SOME CONTEMl'OR.tRV .tnr.LXCr.S IN I'llVSICS -f <M 



l'"uiulanicntall\- llu- tlu-ory is vt-ry simpk-, ami li.is not bvvn lH'lpr<l 

 It) any uri'at rxtriit by llic niori' sophisticated inathcnialics which iu 

 cnu'iifiators iia\c intnKhurd iiilo it. What is observed in electrical 

 conduction is this: when a potentiai-dilTerence is cstablisiied across 

 a piece of metal, the electrons do not fail freely clear across it and 

 enierRe at the positive end with all the kinetic energy which the IM). 

 should ha\e coniiminicated to theni; the\- oo/e gradually through the 

 metal, heating it as they go along and emerging with no unusual 

 amount of energy, as if the\' had rubbed along through the metal 

 like hea\y particles dropping at constant speed through a gas. "Rub- 

 bing along" being a concept foreign to the atomic scale, we have to 

 interpret that each electron falls freely through a small distance, 

 collides with something to which it gives up the energy acquired from 

 the field during its fall, falls again across another short distance, 

 gives up its new quota in another collision, and so forth from side to 

 side of the metal. Furthermore the energy which it gives up at each 

 stoppage must find its way directly or indirectly into the heat of the 

 metal, i.e., into thermal agitation of its atoms. Representing by 7' 

 the time-interval between two consecutive collisions, by E the field- 

 strength in the metal, by e and m the charge and mass of the electron, 

 by U the average kinetic energy acquired by the electron from the 

 field in its free fall between two collisions, we have 



U=\{eET,'m)-m. (1) 



If there are n electrons in unit cube of the metal, and each is stopped 

 1 T times in unit time, the rate at which heat appears in the unit 

 cube is nU/ T; but this rate is by definition the product of the con- 

 ductivity a b>- the square of the fieldstrength E, hence 



ff= '. ne'T m (2) 



The same equation (2) can be reached, if one prefers to think (jf 

 conductivity as the ratio of current-density to fieldstrength. In' con- 

 sidering that during each free fall, the field augments the speed of 

 each electron in the direction of the field-\'ector by the amount eET/ in, 

 which on the average is lost at the collision terminating the fall; so 

 that the result is as if the field imprinted a constant drift-speed equal 

 to \eE m upon all the electrons. Multiplying by ne to get the current- 

 density and dividing by E to get the conductivity, we arrive again 

 at (2j. 



Kquation (2) is the fundamental equation of the electron theory of 

 conduction, and indeed of most of the other theories. Let us begin 

 b> trying the supposition that the electrons are at rest until the field 



