Direction of Force and Acceleration. 



461 



desired acceleration. Referring again to fig. 1, since the 

 body is being accelerated in the Y direction, its total velocity 

 and hence its mass are increasing. This increasing mass is 

 accompanied by increasing momentum in the X direction even 

 when the velocity in that direction remains constant. The 

 component force F^ is necessary for the production of this 

 increase in X-momentum. 



In predicting the path of moving electrons with the help of 



the fifth equation of electromagnetic theory, F = E-f- -vxH, 

 we find an interesting application of equation (5). 



Application in Electromagnetic Theory. 



Consider a charge e constrained to move in the X direction 

 with the velocity v and let it be the origin of a system of 

 moving coordinates YeX (fig. 2). Suppose now a test 

 electron t, of unit charge, situated at the point #=0, y=y 9 



Ffr. 2. 



to 



o 



moving in the X direction with the same velocity v as the 

 charge e, and also having a component velocity in the Y 

 direction u y . Let us predict the nature of its motion under 

 the influence of the charge e. 



The moving charge e will be surrounded by electric and 

 magnetic fields whose intensities at any point are given by 

 the following expressions *, obtained by integrating Maxwell's 



* Abraham, Theorie cler Elehtrizitat, vol. ii. p. 86 et seq. (B, G. 

 Teubner, Leipzig and Berlin,, 1908). 



