280 The Treatment of FAectrodynamics. 



direction of x, and the field, of intensity H, be in the positive 

 direction of z ; and the wire be moved, with velocity V, in the 

 positive direction of y. Then any electron in the wire, being 

 carried with the velocity V, will constitute a current in that 

 direction, and will consequently suffer a mechanical force, 

 perpendicular to its velocity and to the magnetic field, L e. in 

 the direction of x, and as the three-finger rule shows, in the 

 positive sense. It will accordingly be driven along the wire, 

 and there will be an " induced " current in the wire. The 

 mechanical force on each electron amounts to 



evR 



which is the same as if it were placed in an electric field 



rr 



amounting to - — -'. As every electron in the wire is subjected 



to a similar force, it is as if there were an electric field of 

 this intensity prevailing in the wire, so that between the ends 



of it there was a difference of potential or, in electro- 

 magnetic units, vUdl. 



Since, however, we shall need to deal with induction in 

 cases in which the magnetic metals are present, it would be 

 well to write B instead of H, the latter symbol having been 

 applied above to a part only of the magnetic induction. But 

 vl$dlis the rate at which the element of circuit cuts the total 

 magnetic induction. We may then say that the " electromotive 

 force " generated in the element is the rate at which it crosses 

 magnetic induction. By integrating this result over a whole 

 circuit we arrive at the second circuital relation 



lit 



N being the total magnetic induction through the circuit, the 

 negative sign follows from the above case because a positive 

 motion (in y) into a field decreases N and causes a current in 

 the positive direction of x. 



The above treatment has the advantage of deriving the two 

 integral relations of electrodynamics from one, more easily 

 comprehended, differential relation, and puts magnetism in 

 its place as a special case of currents. 



Transvaal University College, 

 Johannesburg, 1908. 



