CHAP. Ill] HYSTERESIS AND EDDY CURRENTS 51 



drawing the straight line log P*=-n log B+log Const. See the author's 

 Experimental Electrical Engineering, Vol., 1, p. L'oj. 



Ans. PA -0.00368 fVB l '. 



21. Eddy Current Loss in Iron. With the thin laminations 

 used in the cores of electrical machinery the eddy -current loss in 

 watts can be represented by the formula 



(22) 



where is a constant which depends upon the electrical resistivity 

 of the iron, its temperature, the distribution of the flux, the wave 

 form of the exciting current, and the units used. V is the volume 

 or the weight of the core for which the loss is to be computed; t is 

 the thickness of laminations, / the frequency of the supply, and B 

 the maximum flux density during a cycle. If B is different at 

 different places in the same core, the average of these should 

 be taken, (B is the time maximum but the space average). 

 Sometimes formula (22) contains also 10 to some negative power 

 in order to obtain a convenient value of e. 



Formula (22) can be proved as follows: The loss of power in a 

 lamination can be represented as a sum of the &r losses for the 

 small filaments of eddy current in it. But t 2 r*=e 2 /Y; it can be 

 shown that the expression in parentheses in formula (22) is pro- 

 portional to the sum of e*/r per unit volume. When the frequency 

 / increases say n times, the rate of change of the flux, d0/dt, and 

 consequently the e.m.fs. induced in the iron are also increased n 

 times. Therefore, the loss which is proportional to e 2 increases n 2 

 times. In other words, the loss is proportional to the square of 

 the frequency. Similarly, the in<lucel voltage is proportional t< 

 the flux density It ; and consequen 1 1 y , t he loss is proportional to B 2 . 



To prove that the loss is proportional to the square of the 

 thickness of laminations one must remember that increasing the 

 thickness n times increases the flux and the induced e.m.f. within 

 any filament of eddy current also n times. Hut the resistance of 

 each path is reduced n times (neglecting the short sides of the rect- 

 angle). Consequently, the expression &/r is increased n* times. 

 However, inasmuch as the volume of the lamination is also 

 creased n times, the loss per unit volume is only /-' t imes lamer. In 

 words, the loss per unit volume increases as (*. A more 

 rigid proof <>t t his proposition is given in problem 21 below. 



