52 THE MAGNETIC CIRCUIT [ART. 22 



For values of the reader is referred to pocketbooks; the 

 numerical values given there must, however, be used cautiously, 

 because the eddy -current loss depends on some factors such as the 

 care exercised in assembling, and the actual distribution of the 

 flux, which factors can hardly be taken into account in a formula. 

 As a matter of fact, formula (22) is used now less and less in prac- 

 ticul calculations, the engineer relying more upon experimental 

 curves of total core loss (Fig. 10). 



Prob. 20. According to the experiments of Lloyd and Fischer [Trans- 

 Amer. Inst. Eke. Engs., Vol. 28 (1909), p. 465] the eddy-current loss in 

 silicon-steel laminations of gauge 29 (0.357 mm. thick) is from 0.12 to 0.18 

 watts per pound at 60 cycles and at B = 10,000 maxwells per sq. cm. What 

 is the value of the coefficient e in formula (22) if P is in microwatts, V is 

 the weight of the core in kg. (not the volume, as before) ; if also t is in mm., 

 and B is in kilolines per sq. cm.? 



Ans. From 5.78 to 8.67 ; 7.2 is a good practical average. 



Prob. 21. Prove that the loss of power caused by eddy currents, per 

 unit volume of thin laminations, is proportional to the square of the thick- 

 ness of the laminations. Solution : The thickness t of the sheet (Fig. 9) 

 being by assumption very small as compared with its width a, the paths 

 of the eddy current may be considered to be rectangles of the length a and 

 of different widths, ranging from t to zero. Consider one of the tubes of 

 flow of current, of a width 2x, thickness dx, and length I in the direction 

 of the lines of magnetic force. Let the flux density vary with the time 

 between the limits B. Then the maximum flux linking with the tube 

 of current under consideration is approximately equal to 2axB ; therefore, 

 the effective value of the voltage induced in the tube can be written in the 

 form e=CaxBf, where C is a constant, the value of which we are not con- 

 cerned with here. The resistance of the tube is p(2a +4x)/(ldx), or very 

 nearly 2ap/(ldx). Thus we have that the i 2 r loss, or the value of e*/r 

 for the tube under consideration, is dPe C^ax^B^ldx^p. Integrat- 

 ing this expression between the limits and t/2 we get P e = CWZ? 2 / 2 // 48p. 

 Hut the volume of the lamination is V = atl Dividing P by V we find 

 that the loss per unit volume is proportional to (//B) 2 . 1 



Prob. 22. Prove that the loss of power by eddy currents per unit 

 volume in round iron wires is proportional to the square of the diameter of 

 the wire. The flux is supposed to pulsate in the direction of the axes of 

 the wires, and the lines of flow of the eddy currents are concentric circles 

 Hint: Use the method employed in the preceding problem. 



22. The Separation of Hysteresis from Eddy Currents. It is 

 sometimes required to estimate the total core loss for a thickness 



*For a complete solution of this and the following problem, including 

 the numerical values of C, see Steinmetz, Alternating Current Phenomena 

 (1908), Chap. XIV. 



