562 PHENOMENA OF INDUCTION IN NON-LINEAR CONDUCTORS. 



For points on the positive side, the effect of the currents is the 

 same as that of a system of the same sign as the real systems, and 

 which would be symmetrical with it in respect of the conducting 

 plane ; we shall call it the positive image of the system. 



The action of the currents of each side of the shell may then be 

 considered as produced by an image of the magnetic system, positive 

 or negative that is to say, of the same sign as the system, or of the 

 contrary sign, according as the point in question is on the positive or 

 negative side of the shell. 



If the conductivity of the shell were infinite, we should have R = ; 

 the second member of the equation (8) will always be zero, and the 

 condition Q = - Q' will be always satisfied. The plate will be an 

 absolute screen (563) for all points on the negative side. The 

 currents will be permanent, and their effect will be represented at 

 each instant, for all points of space, by that of one or the other of 

 the two fixed images. 



In a real sheet the resistance R has a finite value. The currents 

 produced by the sudden introduction of a magnetic system begin at 

 once to decrease, and their effect on each side is at each instant 

 represented by that of two images of the system, which would recede 

 perpendicularly from the sheet on each side with the velocity R. 



580. INDUCTION OF A MOVABLE MAGNETIC SYSTEM. The 

 principle of images enables us to determine induced currents by the 

 variations of any given magnetic system on the positive side of the 

 shell. 



The function Q', which determines the magnetic action, will 



-\r\' ^)]y 



vary by dt, while the system itself will vary by -^rdt. We may 

 consider this latter system as being itself a magnetic system, and 



suppose that at the instant / there is suddenly formed on the 



dM 



negative side of the sheet a positive image of ^T^ which then 



moves perpendicularly away with a constant velocity R. If the 

 system varies continuously, we may suppose that the different images 

 of the variations, relative to the different intervals of time, move 

 according to the same law as soon as they are formed, and thus form 

 continuous trails of images. 



581. Suppose, for instance, that a positive pole +m moves in a 

 right line with a constant velocity #, parallel to the shell, and let us 

 assume that this pole has been suddenly created at the point A 

 (Fig. 120), which gives rise to an image +m at the symmetrical 



