546 PROPERTIES OF THE ELECTROMAGNETIC FIELD. 



CHAPTER VI. 



PROPERTIES OF THE ELECTROMAGNETIC 

 FIELD. 



565, MAXWELL'S THEORY. The preceding considerations are 

 sufficient, as we have seen, to account for all the phenomena of 

 induction in linear conductors ; but it is useful to regard the problem 

 from another point of view, in which the influence of the medium 

 is brought out, as in electrostatics. We shall explain here the 

 principles of Maxwell's theory. 



566. EQUATIONS OF THE MAGNETIC FIELD. Suppose, for 

 greater generality, that the conductors are situate in a magnetic 

 medium whose coefficient of permeability (383) is equal to /*. 

 When the total flow of magnetic induction Q through a closed 

 circuit is annulled, it becomes the seat of a total electromotive 



force which puts in motion a quantity of electricity equal to . 



K. 



This total electromotive force may be regarded as the resul- 

 tant of the elementary electromotive forces acting on each of 

 the elements of the circuit, and arising from the condition of the 

 medium. At each point the elastic reaction of the medium, due 

 to the suppression of the forces, has a determinate direction; it 

 would produce on an element of the conductor ds, situate in the 

 same direction, an electromotive force proportional to the length of 

 this element, and which may be represented by ]ds ; the electro- 

 motive force on an element which made an angle with the 

 direction, would be equal to ]ds cos c. 



If the medium is homogeneous and isotropic, the electromotive 

 force J for unit length is a function of the co-ordinates ; it may be 

 replaced by its components F, G, and H, parallel to the axes, and 

 which would produce the electromotive forces ~Fdx, Gdy, and Hdz 



