The loss due to Joule heating by eddy currents induced in a magnetic material when the flux changes under AC. It is proportional to the square of thickness and frequency and inversely proportional to resistivity.
Japanese name: 渦電流損失
Eddy-current loss appears in 4 practice questions across 2 topics, including Magnetic materials, Electronic, magnetic and optical materials.
Field: Magnetic materials
In the cores of transformers and motors used with alternating current, energy is lost as heat each time the material is magnetized back and forth; this is called core loss (iron loss). Core loss is broadly divided into hysteresis loss, which corresponds to the area of the hysteresis loop, and eddy-current loss, from the Joule heating of currents induced in the core by the changing flux. Hysteresis loss per cycle is nearly constant, so hysteresis loss is proportional to frequency, while eddy-current loss is proportional to the square of frequency. As frequency rises, the share of eddy-current loss grows, so in high-frequency applications suppressing eddy currents becomes central to materials selection.
When a sinusoidal flux of frequency f and peak flux density Bm passes through a thin sheet of thickness t and resistivity ρ, the eddy-current loss per unit volume is P = π²t²f²Bm²/(6ρ), where the skin effect can be neglected. For example, a 3% silicon steel sheet with t = 0.35 mm and ρ = 4.8×10⁻⁷ Ω·m at 50 Hz and 1.5 T gives about 0.31 W/kg, taking the density as 7.65 g/cm³. Raising the frequency to 400 Hz in the same sheet makes the loss (400/50)² = 64 times larger. Because the loss is proportional to the square of thickness and inversely proportional to resistivity, making sheets thinner and raising resistivity are the basic countermeasures.
Subtracting the hysteresis loss and the classical eddy-current loss from the core loss measured on real electrical steel leaves a considerable amount. This is called anomalous eddy-current loss (excess loss), and it arises because eddy currents do not flow uniformly through the whole sheet but concentrate near moving domain walls. The larger the domains and the fewer the walls, the faster each wall must move, and the larger this loss becomes. Fine grooves or strain introduced by laser on the surface of grain-oriented electrical steel to refine the domains serve to reduce this loss. In analyses that separate the losses, it is sometimes treated as a term proportional to frequency to the power 1.5.
To reduce eddy currents, the paths for current are cut finely or the resistivity of the material is raised. Electrical steel is made of thin sheets with insulating coatings stacked together, and about 3% silicon is added to iron to raise the resistivity to several times that of pure iron. There are also sheets with silicon raised to 6.5%. At frequencies of kHz and above, amorphous alloy ribbons about 20 to 30 µm thick, dust cores made by compacting insulated powder, and ferrites of extremely high resistivity are used. On the other hand, the Joule heat of eddy currents is put to active use in induction heating and induction cooktops, eddy-current braking, and eddy-current testing to find flaws at metal surfaces.
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.
Hysteresis loss comes from the irreversibility of domain-wall motion and rotation of magnetization; the value per cycle depends little on frequency, so the loss is proportional to frequency. Eddy-current loss is the Joule heat of induced currents; it is proportional to the square of frequency and depends strongly on sheet thickness and resistivity.
Because silicon greatly raises the electrical resistivity of iron, reducing eddy-current loss. It also lowers magnetocrystalline anisotropy and magnetostriction, helping to raise permeability. Adding too much, however, lowers the saturation flux density and makes the sheet brittle and hard to roll, so it is usually kept to around 3%.
Electrical steel is common at power frequencies (50/60 Hz), thin electrical steel and amorphous alloys from several hundred Hz to several kHz, and nanocrystalline alloys and ferrites at tens of kHz and above. The higher the frequency, the thinner and more resistive the material must be. The boundaries vary with the application and flux density, however.
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.
Assume the eddy-current loss of electrical steel sheet is p…High permeability and saturation flux density are also required, as is high electrical resistivity to reduce eddy-current losses; grain-oriented electrical steel (silicon steel), ferrites and amorphous alloys are used.
Which correctly describes a soft magnetic material suitable…Hysteresis loss is proportional to frequency and eddy-current loss roughly to the square of frequency, so power supplies and motors operating at high frequencies use high-resistivity materials such as ferrites or thin laminated steel sheet.
The area of the hysteresis loop of a core material (the los…Si is added to raise the electrical resistivity and reduce eddy-current loss.
Grain-oriented electrical steel (Fe with about 3% Si) used …Soft magnetic material Coercivity Magnetocrystalline anisotropy Recrystallization Domain wall Ferrimagnetism Magnetic domain Maximum energy product Saturation magnetization Superparamagnetism