As an external field H sweeps back and forth, magnetic domains rotate and domain walls move, but they lag behind H — the material "remembers" its history, tracing a B-H loop instead of a single curve.
B(H) = Bs * tanh((H +/- Hc) / a)
Remanence Br = B(H=0) on the loop
Core loss/cycle ~ Loop area = oint B dH
- Sweep rate — how fast the external field H cycles back and forth (the driving coil frequency).
- Coercivity Hc — reverse field needed to bring B back to zero; wide for hard magnets, narrow for soft.
- Saturation Bs — maximum flux density the domains can align to.
- Soft/Hard magnet — presets: soft (narrow loop, low loss, used in transformer cores) vs hard (wide loop, high remanence, used in permanent magnets).
The enclosed area of the B-H loop is the energy dissipated as heat per cycle — this is why transformer cores use soft magnetic materials (thin loop) while permanent magnets use hard materials (fat loop, high Br).