The relation between `overset(to) (B) and overset(to) (H)` in ferromagnetic materials is complex. It is often not linear and it depends on the magnetic history of the sample.
Figure depicts the behaviour of the material through one cycle of magnetisation.
Let the material be unmagnetised initially. We place it in a solenoid and increase the current through the solenoid. The magnetic field B in the material rises and saturates as depicted in the curve Oa.
This behaviour represents the alignment and merger of domains until no further enhancement is possible. It is pointless to increase the current (and hence the magnetic intensity `H= mu_(0) nI`) beyond this B is not increase.
Now by decrease H and reduce it to zero. At `H=0, Bne 0`. This is represented by the curve `ab`. The value of B at H = 0 is called retentivity. In figure `B_R ~1.2 T` where the subscript R denotes retentivity. The domains are not completely randomised even though the external driving field has been removed.
Next, the current in the solenoid is reversed and slowly increased. Certain domains are flipped until the net field inside stands nullified. This is represented by the curve `bc`. The value of H at C is called coercivity. In figure it is `H_C ~ 90 A//m.`
As the reversed current is increased in magnitude, we once again obtain saturation. This is represented by curve `cd`. The saturated magnetic field `B_S ~ 1.5 T`.
Next, the current is reduced (curve `de` ) and reversed (curve `ea`). This cycle repeats itself.
Here, the curve `Oa` does not retrace itself as H is reduced. For a given value of H, B is not unique but it also depends on the value of B of the previous magnetisation. This phenomenon is called hysterisis. The word hysterisis means lagging behind.
