Magnetics, Cores & Saturation
An iron core multiplies a coil's magnetic field — until it can't. Every core has a flux-density ceiling (Bsat); past it the steel is "full" and behaves like air. Drive the magnetic circuit below, watch the operating point climb the B–H curve, and see how turns, current, and especially core cross-sectional area decide whether you stay in the linear region or saturate.
A coil of N turns carrying current I drives a magnetomotive force ℱ = N·I around the core. Spread over the magnetic path length ℓ, that sets the field intensity H, and the material's permeability µ turns H into flux density B:
Saturation. Permeability isn't constant. As H rises, the core's magnetic domains finish aligning and B flattens out at Bsat. Beyond the knee, µ collapses toward µ₀ — the iron stops helping and inductance falls off a cliff. Silicon steel saturates near 1.8–2.0 T, ferrite under 0.5 T.
Why core area matters. Flux is B·A, so for a required flux Φ a bigger cross-section A carries it at a lower B — further from saturation. Undersize the iron and the same flux pushes B past Bsat. Area is the designer's main lever against saturation (and it sets the core's weight and cost).
Faraday — the electric/magnetic link. A changing flux induces a voltage in the winding, and conversely an applied AC voltage forces a flux. This is the one place electric and magnetic fields couple in a core: