Thk Thka'imknp of V^lfxthodyna.mics. 41 



simplest possible luaiiiier, the relation between field and inducliuu, in 

 that case, i.r. the " deniasj^uetising effect of the ends." 



To deal with the iiifluction of currents, we will take, first, an 

 element of a circuit moved at right angles to itself, in a magnetic field. 

 Let the wire — of length d/ lie in the direction of .«•, and the field, of 

 intensity H, be in the positi\c direction of r ; and the wire be m<ned, 

 with velocity V, in the jxisitive direction of //. Then any electron in 

 the wire, being carried with the velocity V, will constitute a current 

 in that direction, and will conseciuently suiFer a mechanical force, per- 

 pendicular to its velocity and to the magnetic field, i.e. in the direction 

 of .*•, 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 



e » H 



which is tln» same as if it were placed in an electric field amounting 



to As every electron in the wire is subjected to a siniilar 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 were a difference of potential 



or, in electromagnetic units, /• H cU. 



c 



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 vliidl is 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 i-elation 



E = - ^i^ 

 dt 



N being the total magnetic induction through the circuit, the nega- 

 tive sign follows from the above case because a positive motion (in >j) 

 into a field decreases N and causes a current ifV the positive direction 



of .r. '■ .:,,.: 



The abiive treatment has the ad\antage of deriving the two integral 

 relations of electrodynamics from one, more easily comprehended, dif- 

 ferential relation, and puts magnetism in its place as a special case 

 of currents. 



