28 THE BELL SYSTEM TECHNICAL JOURXAL, JANUARY 1954 



mining the design conditions tor attaining a desired performance. For a 

 specific structure, however, the observed magnetization relations, apart 

 from any other interpretation, provide a record of the part of the elec- 

 trical energy input to the coil which is stored in the electromagnet. The 

 performance of the magnet with respect to the mechanical work which 

 this stored energy can do may be determined directly from the way in 

 which this energy varies with armature position. The experimental 

 determination of the flux ip for particular \^alues of AV and x involves a 

 measurement of the electrical ciuantity AV defined b}^ the ec[uation: 



N<p = f {E - iR) dt. (2) 



The electrical energy IJ stored in making this measurement is the time 

 integral of i{E — iR), or: 



U = (E - iR)i dt = i d(N<p). 



Hence a plot of N(p versus / gives a measure of the stored energy [/ 

 represented by the area between the curve and the axis of A^^?. This 

 conclusion is quite independent of any physical meaning attached to A^ 

 other than the definition of eciuation (2). Plotting (p versus A^7, rather 

 than A^^ versus /, is merely a change of scale, which does not affect the 

 value of the area measuring the stored energy U. It is convenient to 

 make this change of scale because the relation between (p and NI is 

 independent of the number of turns A^, provided the location and di- 

 mensions of the coil are unchanged. The preceding expression for U may 

 therefore be written as: 



U 



= f Nidip. (3) 



•/n 



Thus for NI = Nix in Fig. 2, U is measured by the area 0-1-5 for 

 X = Xi, and by the area 0-3-7 for x = .T2 . 



Magnetization curves have the general character shown in Fig. 2. 

 They are approximately linear for small values of <p, but at higher values 

 bend over and approach a limiting value, ^p" . This limiting value is the 

 saturation flux, determined by the material and dimensions of the elec- 

 tromagnet, and designated throughout this paper by the double prime 

 superscript. 



The ratio of the magnetomotive force fF to the flux <p is the reluctance 

 (R, as defined by the eciuation: 



f? = 47rA^/ = (Siip. (4) 



