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This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets. A permanent magnet is an object made from a material that is magnetized and
Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed. Ferromagnetic and ferrimagnetic materials have strong magnetization in a magnetic field, and can be magnetized to have magnetization in the absence of an external field, becoming a permanent magnet. Magnetization is ...
A Halbach cylinder is a magnetized cylinder composed of ferromagnetic material producing (in the idealized case) an intense magnetic field confined entirely within the cylinder, with zero field outside. The cylinders can also be magnetized such that the magnetic field is entirely outside the cylinder, with zero field inside.
For permanent magnets this is usually only a small change, but if you have an electromagnet that consists of a wire wound round an iron core, and you bring a permanent magnet near to that core, then the magnetization of that core can change drastically (for example, if there is no current in the wire, the electromagnet would not be magnetic ...
When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet. When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is magnetically saturated.
This is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) into regions of higher magnetic field. Any non-uniform magnetic field, whether caused by permanent magnets or electric currents, exerts a force on a small magnet in this way.
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