A B-H curve is a graph of the magnetic flux density B produced in a material against the magnetizing force H applied to it. It shows how the material becomes magnetized, rising from the origin, through a knee, up to magnetic saturation where further increases in H barely raise B.

What is retentivity or remanence?

Retentivity, also called remanence, is the flux density Br that remains in the material after the magnetizing force H is removed (H = 0). It is the residual magnetism, and it is the reason permanent magnets stay magnetized.

Coercivity Hc is the reverse magnetizing force needed to bring the flux density B back to zero after the material has been magnetized. A high coercivity means the material strongly resists being demagnetized, as in a permanent magnet.

What is hysteresis loss?

Hysteresis loss is the energy dissipated as heat each time the material is taken around one magnetization cycle. It equals the area enclosed by the hysteresis loop and, by the Steinmetz equation, is proportional to the frequency and to the peak flux density raised to a power (about 1.6 to 2).

Why do transformer cores use soft iron or silicon steel?

Because their narrow hysteresis loop and low coercivity mean very little energy is lost as hysteresis heat each cycle. Combined with lamination to cut eddy currents, this keeps core loss low and efficiency high in transformers, inductors and motors.

B-H Curve & Hysteresis: Loop, Retentivity, Coercivity & Core Loss

Q: What is magnetic hysteresis?

Magnetic hysteresis is the lagging of the flux density B behind the magnetizing force H when H is cycled. Because the material remembers its previous magnetization, B follows a different path when H rises than when it falls, tracing a closed loop called the hysteresis loop.

Q: What is the difference between soft and hard magnetic materials?

Soft magnetic materials (like silicon steel and ferrite) have a narrow hysteresis loop, low coercivity and low loss, so they are used for transformer and inductor cores. Hard magnetic materials have a wide loop and high coercivity, so they keep their magnetism and are used for permanent magnets.

Q: What is permeability on the B-H curve?

Permeability mu is the ratio B/H, the slope of the magnetization curve. It is small near the origin, greatest around the knee, and falls towards saturation. High permeability means the material magnetizes easily for a given H.

Q: Why does the B-H curve saturate?

A magnetic material is made of many tiny domains. As H increases, more domains align with the field. Once nearly all domains are aligned, no more can contribute, so B levels off at the saturation value even as H keeps rising.

What is the B-H Curve?

The B-H curve (or magnetization curve) plots the magnetic flux density B produced inside a material against the magnetizing force H applied to it. It shows, at a glance, how easily — and how far — a material can be magnetized.

Start from an unmagnetized sample and slowly raise H: B climbs steeply, bends over at the knee, and finally flattens at saturation, where almost all the material's magnetic domains are aligned. This first path is the initial or virgin magnetization curve.

Initial magnetization or virgin curve showing flux density B rising with magnetizing force H to magnetic saturation Bs

The initial (virgin) magnetization curve: B rises with H, through the knee, up to saturation B_s.

B

Flux density (tesla, T)

H

Magnetizing force (A/m)

B_s

Saturation flux density

μ = B/H

Permeability (slope)

B vs H — keep them straight

H is the cause — the magnetizing force you apply (from current in a coil, H = NI/l), measured in A/m. B is the effect — the resulting flux density inside the material, measured in tesla. Their ratio is the permeability.

The Hysteresis Loop

Now cycle H up and down. Because the material remembers its magnetization, B lags behind H and traces a different path each way — a closed hysteresis loop. “Hysteresis” literally means “lagging behind.”

B-H hysteresis loop marking saturation Bs, retentivity Br at zero H, and coercivity Hc at zero B, with the virgin curve dashed

The hysteresis loop: B_s saturation, B_r retentivity (at H = 0) and H_c coercivity (at B = 0). The dashed line is the virgin curve.

Follow it round: raise H to saturate at +B_s; reduce H to zero and B only falls to +B_r (residual magnetism); reverse H to −H_c to force B to zero; drive on to −B_s, and back. That lag is hysteresis.

Retentivity, Coercivity & Saturation

Three points on the loop tell you almost everything about a magnetic material.

Retentivity (B_r)

The flux density left over when H returns to zero — the remanence or residual magnetism. It is why permanent magnets stay magnetized.

Coercivity (H_c)

The reverse H needed to push B back to zero — how strongly the material resists being demagnetized.

Saturation (B_s)

The maximum flux density; beyond it, raising H barely raises B because the domains are fully aligned.

Retentivity vs coercivity

They answer different questions. Retentivity: “how much magnetism remains?” (a B value). Coercivity: “how hard is it to remove?” (an H value). A good permanent magnet needs both high.

Permeability μ = B / H

Permeability is the slope of the B-H curve — how much flux density you get for a given magnetizing force. On a curve it is not constant: it changes as the material approaches saturation.

Permeability as the slope of the B-H curve, mu equals B over H, low near origin, maximum at the knee, falling at saturation

Permeability μ = B/H is the slope: low near the origin, greatest at the knee, and falling as the material saturates.

μ = B / H μ_r = μ / μ₀

Absolute permeability and relative permeability (μ₀ = 4π×10⁻⁷ H/m)

High-permeability materials (soft iron, silicon steel, ferrite) reach a large B for a small H — ideal for concentrating flux in cores. See reluctance & permeance for the magnetic-circuit view.

Hysteresis Loss & Core Loss

Every trip around the loop wastes energy as heat. The energy lost per cycle, per unit volume, equals the area enclosed by the hysteresis loop.

Hysteresis loss equals the shaded area of the B-H loop, energy lost per cycle as heat, with the Steinmetz equation

The shaded loop area = energy lost per cycle per m³, dissipated as heat. A fatter loop means more loss.

P_h = k_h · f · B_maxⁿ

Steinmetz equation: hysteresis loss rises with frequency f and peak flux density (n ≈ 1.6–2)

Core loss = hysteresis + eddy currents

Total core (iron) loss is hysteresis loss plus eddy-current loss. Hysteresis loss is cut by using low-coercivity materials; eddy-current loss is cut by laminating the core. Both matter in transformers and inductors.

Soft vs Hard Magnetic Materials

The shape of the loop decides what a material is good for — and it splits magnetic materials into two great families.

Soft magnetic material with a narrow low-coercivity loop versus hard magnetic material with a wide high-coercivity loop

Soft = narrow loop (low H_c, low loss) for cores; hard = wide loop (high H_c) for permanent magnets.

Property	Soft magnetic	Hard magnetic
Loop	Narrow, tall	Wide, fat
Coercivity H_c	Low	High
Hysteresis loss	Low	High
Magnetized/demagnetized	Easily	With difficulty
Examples	Silicon steel, soft iron, ferrite	Alnico, ferrite magnets, NdFeB
Used for	Transformer/inductor/motor cores	Permanent magnets, loudspeakers

Why It Happens: Magnetic Domains

A ferromagnetic material is divided into tiny regions called domains, each already magnetized. Un-magnetized, they point every which way and cancel out.

Magnetic domains randomly oriented at zero field, partly aligned as H rises, and fully aligned at saturation

As H rises, more domains swing into line. When nearly all are aligned, the material saturates.

Applying H makes domains grow and rotate to line up with the field, raising B. At saturation almost all are aligned. When H is removed, some stay put — that “stuck” alignment is the retentivity, and the energy spent forcing domains back and forth each cycle is the hysteresis loss.

Where the B-H Curve Matters

The B-H curve is the single most important chart for choosing and using magnetic materials in power engineering.

Transformer & inductor cores

Pick a soft, high-μ, low-loss material and keep B below saturation to avoid distortion and overheating.

Permanent magnets

Choose hard materials with high B_r and H_c so they hold their field for motors, speakers and sensors.

Power electronics

Core loss and saturation set the size, efficiency and switching limits of high-frequency magnetics.

Data storage

Magnetic recording relies on retentivity to store bits and coercivity to keep them stable.