252 THE MAGNETIC CIRCUIT [ART. 71 



Formulae for the average force of direct current electromagnets. 

 In a tractive magnet (Fig. 60) or a rotary magnet (Fig. 63) 

 it is often required to know the average pull over a finite travel 

 of the moving part. For the average force, the equation 

 F ave dS=JW m =: 4W 8 holds, which is analogous to eq. (177) ; 

 the only difference being that finite instead of infinitesimal incre- 

 ments are used. If the motion takes place at a constant flux, 

 or at least the values of the flux are the same in the initial and 

 the end-positions, we get from the preceding formulae : 



. . . (183) 

 - Sl ); . . (184) 

 -s l ). . . . (185) 



The finite travel of the plunger often takes place at a con- 

 stant current, for instance, in the regulating mechanism of a 



FIG. 63. A rotary electromagnet. 



series arc-lamp, also approximately in a direct-current electro- 

 magnet connected across a constant-potential line. Under such 

 conditions the foregoing formulae are not directly appliable, 

 because they have been deduced under the assumption of no 

 interchange of energy between the electric and the magnetic 

 circuits, so that this case has to be considered separately. 



Let the motion be in the direction of the magnetic attraction, 

 and let the current remain constant during the motion. The 

 stored energy is larger in the end-position than in the initial 

 position, because the flux is larger and the current is the same. 

 Therefore, the energy supplied during the motion from the line 

 must be sufficient to perform the mechanical work, and to 



