In the 3 magnetic elements (Iron, Nickel and Cobalt), the atomic structure (lattice) is arranged (or becomes arranged) in straight lines. The atoms line up kind of in a "Hand-in-Hand" fashion, which results in a circulating flow - hence the magnetic attraction.
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how does a magnetic circuit work
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When electrons flow in a conductor, there is a resulting Magnetic field produced (at a right angle to the flow).
In the core of a transformer, or a solenoid's core, the winding produces a magnetic flux in the core - via Induction. The magnetic flow acts similar to the electrical flow, and changes are made correspondingly.
The simplest explantion is that a magnetic field is associated with a moving electron. It is a "force" in the way if affects its surrounding. That is its ability to attract or repel other "particals" in its space.
Whether and electron is moving through a medium, such as a conductor, or around the nucleus of an atom, it affects the space around it. By, itself, the elctron's effect is weak, but when coupled with the effects of other electrons in the same space, the effect is stronger. But, that is only true if the electrons are alligned the same way, or else their effects will cancel.
Iron atoms, unlike others, have the ability of their elctrons in orbit to align them selves in the same direction. This is called polarisation. The total effect of this can be felt far outside the iron mass.
Electrons moving together in unison in a conductor also produce a magent field. If that conductor is wound in the form of a coil, the magnetic field produced in each turn is magnified, and the effect is stronger. A force is felt far from the coil, but drops off in strength per the square of the distance from the coil.
The force produced in a conductor is caculatable and is the defining point for the unit ampere.
"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per metre of length."
