CHAPTER X. 



CONDUCTION IN DIELECTRICS. 



206. Variable Flow. Relaxation-Time. We have hitherto 

 supposed dielectrics to be perfect insulators. This can hardly be 

 said to be the case, even for the best insulators. On the other 

 hand, although, as we have seen, the greater the inductivity of a 

 dielectric, the more nearly does it act, as far as concerns electro- 

 static distributions, like a conductor, it is by no means likely that 

 the inductivity of conductors is infinite. Still less is it likely that 

 it is zero. We shall now consider the consequences of considering 

 a dielectric to possess, in addition to its electrical iiiductivity u, an 

 electric conductivity \. We shall now deal with currents which 

 are not in the steady state, and shall require to assume that at 

 any instant Ohm's Law determines the distribution of the currents, 

 namely 



This assumption is justified by experiment. Instead of the sole- 

 noidal condition for the current, however, we must obtain a new 

 equation. This is obtained by the consideration that, if we consider 

 a portion of substance r bounded by a closed surface S, the total 

 charge within that surface increases in any interval of time by the 

 amount of total current flowing into T through the surface, that 

 is, if n is the internal normal 



( I ) 1 1 Ipdr = 1 1 [u cos (nx) + v cos (ny) -h w cos (nz)} dS 



du dv dw) , 

 ^- + 5- + 3- 1 dr. 

 dx oy oz) 



Since this equation must hold for any portion of space, we must 



have everywhere 



dp _ (du dv dw\ 

 di = ~\fa + dy + W 



