Eddy Currents and Hysteresis Losses With easy examples.

When the magnetic field in an iron core alternates, as in every 50 Hz transformer, two kinds of energy loss appear as heat. Eddy currents are loops of current induced inside the conductive core itself by the changing flux, circulating uselessly and warming the iron. Hysteresis loss is the energy spent re-magnetising the iron each cycle as domains are dragged around the B–H loop.

These "core losses" matter because they are present even when a transformer supplies no load at all. A distribution transformer humming on a pole 24 hours a day burns core loss the whole time, paid for by the utility. Cutting these losses — thin laminations for eddy currents, good steel for hysteresis — is one of the oldest battles in electrical engineering.

Key Concepts

• Faraday's law: a changing flux induces voltage in any conductor, including the core itself — that is the source of eddy currents.
• Laminations: the core is built from thin insulated sheets so eddy-current loops are broken into tiny paths; thinner sheets mean much lower loss.
• Hysteresis loop: the B–H curve traced each cycle; its area equals the energy lost per unit volume per cycle.
• Coercivity: how hard it is to demagnetise the material; remanence: the flux left behind at zero field. Soft iron (low coercivity) suits transformers; hard steel (high coercivity) suits permanent magnets.
• Steinmetz equation: the empirical formula for hysteresis loss, Ph = kh × f × Bmⁿ with n ≈ 1.6 for electrical steel.
• Ferrites: ceramic magnetic materials with very high resistivity — the choice for high-frequency transformers.

Formulas

• Eddy-current loss: Pe = ke × f² × Bm² × t², where t is the lamination thickness — note the squares: halving the thickness quarters the loss.
• Hysteresis loss (Steinmetz): Ph = kh × f × Bm^1.6 (per unit volume).
• Total core loss: Pc = Pe + Ph.

Assumptions: sinusoidal flux, uniform peak flux density Bm, and material constants ke and kh measured for the actual steel grade and thickness.

Worked Example

1. A transformer core loses 100 W at 50 Hz: 60 W eddy-current loss plus 40 W hysteresis loss.
2. Run it at 100 Hz with the same Bm: eddy loss scales with f², so 60 × 4 = 240 W; hysteresis scales with f, so 40 × 2 = 80 W.
3. New core loss = 320 W — more than tripled, which is why a 50 Hz transformer overheats badly on a 400 Hz aircraft supply unless it is redesigned.
4. Halve the lamination thickness instead: eddy loss falls to 60/4 = 15 W, total 55 W — why modern cores use 0.23–0.35 mm sheets.

Common Misconceptions

• "Eddy currents are pure waste." The same effect drives induction furnaces, induction cooktops and eddy-current brakes; it is waste in a transformer and a tool elsewhere.
• "A thicker, chunkier core is better." For AC, thick solid iron is an eddy-current heater; thin laminations or ferrite beat bulk every time.
• "Hysteresis loss depends on the load current." It depends on the peak flux density and the frequency, which is why it is there at no load and barely changes with load.

Real-World Applications

• Laminated transformer and motor cores in every power system.
• Induction heating, hardening and melting furnaces.
• Eddy-current brakes in trains, roller coasters and dynamometers.
• Ferrite cores in switched-mode power supply transformers.

Every alternating flux pays two taxes — eddy currents, tamed by laminations, and hysteresis, tamed by good steel. Both grow with frequency, so match the core material to the job: grain-oriented steel at 50 Hz, ferrite at 50 kHz, and never a solid iron block at either.