# Can the Lorentz force explain magnetic attraction when E=0?

1. Sep 2, 2011

### kmarinas86

Given that the Lorentz force on a current when E=0 exists only at right angles to the current, such would not change the speed of the current, but only its direction. Also, when the current is parallel to a magnetic field line, no deflection of the current by the magnetic field occurs.

A magnet consists of many bound currents. It would appear the apparent acceleration of magnets would simply be due to the deflection of their internal bound currents, and when these bound currents are slightly deflected toward magnetic fields, they would travel further along the magnetic field lines than they would cutting through them, all without gaining or losing speed or kinetic energy.

It would then seem that one does not have to have a changing electric field to explain how magnets accelerate. Magnets would simply be taking the kinetic energy of charges and somehow aligning their motions, which thereby makes them apparent to a real world observer. Additionally, when magnets decelerate through the opposition of like magnetic poles facing each other, the opposite would occur.

Is my explanation wrong in some way?

Last edited: Sep 2, 2011
2. Sep 3, 2011

### clem

"Is my explanation wrong in some way?"

Yes. For starters ferromagnetism is caused by aligned spin magnetic moments of electrons, and not bound currents.

3. Sep 3, 2011

### kmarinas86

The bound currents which I spoke of do exist:

http://scienceworld.wolfram.com/physics/BoundSurfaceCurrent.html
http://scienceworld.wolfram.com/physics/BoundCurrentDensity.html

Though I must admit that if we are actually taking about ferromagnetic materials, then of course then discussion of spin (as opposed to loop currents) becomes necessary.

In any case I think I answered my question, "Can the Lorentz force explain magnetic attraction when E=0?"

The answer was yes. But for some reason, I was also reading this question as, "Can the Lorentz force explain why magnets attract when E=0, given that some had said that the E-field is what does the work?"

The latter is what I really meant to ask.

It seems that I have split the the other half of the question into a separate thread (https://www.physicsforums.com/showthread.php?p=3483915&posted=1).

Anyway, if we are talking about electron spins rather than bounded currents, it would seem that the Lorentz force has nothing to do with it. Is that correct?

4. Sep 3, 2011

### Ken G

Is your question tantamount to why do two currents in the same direction attract each other, and can accelerate two parallel wires toward each other as a result? If so, remember that whether you have a B or an E is a matter of reference frame. One way to see why a current is attracted to another pointing in the same direction is to first look from the point of view of the stationary positive ions-- they see moving electrons in the other wire, which are length-contracted by relativity, so have a higher charge density than the stationary positive ions in the other wire. So the positive ions are attracted to that excess negative charge density. But entering the frame of the electrons in that first wire, we then see the positive ions as length contracted, so they think the charge overdensity is positive, and are also attracted. Those are electric fields doing that.

5. Sep 3, 2011

### kmarinas86

The E-field would be able to change the speed but the B-field would not be able to do that, if we use the Lorentz force that is. I do not see how simply changing from one inertial frame to another which changes the B-field to an E-field could change the situation as to whether or not the speed of the currents are constant. While, when seen as a B-field, the currents should only be deflected, not change in speed, as a result of these interactions, you say this interaction can be described as an E-field in a different frame, in which case we should see forces on the charges (via the E-field) which should be capable of doing work. How is this reconciled? Is it by uniformity of the E-field along the length of these parallel wires?

Last edited: Sep 3, 2011
6. Sep 4, 2011

### Ken G

The Lorentz force is really just a force fragment, the complete force is called the "generalized Ohm's law". Look at http://en.wikipedia.org/wiki/Ohm's_law and scroll down to "magnetic effects." The Lorentz force explains why there is an attractive force, but since you are wondering about where the kinetic energy comes from, in the frame you are using you will not see any kinetic energy until there is motion of the conductor. In other words, the rate of change of kinetic energy depends on the product of the force times the velocity, so you'll never see any rate of change of kinetic energy until you consider the force on a conductor that has a velocity.