442 Induction of Currents in Linear Circuits [CH. xiv 



Thus the motion of the pole must have set up an additional electromotive 



force in the circuit of amount m -y- , to counteract which the additional 



at 



electromotive forces are needed. The electromotive force m -=- which 



at 



appears to be set up by the motion of the magnets is called the electromotive 

 force due to induction. 



The number of tubes of induction which start from the pole of strength m 

 is 47rm, and of these a number mw pa,ss through the circuit. Thus if n is the 

 number of tubes of induction which pass through the circuit at any instant, 



the electromotive force may be expressed in the form -y- . 



So also if we have any number of magnetic poles, or any magnetic system 

 of any kind, we find, by addition of effects such as that just considered, that 



dN 



there will be an electromotive force -7- arising from the motion of the 



at 



whole system, where N is the total number of tubes of induction which cut 

 the circuit. 



It will be noticed that the argument we have given supplies no reason for taking ^V to 

 be the number of tubes of induction rather than tubes of force. But if the number of 

 tubes crossing the circuit is to depend only on the boundary of the circuit we must take 

 tubes of induction and not tubes of force, for the induction is a soleuoidal vector while 

 the force, in general, is not. 



dN 



507. The electromotive force of induction -7- has been supposed to 



at 



be measured in the same direction as the current, and on comparing this 

 with the law of signs previously given in 483, we obtain the relation 

 between the directions of the electromotive force round the circuit, and of the 

 lines of induction across the circuit. The magnitude and direction of the 

 electromotive force are given in the two following laws : 



NEUMANN'S LAW. Whenever the number of tubes of magnetic induction 

 which are enclosed by a circuit is changing, there is an electromotive force act- 

 ing round the circuit, in addition to the electromotive force of any batteries 

 which may be in the circuit, the amount of this additional electromotive force 

 being equal to the rate of diminution of the number of tubes of induction 

 enclosed by the circuit. 



LENZ'S LAW. The positive direction of the electromotive force (""yrj ana 



the direction in which a tube of force must pass through the circuit in order to 

 be counted as positive, are related in the same way as the forward motion and 

 rotation of a right-handed screw. 



