# Reconciling Magnetism in material and the Lorentz Force equation

1. Mar 21, 2009

### xerxes73

Hello,

The Lorentz force equation, F = q (E + v x B), is a complete description of the force on bodies arising from Magnetism and Electricity, right? So somehow it must be possible to get from the magnetism that exists in materials (like in a magnet) to this equation. I don't see how the connection can be made. How could one get from having a magnet that always gives off a magnetic field that will cause a force on a piece of steel to this equation which has the velocity of charges? Is there a velocity of an electron in the magnet that will make this all work out. I am guessing that because of the bizarre nature of electrons the answer would be no, so how can one explain the nature of magnets with this equation.

And another question is how in how in heck did they make sense of this connection from magnets to this equation back in Maxwell's time when they didn't even know that an electron existed....?

Anyway, insight into this would be greatly appreciated. Thanks! -xerxes73

2. Mar 22, 2009

### tiny-tim

Hello xerxes73!

It's because the electrons in the steel are moving (spinning) charges, and so the magnetic field will pull them "sideways".

In most materials, these forces are random, because the electron spins are random, and so the net force is zero, and the material goes nowhere.

But in a magnetisable material such as steel, the electrons can all be persuaded to face the same way, so the forces add up.
I think they only dealt with magnetic fields from currents in wires.

3. Mar 22, 2009

### xerxes73

Thanks Tiny-Tim So if you took the spins calculated what forces are in play and what E and B fields are there, they would follow this classical Lorentz force law, or does this break down pretty quick in the face of quantum mechanics?

I guess I have heard that Maxwell came up with a strange model with vortexes and things like that to explain the inner-workings of these forces in space and in atoms and perhaps that was in response to this need to explain magnetism in materials. Because even though he did a complete classical description of electricity and magnetism, electron spins would be something that he didn't have access to and so that must have been a big area of mystery to him and the other guys working this problem. Anyway, anyone with insights into that I would greatly appreciate hearing from.

Thanks! -xerxes73

4. Mar 22, 2009

### Meir Achuz

Ferromagnetism is due to the aligned magnet moments and spins of the electrons in iron.
These are quantum effects, and spin angular momentum of a point particle is not a classical concept. The force grad(m.B) and torque mXB on an electron magnetic moment cannot be derived directly from the Lorentz force law, because there is no current involved. It is a new type of force, but can be inferred by analogy with the interaction of a current loop. In another thread, it was noticed that the energy of a QM magnetic moment in a magnetic field had a sign (-m.B) opposite that of a current loop in a magnetic field (+m.B).

Early on, Farady conjectured that ferromagnetism was due to current loops in molecules, and (although that was before my time) I think that was the general feeling until QM spin entered.

5. Mar 22, 2009

### Bob S

Hello Xerces73-
Who needs equations like Maxwell's equations or the Lorentz Law of Force, which were developed in the 1860's and 1870's. Look here http://www.sparkmuseum.com/MOTORS.HTM to see the electric motor Faraday built in 1821, ten years before J. C. Maxwell was even born.