646 BELL SYSTEM TECHNICAL JOURNAL 



The relation between the applied electric field, E, and the polariza- 

 tion induced by it per unit volume is given by 



P = i^ E (2) 



47r ^ ^ 



for isotropic materials. The constant (e — l)/47r is the susceptibility 

 of the dielectric in e.s.u., and e is the dielectric constant, which is 

 defined as C/Co, where C is the capacitance of the measuring condenser 

 while it contains the dielectric and Co is its capacitance when empty. 



For some purposes there are advantages in considering the actual 

 polarization, which is produced by a discontinuous distribution of 

 charged particles, to be replaced by a vector point function which gives 

 equivalent external effects. Then a vector P may be considered to be 

 associated with every point in the space occupied by the dielectric and 

 the dielectric may be considered to have a continuous volume density 

 of polarization,^ P. In non-isotropic bodies the polarization vector P 

 induced by an applied field E is not always in the same direction as E, 

 but is assumed to be a linear vector function * of E (involving, in the 

 general case, six independent constants), where both E and P are 

 vector point functions. 



In deriving the relationship between the dielectric constant and the 

 molecular structure of a material it cannot be assumed in general that 

 the local field which is impressed upon the elementary particles in the 

 dielectric is simply the field E which can be computed by dividing the 

 applied voltage V by the distance between the plates of the condenser, 

 the intensity of the field being assumed to be uniform. For there is an 

 interaction between the molecules of the dielectric such that each mole- 

 cule exerts a force on every other molecule. In the absence of an 

 applied electric field these forces combine with other influences to 

 create a distribution for which the polarization per unit volume has 

 the value Po (frequently zero, as has been mentioned). Then when 

 a field is applied each element of volume in the dielectric is put into a 

 polarized condition and in general the forces which it exerts upon the 

 particles in other volume elements changes, because the charges in 

 each volume element have been displaced to new positions. Conse- 

 quently, the value assumed by P in a given cube of Fig. 2 will depend 

 not only upon the direct action of the charges on the plates of the 

 condenser — which determines the strength of the field E — but also 



* Cf. Mason and Weaver, loc. cit. Chap. III. 



* Cf. P. Debye, "Polar Molecules," Chemical Catalogue Co., New York (1929), 

 pp. 32-35. 



