Hysteresis: The B-H Loop

Definition. Hysteresis literally means "lagging behind", and it names the characteristic phenomenon, unique to ferromagnetic materials, in which the flux density $B$ inside the material always lags behind changes in the applied magnetising field $H$ -- so that $B$ at any instant depends not only on the CURRENT value of $H$ but also on the material's entire recent magnetic HISTORY. Only a qualitative treatment -- the shape of the loop and its physical significance -- is required at this level; no formula for the enclosed energy is needed.

Tracing the B-H loop (Figure 1). Starting from an unmagnetised sample at the origin $O$, increasing $H$ from zero traces the initial magnetisation curve $OA$, rising steeply at first and then flattening as the sample approaches saturation at $A$. Reducing $H$ back toward zero does NOT retrace curve $OA$; instead $B$ follows a DIFFERENT, higher path, so that when $H$ reaches exactly zero, $B$ has NOT returned to zero either -- it sits at the retentivity value $B_r$ (Section 1.11). Continuing to reduce $H$ into NEGATIVE values (reversing the field's direction), $B$ keeps falling and reaches zero only when $H$ has reached $-H_c$, the negative of the coercivity (Section 1.11). Pushing $H$ further negative drives the sample to saturation in the OPPOSITE direction, at a point $A'$ that mirrors $A$. Bringing $H$ back up from $A'$ traces a fourth curve, passing through $-B_r$ (at $H=0$) and $+H_c$ (at $B=0$), and rejoining the original curve at $A$ -- completing one full CLOSED loop, symmetric about the origin, that never exactly retraces itself in either direction.

Why the loop never closes on the same path. As the atomic dipoles (Section 1.10) are forced to realign every time $H$ changes direction, internal friction-like effects between neighbouring magnetic domains dissipate energy as heat; this irreversible energy loss is what prevents $B$ from simply retracing its own path when $H$ is reversed, and is the direct cause of the loop enclosing a finite area rather than collapsing onto a single curve. The AREA enclosed by the complete loop represents (qualitatively) the energy dissipated as heat, per unit volume of the material, in one complete cycle of magnetisation. …