About Magnetic Hysteresis Loop
When a ferromagnetic material is subjected to a cyclic applied field H, the resulting magnetic flux density B does not follow the same path on the way up as on the way down — it lags behind H in a phenomenon called hysteresis. The B-H curve forms a closed loop whose area equals the energy dissipated as heat per unit volume per cycle (in joules per cubic metre). Three key parameters characterise the loop: saturation flux density Bs (the maximum B achievable), remanence Br (the residual magnetisation when H returns to zero), and coercivity Hc (the reverse field needed to demagnetise the material).
The simulation lets you cycle through the B-H loop at adjustable speed and switch between a hard magnetic material (high Hc, wide loop — used in permanent magnets) and a soft material (narrow loop, low losses — used in transformer cores). Animated magnetic domains illustrate how domain-wall motion underpins the macroscopic curve.
Frequently Asked Questions
Why does the B-H curve form a loop rather than a single line?
Hysteresis arises because magnetic domain walls pin to crystal defects and impurities. Energy is required to unpin and move walls in one direction; when H is reversed the walls re-pin at different positions, so the path back is different from the path up. The enclosed loop area represents irreversible energy loss, converted to heat inside the material each cycle.
What is the difference between a hard and a soft magnetic material?
A hard magnetic material (e.g., NdFeB, AlNiCo) has high coercivity Hc — its domain walls are strongly pinned, making it difficult to demagnetise and ideal for permanent magnets. A soft material (e.g., silicon steel, mu-metal, ferrite) has a narrow hysteresis loop with low Hc and low core loss, which is why transformers and inductors use soft magnetic cores: energy losses per cycle stay small even at 50–60 Hz.
How is hysteresis energy loss calculated?
The energy loss per cycle per unit volume W = ∮ H dB, which equals the area enclosed by the B-H loop in SI units (J m⁻³ per cycle). Power loss per unit volume is P = W × f, where f is the operating frequency. At 50 Hz a transformer core with loop area 100 J m⁻³ dissipates 5 kW per cubic metre — a key driver for choosing low-loss grain-oriented silicon steel in large power transformers.
What causes magnetic saturation?
Saturation occurs when essentially all magnetic domains in a material are aligned with the applied field — there are no more domain walls to move. Adding more H produces only a tiny paramagnetic increase in B (slope ≈ μ₀). For iron, Bs ≈ 2.1 T; for NdFeB, Bs ≈ 1.6 T; for soft ferrites used in switching supplies, typically 0.3–0.5 T.
What is remanence (residual magnetism) used for?
Remanence Br is the flux density remaining when H returns to zero after saturation. Permanent magnets exploit high remanence: an NdFeB magnet has Br ≈ 1.0–1.4 T. Data storage on hard disks and magnetic tape also relies on remanence — a recorded bit is a tiny patch of material left magnetised in one of two stable directions after the write head passes.
What is the Curie temperature and how does it relate to hysteresis?
Above the Curie temperature TC, thermal agitation destroys the long-range exchange interaction that aligns neighbouring spins, and the material becomes paramagnetic with no hysteresis loop at all. For iron TC = 770 °C; for nickel 358 °C; for NdFeB only about 310 °C — a key limitation for motors operating in high-temperature environments.
Why do transformer cores use laminated sheets?
A solid iron core would allow large eddy currents to circulate, generating additional resistive losses on top of hysteresis loss. Laminating the core into thin sheets (typically 0.27–0.35 mm for power transformers) insulated from each other forces eddy current paths to be short and thin, reducing eddy-current losses roughly as the square of lamination thickness.
What are Barkhausen jumps?
When H increases slowly and continuously, the magnetisation of a ferromagnet does not increase smoothly — instead domain walls snap from one pinning site to the next in discrete jumps. These Barkhausen jumps can be heard as crackling noise through a pickup coil and amplifier, and their statistics encode information about defect density and material stress — used in non-destructive testing of steel structures.
How do ferrites differ from metallic ferromagnets in hysteresis?
Ferrites are ceramic oxides (e.g., MnZn or NiZn ferrite) with much lower electrical conductivity than iron, so eddy-current losses are negligible even at MHz frequencies. Their saturation flux density (0.3–0.5 T) is lower than silicon steel, but their loop shape can be engineered for square (memory/switching) or low-loss (RF inductor) applications. This makes ferrites the material of choice in switch-mode power supplies and radio-frequency transformers.
What is a minor hysteresis loop?
If H is cycled between values smaller than those needed for full saturation, the material traces a smaller inner loop called a minor loop. The tip of each minor loop does not reach the major (saturated) loop. Understanding minor loops is important in magnetic recording and in the design of magnetic amplifiers, where the operating point intentionally stays within the major loop.
Can hysteresis occur in non-magnetic systems?
Yes — hysteresis is a general feature of bistable systems with memory. It appears in shape-memory alloys (stress-strain curves), ferroelectric capacitors (polarisation-electric field loops exploited in FeRAM memory chips), superconductors (flux pinning creates a Bean critical-state loop), and even in social or biological systems where a threshold must be exceeded to change state.