# Why does Lorentz Force law work?

1. Nov 20, 2007

### Brock

Last edited: Nov 20, 2007
2. Nov 20, 2007

### cesiumfrog

Special relativity might answer your question today, but that would only prompt another "why" question, which physicists can't really help you with (rather than taking my word, read Feynman's little volume for the public on quantum electrodynamics, "QED").

3. Nov 20, 2007

### Brock

Thanks, but I can't find that Feynman book so far. I did find these lectures http://www.vega.org.uk/video/subseries/8

Does he explain it in there? He says chemistry is really quantum physic's interactions, details on this is what I'm looking for, but for electric motors, or force laws.

4. Nov 20, 2007

### cesiumfrog

What I meant was, in QED he firmly emphasises that physics cannot answer "why" questions.

5. Nov 21, 2007

### Parlyne

The right hand rule has no actual physical meaning. It's simply a sign convention (i.e. that $(\vec{A} \times \vec{B})_x = A_yB_z - A_zB_y$ rather than $A_zB_y - A_yB_z$, and so on). This amounts to an ambiguity in direction for certain quantities. At a formal mathematical level, what we can say is that of the three quantities involved in a cross-product, only two can be normal vectors. The third must be what's known as an "axial vector" or "pseudovector."

In the case of the Lorentz force law, the pseudovector is the magnetic field, since we already know there's ambiguity in the direction of a velocity or a force. Since the magnetic field is a pseudovector, it should be possible to construct it as a cross-product between two normal vectors. (Or, objects that transform like normal - or "polar" - vectors.) And, in fact, we have such a notion. The magnetic vector potential is a normal vector. So, when we write $\vec{B} = \vec{\nabla} \times \vec{A}$, we introduce a quantity that lacks the sign ambiguity. (You may want to try writing the Lorentz force law in terms of $\phi$ and $\vec{A}$, to convince yourself that the right hand rule is actually irrelevant here.)

From the point of view of quantum physics, the vector and scalar potentials are the fundamental EM degrees of freedom; and, the only ambiguity they have is gauge invariance, which is (in a certain sense) seem as a feature of the theory.

6. Nov 21, 2007

### Brock

well I have a theory of how it works. I've connected the dots with already existing magnetic, and physical effects. It seems to make practical sense. I don't know if, or where I should submit this, it might be worthless, or be seen as worthless, and I don't want to submit it somewhere, and have it brushed away.

7. Nov 21, 2007

### Schneibster

If you're asking how it works, in somewhat less technical language, here it is:

Magnetism is a relativistic correction to the action of the electrostatic field. It therefore acts in opposition to the electric field, and at right angles to the motion of the object subject to the correction. A good example is:

Suppose two electrons are moving by your position as an observer. Suppose they are moving quite slowly. Their electrostatic fields will act upon each other, pushing them apart. This action will take place at a certain rate; the electrons will be accelerated away from one another. Now suppose that they are moving at relativistic velocities. The electrons will experience time dilation (from the point of view of an observer). This will cause them to accelerate more slowly.

If you ignore relativity, then you will conclude that there is some extra force opposing the electric force; this force acts at right angles to their motion, and oppositely to the electric force. We call this force, "magnetism." Magnetism acts orthogonally to the motion of an electric charge, oppositely to the direction of the electric force. Magnetism only acts on moving charges; without motion, there's no relativistic effect.

We ordinarily encounter magnetism in permanent magnets. The situation here is, the electrons in the atoms in the permanent magnet revolve (in quantum fashion) around the nuclei of the atoms, and this revolution is the moving charge that generates the magnetic field; as always, perpendicular to the motion, so it emerges perpendicular to the rotation. The "orbit" analogy for the atom works well here, as long as you don't confuse "orbits" with orbitals, the complex figures that represent the probability of finding electrons at various locations around the nucleus. It's merely that the average of the electron's motions adds up to circular motion; the electron doesn't actually move that way.

8. Nov 22, 2007

### Brock

My theory has to do with why homopolar motor/generators work. Does not explain other motors (yet). Here's a question. When a metal disc, lets say copper, spins the atoms spin that's for sure, but do the free floating electrons spin to? Free floating electrons are not bound to any atoms, but they are bound to the piece of metal as a whole, and have to stay spread out, to flow the law's of entropy. Am I right?

9. Nov 22, 2007

### cesiumfrog

You do realise that the mainstream theory of electrodynamics already explains both quite nicely?

10. Nov 22, 2007

### Brock

It must be explainable right down to quantum mechanical effects, don't you think?