CHAPTER XV. 



INDUCTION OF CURRENTS IN CONTINUOUS MEDIA. 



GENERAL EQUATIONS. 



528. WE have seen that when the number of tubes of induction, N, 

 which crosses any circuit, is changing, there is an electromotive force r- 



acting round the circuit. Thus a change in the magnetic field brings into 

 play certain electric forces which would otherwise be absent. 



We have now abandoned the conception of action at a distance, so that 

 we must suppose that the electric force at any point depends solely on the 

 changes in the magnetic field at that point. Thus at a point at which the 

 magnetic field is changing, we see that there must be electric forces set up 

 by the changes in the magnetic field, and the amount of these forces must be 

 the same whether the point happens to coincide with an element of a closed 

 conducting circuit or not. 



Let ds be an element of any closed circuit drawn in the field, either in a 

 conducting medium or not, and let X, Y, Z denote the components of electric 

 intensity at this point. Then the work done by the electric forces on a unit 

 electric charge in taking it round this circuit is 



ds ^ ds -(for" (4< 



^jV 



and this, by the principle just explained, must be equal to -7- where N is 



dt 



the number of tubes of induction which cross this circuit. 



529. We have (cf. 437), 



rr 



(462), 



so that on equating expression (461) to -y- , we have 



ctt 



dx d I dz\ , da db dc 



