Materials with 'hard' magnetic B/H characteristics often show a strong residual magnetism. This makes them suitable for making permanent magnets. If the ring material were magnetised, then the magnetised material itself will create a flux in the ring. No current carrying coil will be required.

For a permanent magnet, flux is produced by the alignment of magnetised domains within the material itself. (c.f earlier notes relating to residual magnetism in B/H curve).  In this case, the flux exists without the need for a coil, i.e. N.I = 0. Hence applying Ampere's Law results in:

Hence eqn 1 and the B/H curve must be simultaneously satisfied and to give the flux density and magnetic field strength in the magnetic material (and hence also the air gap)

from equation (1)  B_c/H_c=-L_c/L_gµ₀         

which is slope of a straight line. The flux density and magnetic field in the magnetic circuit is given by the point at which eqn (1) cuts the B/H curve. Permanent magnets are widely used in transducers:- loud speakers, measuring meters, D.C. motors etc.