Effects related to the Hall Effect. 247 



As the second terra in the parentheses is very small 

 compared with unity, this reduces to 



dr _ aeX 



dt ~ 2mv~r' W 



Let there be N free electrons in unit volume of the metal. 

 Then the radial current in the disk is 



irdae 2 A.N 

 \j = — ■ ■ • 



mv 



Substituting the value of a, we get 



2mv 



T = 



AJN T * 



Let T be the free time of an electron so that \~vT, The 

 specific resistance of the metal is then given by 



T= ?TN ^ 



This is the same expression for the specific resistance 

 which is obtained by considering the flow of electrons along 

 a straight bar. 



Now suppose that the disk, carrying the radial current C, 

 is placed in a uniform magnetic field of intensity H, at right 

 angles to the plane of the disk. Let the directions of r, 6, 

 H form a right-handed system. 



The equations of motion of an electron are : 



idt* T \dt))- r +tle \it> 



d (uW\ 

 dt \ dt) 



TT dr 

 — r \ T —-. r)=- H^-r, 



r dt \ dt) dt ' 



where, of course, e must be taken as negative for the 



dr 

 electrons. In the second of these equations for -=- we may 



put the average velocity acquired by the electron under the 

 electric force alone, since the effect of the magnetic field 

 is small. This average radial velocity is given by (5). 

 We thus find : 



2 d0 lHe 2 Tad „ 



at I mr 



- 7/1 



At the. beginning pf a .free, path, when t = Q : r , —0 on 



