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A permanent magnet produces lines of magnet flux that we call a "magnetic field". Those lines come from inside the magnet, come out of the N pole, loop outside the magnet, & return back into the S pole to complete a magnetic circuit. Using ferromagnetic materials, other magnets, &/or test equipment, we feel & measure forces that are caused by a magnet/s when other materials are placed within close enough proximity to the magnet/s (i.e. within their magnetic field/s). We therefore conclude that the magnetic lines flow in a specific direction & exert definite forces (i.e. magnitudes/strength) on some materials (ferromagnetic & other magnets), depending on where those materials are placed within the magnetic field of a magnet/s.

We label those forces as "H Field" & "B Field".
We measure H in terms of Amperes/meter. We measure B in terms of Newtons/meter/Ampere (or Tesla). We also commonly defined B in terms of the force that it exerts on moving electric charges (i.e. the Lorentz force).

An "Ampere" is basic unit of electrical current in the SI system, which = 1 Coulomb per second--which is formally defined to be the constant current which if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10 −7 newton per meter of length.

A "Coulomb" is the standard unit of quantity of electricity in the SI system, which = the quantity of charge transferred across a conductor in which there is a constant current of 1 Ampere/Second.

Consequently, those "magnetic lines" are currents (or flows) of charges that don't appear to need any external source of energy to continue generating their currents.

We also know those magnetic lines exist inside a vacuum, so they are independent of air molecules to flow outside of a magnet.

So now my questions:

  1. Exactly what charged particles are flowing outside (and inside) a permanent magnet that create the magnetic "lines"?

  2. Do those particles come from something inside the magnet or does the magnet do something outside of it to affect unknown particles to make the lines?

  3. If there is a current (i.e. a continuous flow of charged particles), then why don't we harness that current like a water wheel (instead of 'using energy' to rapidly move copper wires through magnetic fields--like we do with electricity generators?) Shouldn't we be able to get the line currents to charge a capacitor (or or other device) & then otherwise discharge the capacitor for the energy that we want?

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Stationary electric charges produce electric fields who's behavior is pretty easy to understand. However, when you move an electric charge, that electric field gets a bit more complicated because of relativity. We call that relativistic electric field a "magnetic" field. So a magnetic field is simply a relativistic electric field. The magnetism is produced by the moving charges in the material (the spin and orbit of electrons orbiting the nuclei, and the free electrons moving when there is electric current). A permanent magnet has its electron orbitals lined up so they contribute to an overall magnetic field.

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  • $\begingroup$ the electrons move very slowly (cm/sec) in a metal, their speeds are nowhere near relativistic speed and the resulting current still generates macroscopic magnetic fields: $curl \vec H = \vec J$ $\endgroup$ – hyportnex Dec 25 '15 at 1:36
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    $\begingroup$ @hyportnex, the Lorentz transform doesn't wait for the speed to exceed some nominal value before it takes effect. See en.wikipedia.org/wiki/Relativistic_electromagnetism $\endgroup$ – Digiproc Dec 25 '15 at 2:08
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This question was cross-posted on Electronics Stack Exchange. Here is my answer from over there:

Exactly what charged particles are flowing outside (and inside) a permanent magnet that create the magnetic "lines"?

The magnetic field of a permanent magnet is not caused by flowing particles.

The electrons within a ferromagnetic material, even if they aren't flowing, have quantum mechanical spin. If the spin vectors of many of the electrons within the material are aligned, they produce a net magnetic dipole moment, producing the macroscopic magnetic field lines associated with a permanent magnet.

(This is just another way of saying, even when electrons aren't moving, they produce a magnetic field. We don't really know "why" that is, but we have a mathematical model of how much field they produce and how it interacts with other objects, and we call that model the "spin" of the electron).

You can read more about this in the Wikipedia article on Ferromagnetism.

Do those particles come from something inside the magnet or does the magnet do something outside of it to affect unknown particles to make the lines?

It comes from the electrons in the magnetic material.

If there is a current (i.e. a continuous flow of charged particles), then why don't we harness that current like a water wheel

Since the magnetic field doesn't derive from the flow of particles, we can't harvest it as if it were a flow of particles.

We measure B in terms of Newtons/meter/Ampere ... Consequently, those "magnetic lines" are currents (or flows) of charges

The B-field has amperes in its units because it produces a force on a moving charge according to the Lorentz law:

$$\vec{F}=q\vec{v}\times{}\vec{B}$$

Since it is multiplied by a charge and a velocity to produce a force, it must have units $\dfrac{[\mathrm{N}][\mathrm{s}]}{[\mathrm{C}][\mathrm{m}]}$ in order for the equation to balance.

Just as a force itself has $[\mathrm{kg}]$ in its units because it has an effect on something with mass, although a force does not have mass itself; a B-field must have charge in its units because it effects charges, not because it is composed of charge or contains charge.

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