564 PHENOMENA OF INDUCTION IN NON-LINEAR CONDUCTORS. 



For a magnet reduced to its two poles, and turning about its 

 centre, the induced currents are also equivalent to the system of two 

 magnetic ribbons coiled on the same cylinder. Lastly, the currents 

 produced by the displacement of any magnetic system, rotating 

 uniformly, are equivalent to a system of magnetic ribbons which 

 correspond, point to point, to the different masses of the system. 



583. CALCULATION OF THE ACTION OF INDUCED CURRENTS. 

 To calculate the effect of these images, let us denote by Q T 

 the value of the potential Q, determined by the currents of the 

 shell at the point whose co-ordinates are x, y, z + RT, and at the 

 period / - T ; by Q' T , the value of the potential Q', determined by the 

 magnetic system at the point x, y, (z + RT), and at the same 

 period / - T. The potential Q T , being a function of the co-ordinates 

 x t y t 2 + Rr, and of t - T, we have 



,, JQ, R 3Q, JQ, 



~ =:K ~~ 



Equation (6) applied to this function becomes then 



Integrating this equation in reference to T between the limits 

 T = 0, and T = co , we shall have the value of the function Q for the 

 period /, which gives 



() 



r/03 

 <V T ~~(V 



Jo 



The function Q on which the solution of the problem depends, 

 since it enables us to calculate the action of induced currents at 

 each point, is thus determined by the function Q' T defined at each 

 instant by the condition and the motion of the external magnetic 

 system. 



584, CASE OF A SINGLE POLE. We may apply this method 

 of calculation to the case, considered above, of a single pole of 

 mass m, which moves uniformly in a rectilinear path in the 

 presence of an unlimited conducting plane ; but it is simpler 

 to treat the problem directly by the consideration of magnetic 

 images. 



