ELECTROMAGNETIC ROTATION. 433 



The work al of the magnetic force corresponding to an infinitely 

 small displacement will be given by the equation 



(7) </T = -<AV= -IIVM. 



455. ELECTROMAGNETIC ROTATION. We have seen that the 

 reciprocal action of a magnet and of a rigid current cannot produce 

 a continuous motion. This would also be the case with two rigid 

 currents, but the impossibility ceases if one of the systems can be 

 deformed, and the preceding considerations enable us to give a 

 simple explanation of most of the experiments of this kind. 



Consider, for instance, an unlimited rectilinear current, the 

 outline of which is at O (Fig. 99), and a magnet PP', one of whose 

 poles P' can slide along a groove AB perpendicular to the current, 

 while the other pole P may describe a circumference about the 

 current, by means of a movable contact which opens the passage to 

 it at each turn. The pole P will rotate for an unlimited time about 



Fig. 99. 



the current, and apart from friction the velocity will go on increasing, 

 since the magnetic action of the current performs, at each turn, work 

 equal to the product of 4?rl by the mass of the pole. A regular 

 condition is established from the time in which the passive resistances 

 balance the motive force. We shall see several examples of the 

 same kind in one of the following chapters. 



The action of a current on itself may also give rise to deforma- 

 tions, or to continuous motions. 



Let ACB (Fig. 100) be a portion of a circuit movable about an 

 axis passing through the two points A and B by which it is attached 

 to the general circuit. We may suppose that the line A B is traversed 

 by two currents in contrary directions, of the same intensity as the 

 current itself, and may thus decompose the system into two distinct 

 closed circuits s and s'. 



F F 



