Past exam of the physics B course of the University of Cambridge / 2016 / Paper 2 / Section B / B6 / d

A permanent magnet retains a substantial magnetization without an applied coil electric current. In a ferromagnetic material this reflects microscopic magnetic moments, magnetic domains and their resistance to rearrangement. The history-dependent relation between applied field and magnetization gives magnetic hysteresis, remanence and coercivity. A soft core used in an electromagnet or electrical transformer is chosen for easy magnetization and small hysteretic loss; a permanent-magnet material must resist demagnetization.^[ref]

The macroscopic fields obeyin magnetostatics. The magnetization can be represented by equivalent bound currents,Thus both permanent magnetic matter and free coil electric currents generate a magnetic field. Its magnetic field lines form continuous loops; apparent north and south poles are not isolated magnetic charges.

In a long ideal solenoid, $H\simeq nI$. A linear core would give $B\simeq {\mu }_0{\mu }_{r}nI$, until saturation or other nonlinear effects invalidate a constant magnetic permeability. In a finite magnetic circuit, air gaps and demagnetizing fields affect the field strongly: because the gap has low magnetic permeability, it often needs most of the available magnetomotive force. A permanent magnet can have a nonzero internal $\mathbf{H}$ even when ${\mathbf{J}}_f=0$, because its boundaries create a demagnetizing field. Hence setting $\mathbf{H}=0$ merely because there is no free coil electric current is generally incorrect.