internal restoring force must be weakened, as it would 

 be if the atomic charges were unable to take up their full 

 displacement corresponding to the field instantly on reversal. 

 Let OA, OB be the amplitude of the instantaneous polari- 

 zation .i' , AC and BD the secondary polarization .v } . Let 

 the field be reversed so that A and B are interchanged. 



* Moscicki, E. T. Z. loc. cit. 



