118 THE BELL SYSTEM TECHNICAL JOIRXAL, JAXIAHY 1054 



MAGNETOMOTIVE FORCE, J — i 



Fig. 3 — Field energy relations in the operation of an electromagnet. 



ment. In the later motion, 2-3, the reluctance changes more rapidly 

 with X, and the velocity is high, increasing d<p/dt so as to result in a 

 temporary decrease in J. Operation is complete at 3, with (p and F still 

 below their steady state values at 4, which they then approach exponen- 

 tially with .r = . 



The mechanical work done in operation is represented in Fig. 4 by 

 the area under the dynamic pull curve (dotted line), and in Fig. 3 by 

 the area bounded by 0-1-2-3-0. This, of course, is less than the work 

 that would be done if -J were equal to its steady state value Js throughout 

 the motion, represented by the area under the JFs curve in Fig. 4, and 

 by the loop 0-3-4-5-0 in Fig. 3. In Fig. 4 it can be seen that the work done 

 exceeds the static load V by an amount represented by the shaded area 

 T, corresponding to the kinetic energy of the armature and the parts 

 that move with it. At the end of the stroke this energy is partl^y dissipated 

 in impact, and partly transferred to ^'ibratory motion of the relay and 

 its parts. 



The initial flux development, 0-1 is governed wholly by equation (2). 

 This same relation dominates in controlling the performance in the early 

 travel 1-2, in which the velocity is small, and the reluctance changes 

 slowly. In the later travel, where the velocity is high and the reluctance 



