MAGXirriC DHSIGX OF KKLAVS 31 



limiting saturation flux, and the latc of increase of ll^ — Wi becomes 

 progressively smaller. The satuiatioii flux ihei-efore puis a ceiling on the 

 mechanical work attainable. 



If the armature travel is increased, increasing the unoperated gap 

 Xi , the corresponding magnetization curve is lowered, reducing ITi with 

 a conse([uent increase in the work ( apacity. However large Xi may be 

 made, there remains a leakage field, to which corresponds a limiting 

 magnetization curve. An extreme upper limit to the work capacity is 

 represented \)\ the area between this limiting magnetization curve and 

 that for the operated position of the armature. 



The magnetization curves thus suffice for the evaluation of l)otli the 

 field energy and the mechanical output associated with armature motion, 

 and therefore completel}^ define the static performance of the electro- 

 magnet. The problem of relating this performance to the design then 

 reduces to the problem of relating the magnetization characteristics to 

 the design. 



3 THE MAGNETIC CIRCUIT COXCEPT 



A rigorous determination of the magnetization relations from the di- 

 mensions and configuration of the electromagnet would require the solu- 

 tion of the static magnetic field equations. For the geometry obtaining 

 in actual structures, such solutions can at best be obtained only for 

 specific cases, and then only by tedious numerical or graphical methods. 

 Approximate solutions, however, may be obtained by a procedure in 

 which the actual distributed field is taken as confined to a limited number 

 of paths, which together form a network analogous to an electrical cir- 

 cuit. The extent to which this procedure may provide a valid approxima- 

 tion is indicated in the following brief review of the basic postulates of 

 static field theory. For the present purpose, these may be stated as 

 follows: 



The energy of a static magnetic field is the volume integral of the 

 product of the magnitudes of the B and H vectors over the space con- 

 taining the field. These vectors coincide in direction at all points, and 

 are subject to the conditions: (1) that B can be represented by closed 

 continuous lines, ("lines of induction"), whose density measures the 

 magnitude of B, (2) that the ratio n oi B io H at any point is determined 

 by the medium in which the point is located, (3) that the line integral 

 f)f H around a closed path is equal to 47r times the total current in all 

 circuits linking this path. This integral is the magnetomotive force 5"; 

 it has the value 47rAV for a coil of -V turns with current / flowing in 

 them. 



