the Electron Theory to Induction Currents. 707 



the conductor ; and therefore, if the electrons cannot escape 

 from the conductor, no effect on the current, except the Hall 

 effect, is produced in this way. But if the conductor is 

 moved bodily, the motion of the positive and negative elec- 

 trons so produced will cause a_ component electromagnetic 

 force on the positive electrons to act along the conductor in 

 one direction and on the negative in the opposite. These 

 forces drive the positive electrons in one direction and the 

 negative in the other, so that their effects add together and 

 produce the induction current. 



Consider then the motion of the secondary circuit in a 

 fixed field, and attend at first to the positive electrons only. 

 Let 



ds be the vector representing the element ds of the 



conductor, 

 v be the vector representing the velocity of this 

 element, 

 (L<T = vdt = vector distance travelled in an infinitesimal 

 time dt, 

 n'ds = number of positive electrons in the element, 

 e' = charge of each positive electron, 

 m! = mass of each positive electron. 



The electromagnetic force on each electron is 



e'(vxH). 



The component of this along ds is 



/(vxH). te/ds. 



Neglecting collisions for the present, we have the accelera- 

 tion of an electron alono- the wire 



ds 



(vxH).ds; 



and the velocity generated in time dt 



= ^ds (YXR) - dS > 



and the current generated in the time between two collisions 

 is given by 



G'ds = e f ri ds -4-p (do- X H) . ds 

 m ds 



n' e n 

 = ~ r (do- x H) • ds. 



3B 2 



