Magnetic Hysteresis

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Ferromagnetic materials exhibit hysteresis, meaning dependence of magnetization on the history of the applied magnetic field. A ferromagnet can thus be described as exhibiting memory of its previous magnetic states. A sample of iron is comprised of domains, microscopic regions in which the atomic magnets are locally aligned. These are represented in the graphic by blue arrows. In the unmagnetized state, the domains are randomly oriented. When an external magnetic field , expressed in units of amperes/meter (A/m), is applied, the domains begin to align themselves in the direction of the magnetic field. The iron becomes magnetized, acquiring a magnetic flux density (or magnetic induction) , expressed in units of tesla (T).


In this Demonstration, is increased until the magnet becomes saturated, with all the domains aligned for a maximum induction . The iron bar will retain its magnetization indefinitely, even after the external field is removed. In order to demagnetize the bar, a magnetic field in the opposite direction must be applied. The iron resists demagnetization, with lagging behind changes in . When is reduced to zero, the flux density is reduced slightly to , known as the remanence. Only when the magnetic field is increased to a value in the opposite direction, known as the coercivity, does the iron lose its magnetization and do its domains return to random orientations. The area enclosed by one cycle on the vs. plot is equal to the energy dissipated as heat.

The parameters in this Demonstration are representative of many iron alloys (including steels). Other magnetic materials, including rare-earth elements such as neodymium, are capable of much higher magnetic fluxes. The slider that cycles the magnetic field represents possible physical behavior only when moved from left to right.


Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: saturation of magnetic flux

Snapshot 2: remanence exhibited when

Snapshot 3: coercive field demagnetizes iron bar

Snapshot 4: saturation in the opposite direction

Snapshot 5: lower coercivity reduces energy loss per cycle, desirable in transformers and motor cores

Snapshot 6: higher coercivity is desirable for permanent magnets and magnetic recording devices

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.