Effects related to the Ball Eject. 245 



suspended in a magnetic field so that its normal is inclined 

 to the lines of force. A torque is produced tending to turn 

 the disk. 



(3) A radial current is induced in the disk on exciting a 

 magnetic field at right angles to its plane. An equal and 

 opposite radial current is induced when the fieid is des- 

 troyed . 



It is necessary to consider the motion of electrons in a 

 circular disk when a radial current flows. Let be the 

 whole radial current, t the specific resistance of the metal, d 

 the thickness of the disc, r x and r 2 its internal and external 

 radii. The current must be thought of as entering the disk 

 through a wire of radius r x at its centre, and as leaving 

 uniformly from all points of its periphery of radius r 2 . 



The radial force acting on an electron of charge e is 



Or a , Ct 



„ , = — where a= - — 7 



lirra r %ird 



and there is no tangential force. The equations of motion 

 of an electron are : 



d 2 r 

 i 



it 2 V \dt) "mr 9 { } 



Jit-f)-* .•■» 



m is the mass of the electron. (2) gives 



^= k > • • • (3) 



and this with (1) gives 

 Integrating : 



♦ 



d 2 r _ k 2 ae 

 dt 2 7 :6 mr 



/dr\ 2 A k 2 2ae, /f x 



^) =A r> -\ loor (I) 



\dt) r 2 ^ m * V ' 



The electrons are assumed to move equally in all directions 

 with velocity v between collisions when there is no electric 

 field. The effect of the electric field is to give them a drift 

 in its direction. After a collision the electron begins to 

 move with velocity v in a wholly random direction. During 

 its free path, until its next collision, it is acted upon by the 

 electric force; we must now find the average velocity ii 



