MAGNETIC IMAGES. 561 



would rapidly lose their energy owing to the resistance of the 

 conductor. Equation 



gives then 

 (7) 



Hence the value of the function Q, at the time /, in a point at a 

 distance z from the plane on the side of the positive face, and the 

 co-ordinates of which are x, y, z, is the same as for the time /= 0, at 

 the point x, y, and z + R/. 



It follows that if a system of currents has been established in an 

 unlimited and uniform plane, and then left to itself, the magnetic 

 effect of these currents on a point on the side of the positive face, is 

 the same as if the plane moved parallel to itself along the normal and 

 on the negative side with a constant velocity R. The diminution of 

 electromotive force in consequence of the enfeeblement of the 

 currents is exactly represented by the diminution of the magnetic 

 field which results at each point from this imaginary motion. 



579. MAGNETIC IMAGES. The integral of equation (6), in 

 respect of /, gives for points on the surface of the shell 



(8) 



If we suppose that, Q and Q' being at first null, the external 

 system is suddenly created on the positive side, in such a manner 

 that the corresponding potential Q' passes suddenly from to Q', 

 we shall have at the outset and for the surface of the shell, since 

 the integral is null, 



Q=-Q'. 



Hence, for all points of the plate, and therefore for all points of 

 the negative face, the initial system of currents produces an effect 

 equal, and of opposite sign, to that of the real system placed on the 

 positive side. Their effect is then the same as that of a magnetic 

 system identical and of contrary sign to the real system, and which 

 would coincide with it. 



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