Hysteresis Loop Simulator: B-H Curve of Magnetic Materials

simulator intermediate ~10 min
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B_r = 1.05 T, H_c = 40 kA/m — semi-hard magnetic material

With saturation of 1.5 T, coercivity of 40 kA/m, and squareness of 0.7, the material has a remanence of 1.05 T — intermediate between soft transformer steel and hard permanent magnet material.

Formula

B = μ₀(H + M), where M follows hysteresis path
B_r = S × M_s (remanence from squareness ratio)
(BH)_max ≈ μ₀ × M_s² / 4 (ideal energy product)

The Magnetic Memory

Hysteresis — from the Greek 'to lag behind' — is the defining characteristic of ferromagnetic materials. When you apply a magnetic field to iron, its magnetization does not simply follow the field; it lags, creating a loop when the field cycles. This loop encodes the material's magnetic history and determines whether it serves as a permanent magnet, a transformer core, or a recording medium. The shape of the B-H curve is the fingerprint of a magnetic material.

Anatomy of the Loop

The hysteresis loop reveals four critical parameters. Saturation magnetization (M_s) is the maximum magnetization when all atomic moments are aligned — an intrinsic property of the material's chemistry and crystal structure. Remanence (B_r) is the flux density remaining after the field is removed. Coercivity (H_c) is the reverse field needed to demagnetize the material. Squareness (S = B_r/B_s) measures how abruptly domains switch, ranging from gradual (low S) to snap-like (high S).

Hard vs. Soft

The width of the hysteresis loop separates the magnetic world into two classes. Soft magnetic materials — silicon steel, ferrite, permalloy — have razor-thin loops (coercivity under 1 kA/m), switching easily with minimal energy loss. They are essential for transformers, inductors, and magnetic shielding. Hard magnetic materials — NdFeB, SmCo, ferrite magnets — have wide loops (coercivity above 100 kA/m), resisting demagnetization tenaciously. They power electric motors, headphones, and MRI machines.

Energy and Loss

The area enclosed by the hysteresis loop equals the energy dissipated per unit volume per magnetization cycle. In a transformer operating at 60 Hz, this loss occurs 60 times per second and must be minimized — hence the use of grain-oriented silicon steel with extremely thin loops. Conversely, permanent magnets benefit from wide loops, as the maximum energy product (BH)_max — proportional to the area of the largest rectangle inscribable in the second quadrant — determines the magnet's strength per unit volume.

FAQ

What is a hysteresis loop?

A hysteresis loop (B-H curve) traces how a ferromagnetic material's magnetic flux density B responds to an applied magnetic field H through a complete cycle from positive saturation to negative saturation and back. The loop shape reveals key material properties: coercivity (field needed to demagnetize), remanence (residual magnetization), saturation, and energy loss per cycle.

What is coercivity?

Coercivity (H_c) is the magnetic field strength required to reduce a saturated material's magnetization to zero. Soft magnetic materials (transformer steel, permalloy) have very low coercivity (<1 kA/m), making them easy to magnetize and demagnetize. Hard magnetic materials (NdFeB, SmCo) have very high coercivity (>100 kA/m), making them resistant to demagnetization — ideal for permanent magnets.

Why does the hysteresis loop have area?

The area inside the hysteresis loop represents energy dissipated as heat during each magnetization cycle. This hysteresis loss occurs because domain walls must overcome pinning sites (defects, grain boundaries, inclusions) as they move. In transformers operating at 50/60 Hz, hysteresis loss is a major source of energy waste, which is why soft magnetic materials with thin loops are used.

What determines loop squareness?

Squareness (S = Mr/Ms) reflects how uniformly the magnetic domains switch. A perfectly aligned single-domain material has S = 1 (perfectly square loop). Polycrystalline materials with random grain orientations have lower squareness because domains oriented at different angles switch at different field strengths, rounding the loop corners.

Sources

Embed

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