DIELECTRIC PROPERTIES OF INSULATING MATERIALS 507 



because of the "friction" (i.e., the molecular equivalent of macroscopic 

 friction) which the molecules experience as they change from the one 

 equilibrium distribution of orientations to the other. Evidently, the 

 dielectric loss may be quite as characteristic of the structure of the 

 material as is the dielectric constant. 



In an ideal insulating material there would be no free ion conduction, 

 but in actual materials there are some free ions or electrons and these 

 produce Joule heat as they drift towards the electrodes in the applied 

 field. The total heat developed is the sum of the dielectric loss and 

 the Joule heat; and, as the latter is proportional to the d-c or free ion 

 conductivity, the dielectric loss is proportional to the total a-c conduc- 

 tivity (as measured on a bridge for example) less the d-c conductivity. 



To give the discussion a more concrete basis, let us consider a di- 

 electric which has a dielectric constant e' and a loss-factor e" (or in 

 other words which has a complex dielectric constant e' — ie"). Let it 

 be contained in a parallel-plate condenser having a plate separation 

 of d centimeters, and area A cm^ for one surface of one of the plates. 

 If a potential difference V is maintained between the plates of this 

 condenser, a charge q per unit area will appear on either plate and a 

 polarization P will be created in the dielectric. The current flowing 

 in the leads to this condenser is Adq/dt, if we assume for the present 

 that the conductivity due to free ions may be neglected. The conduc- 

 tivity is then given by 



where E = Vjd. The charge g can be calculated from the dielectric 

 constant of the material by means of relations which are provided by 

 the general theory of electricity, namely 



eE = D, (4) 



D = E + AtP, (5) 



D = 4:wq (for a parallel-plate condenser). (6) 



So (3) becomes 



yE=^ = -—=~^— (7) 



^ dt 4r dt 4:Td dt' ^^ 



where all of the electrical quantities are expressed in electrostatic 

 units. When the applied potential is alternating, V may be expressed 

 as the real part of F = Foe'"', where Fo is the amplitude. The di- 

 electric constant may then be written as the complex quantity t' — ie" , 



