256 



THE MAGNETIC CIRCUIT 



[ART. 72 



path, and the torque is due to the tendency of the tubes of force 

 to shorten themselves longitudinally, and to spread laterally. 



Consider the simplest generator or motor, consisting of a 

 very long straight conductor which can move at right angles 

 to a uniform magnetic field of a density B (Fig. 64). Let the 

 ends of the conductor slide upon two stationary bars through 

 which the current is conducted into a load circuit in the case of 

 a generator action, and through which the power is supplied 

 in the case of a motor action. If the magnetic circuit contains 



no iron, the resultant field is a 

 superposition of the original uniform 

 field and of the circular field created 

 by the current in the conductor. 

 With the direction of the current 

 indicated in Fig. 64, the resultant 

 field is stronger on the left-hand side 

 of the conductor than it is on the 

 right-hand side, and there is a 

 resultant lateral pressure exerted 

 upon the conductor to the right. 

 In the case of a motor action the 

 direction of the motion is in the 

 same direction as the pressure from 

 the stronger field. In the case of a 

 generator action the conductor is 

 moved by an external force against this pressure. Compare 

 also the rule given in Art. 24. 



To find the mechanical force between the conductor and the 

 field, we will apply again the principle of virtual displacements. 

 Let the current through the conductor be i, and let the con- 

 ductor be moved against the magnetic pressure by a small amount 

 ds. Assume that the stored magnetic energy of the electric 

 circuit to which the conductor belongs is the same in the various 

 positions of the conductor. (Such is the case in actual machines.) 

 Then the work done by the external force is entirely converted 

 into electrical energy, and we have 



Fds=iedt, (192) 



where e is the induced e.m.f. Let both F and e refer to a length 



Generator 



FIG. 64. A straight conductor 

 in a uniform magnetic field. 



