Assume the eddy-current loss of electrical steel sheet is proportional to t²f²Bm², where t is the sheet thickness, f the frequency and Bm the peak flux density (with the same resistivity). At the same frequency and flux density, by roughly what factor does the eddy-current loss change if the thickness is reduced from 0.50 mm to 0.35 mm?

Answer: B. About 0.49 times

The eddy-current loss is proportional to the square of the thickness, so (0.35/0.50)² = 0.70² = 0.49, about 0.49 times the original, or roughly half. About 0.70 times assumes it is proportional to the thickness, and about 0.34 times assumes it is proportional to the cube. In a thinner sheet the emf induced across its cross section by the changing flux is smaller and the current paths are narrower, so the loss falls as the square of the thickness. That is why cores are built by stacking thin sheets with insulated surfaces. Hysteresis loss, however, hardly depends on thickness, so the total core loss does not fall all the way to half. Adding Si to raise the resistivity is another way to suppress eddy currents.