Theory and calculation of alternating current phenomena . ^ d-lO-^ = rfMO-^ 0 loss of energy per cubic centimeter and cycle, W = e\fB^ = J d^\JB^ 10-« = d^\fB- IQ-^ ergs = ^2/^2 10-4 ergs;or, IF = eXfBnO- = d2j52io-n loss of power per cubic centimeter at frequency,/, is p = fW = €X/^B2io-v = <^2/252io-n watts;the total loss of power in volume, V, is P = Vp = Vd^PBnO-^^ an example, d = I mm. = cm.;/ = 100; B = 5,000; V = 1,000 ;e = 1,645 X 10-11;Tr = 4,110 ergs = joules;V = watts;P = watts. In some of the mode
Theory and calculation of alternating current phenomena . ^ d-lO-^ = rfMO-^ 0 loss of energy per cubic centimeter and cycle, W = e\fB^ = J d^\JB^ 10-« = d^\fB- IQ-^ ergs = ^2/^2 10-4 ergs;or, IF = eXfBnO- = d2j52io-n loss of power per cubic centimeter at frequency,/, is p = fW = €X/^B2io-v = <^2/252io-n watts;the total loss of power in volume, V, is P = Vp = Vd^PBnO-^^ an example, d = I mm. = cm.;/ = 100; B = 5,000; V = 1,000 ;e = 1,645 X 10-11;Tr = 4,110 ergs = joules;V = watts;P = watts. In some of the modern silicon steels used for transformer iron, X reachesvalues as low as 2 X 10\ and even lower; and the eddy current losses arereduced in the same proportion (1915). 140 ALTERNATING-CURRENT PHENOMENA 108. (h) Iron Wire. Let, in Fig. 92, d = diameter of a piece of iron wire; then ifu is the radius of a circular zone of thickness, du, and one cen-timeter in length, the conductance of this zone is ^—, and themagnetic flux inclosed by the zone is Bu~ Fig. 92. Hence, the generated in this zone is bE = \^2ir^fBu- in units,and the current produced thereby is dl =^X \/2 TT^/fiW^ • = —^— XfBu du, in units. The power consumed in this zone is, therefore, dP = SEdl = T^xpBhihlu, in units;consequently, the total power consumed in one centimeter lengthof wire is ( dW = X^XPB^J uHu = W7 XPE^d^, in the volume of one centimeter length of wire is V = 4 the power consumed in one cul)ic centimeter of iron is aP TT^ p = — = T^ XpB^d^, in units or erg-seconds, FOUCAULT OR EDDY CURRENTS 141 and the energy consumed per cycle and cubic centimeter of iron is Therefore, the coefficient of eddy currents for iron wire is e = ^d- = rf2; or, if X is expressed in practical units, or 10-^ units, e = f^d^ 10-9 = rf2 Substituting X = 10», we get as the coefficient of eddy currents for iron wire, o e = ~ d^ 10-9 = 0.
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