Worked example: A transformer core (soft iron) has a hysteresis loop of area 500 J/m³ per cycle, volume 0.002 m³, operating at 50 Hz. (a) Find the hysteresis power loss. (b) Why not use a hard steel core? Step 1: Energy per cycle = area × volume = 500 × 0.002 = 1 J. Step 2: Power = energy × frequency = 1 × 50 = 50 W — pure waste heat, on top of eddy-current losses (which laminations reduce). Step 3: Hard steel's loop area might be 50× larger → 2.5 kW of waste heat — the transformer would cook itself. This is the economic reason soft iron (narrow loop, tiny area) owns the transformer business, while hard magnets (wide loop) own the fridge door. Bonus: the same area logic picks ferrites for high-frequency cores.