How Magnets Interact & What Happens to Magnetization

[da_willem]

It is well known the magnetic force cannot do work. What causes a magnet to move in the precense of another magnet? Does the magnetization of the two magnets diminish in the proces?

 

[joshuaw]

Well, i believe that I have to disagree with this idea some what. If you were to take a naturally magnetic material and let us assume that it is strong enough to move a paper clip. If you bring the material close to the paper clip, the clip will move. The clip feels a force and moves a distance. Now many would argue(Griffiths) that the work was provided by another source. But, last time I checked it is the magnetic fields that caused the clip to move. Since the magnetization is "intrensic", the magnetic domains give the property needed to move the clip. So I guess he would argue that the magnetic moments have done the work.

David Griffiths argues that magnetic fields do not do work using a crane used to move cars(page 207 D.J.Griffiths "Introduction to Electrodynamics" 3rd ed.). This is an induced magnetic field. I agree that the work is "produced" by the current in the coils. But he never discusses naturally occurring magnetic materials.

For me, this is a grey area. You really have to be careful about what causes the magnetic field.

 

[Crosson]

I would like to discuss Grifith's arguments that the magnetic force does not do work, I have never known whether or not to believe them and would like to see what you guys think about it.

His first argument is "The magnetic force is always perpendicular to the velocity, hence it does no work".

I disagree because of rotational work; look at the action of the magnetic dipole in a magnetic field. The potential energy is:

$$U =- \vec{\mu} \cdot \vec{B}$$

Where mu is the magnetic moment equal to I*A for an elementary loop.

Grifith's text is one of the best, so I hesitate to disagree with him; but isn't work the negative of potential energy?

 

[Reality_Patrol]

There's a little bit of mixing apples with oranges going on here.
The statement that "magnetic forces do no work" comes from
considering the Lorentz Force law. This is the expression used to obtain the
equations of motion for an eletrically charged particle
(like an electron). Let's call this the apple.

Now for the orange, magnetic fields can do work on magnetic
dipoles (permanent magnets, electromagnets, fundamental
particles with intrinsic dipole moments...). In which case the working
force can be derived from the magnetic potential as Crosson has indicated
above. That expression leads to a fairly different looking "force law"
from the well-known "Lorentz Law" and it has no official name.

 

[joshuaw]

This is where I had a problem. Since there are no magnetic monopoles, we have to be careful. I do not believe that just saying a particle has an intrinsic magnetic moment is valid enough. The question for me is where does this moment come from. If it is really an intrensic property, then I would have to lean to believe that the magnetic fields do work in this situation. If we find that it is really doe to the localization of a charged particle, then I do not believe we can say this. This is why believe it is a grey area.

 

[Q_Goest]

Magnets, gravity, electric fields, stretched springs or rubber bands... any two masses that are separated but affected by some force pulling them together has potential energy. Release the two objects so they come together and that potential energy converts to kinetic energy. When the two objects slam into one another (assuming they don't bounce off) the kinetic energy is converted to thermal energy in the form of noise and heat. Energy is always conserved.

Note also that the objects could also do an amount of work equal to the potential energy that exists when they are separated. But once they do that work, that's all the work they can do without being separated again, or 'reset'.

Electric motors which use magnetic fields simply convert one form of energy (electricity) into another form of energy (rotational motion) by manipulating magnetic fields. In affect, electric motors 'reset' the potential energy of the magnetic field in order to continue producing work.

 

[da_willem]

There's a little bit of mixing apples with oranges going on here.
The statement that "magnetic forces do no work" comes from
considering the Lorentz Force law. This is the expression used to obtain the
equations of motion for an eletrically charged particle
(like an electron). Let's call this the apple.

Now for the orange, magnetic fields can do work on magnetic
dipoles (permanent magnets, electromagnets, fundamental
particles with intrinsic dipole moments...). In which case the working
force can be derived from the magnetic potential as Crosson has indicated
above. That expression leads to a fairly different looking "force law"
from the well-known "Lorentz Law" and it has no official name.

But isn't it true that also non-intrinsic magnetic moments like current loops obey the force law dervied from the potential

$$U=-\vec{\mu} \cdot \vec{B}$$

So it cannot have anything to do with the 'intrinsicality' of the dipole. Anyways this would be strong evidence for the intrinsic nature of the magnetic moment of the electron, which is still debated.

So the question remains how come there is this force

$$F= \nabla (\vec{\mu}} \cdot \vec{B})$$

that can do work?

A current loop is a dipole, which is nothing more than moving charged particles which can be described by the Lorentz force law which cannot do work, so where is the solution to this paradox? Has it got something to do with the inhomogeneity of the magnetic fields, with quantum mechanics, or what?

 

[seratend]

But isn't it true that also non-intrinsic magnetic moments like current loops obey the force law dervied from the potential

$$U=-\vec{\mu} \cdot \vec{B}$$

So it cannot have anything to do with the 'intrinsicality' of the dipole. Anyways this would be strong evidence for the intrinsic nature of the magnetic moment of the electron, which is still debated.

So the question remains how come there is this force

$$F= \nabla (\vec{\mu}} \cdot \vec{B})$$

that can do work?

A current loop is a dipole, which is nothing more than moving charged particles which can be described by the Lorentz force law which cannot do work, so where is the solution to this paradox? Has it got something to do with the inhomogeneity of the magnetic fields, with quantum mechanics, or what?

A magnetic field can only exchanges momentum with the system it interacts with (no work).

A magnetic momentum of a system or a spin is the tool that exchanges the momentum provided by the magnetic field and the position and momentum of the system (its energy) (i.e. form the orbital momentum or spin i.e. L=rxp).
In other words, you can view the orbital momentum or the spin as an energy source/sink that exchanges the energy between the system and the spin/orbital momentum (if the spin/orbital momentum is attached to a fixed position of the system like magnets).

A good example is the moving wire with a current under a magnetic static field. The magnet loose no energy (just momentum). The wire starts moving in order to keep the orbital momentum of the electrons compatible with the current path in the wire and the magnetic field. Now, because the wire starts moving, it takes its energy from the electrons and not from the magnetic field.

Seratend

 

[pmb_phy]

Well, i believe that I have to disagree with this idea some what. If you were to take a naturally magnetic material and let us assume that it is strong enough to move a paper clip. If you bring the material close to the paper clip, the clip will move. The clip feels a force and moves a distance. Now many would argue(Griffiths) that the work was provided by another source. But, last time I checked it is the magnetic fields that caused the clip to move. Since the magnetization is "intrensic", the magnetic domains give the property needed to move the clip. So I guess he would argue that the magnetic moments have done the work.

It is not the magnetic field doing work in the example you gave. As I recall, it is another force in the system that is doing the work. It may appear to you that it is the magnetic force doing work but it is actually another force (force of conductor on charge I think) that is doing work. There was an article on this topic in AM. J. Phys. If anyone wants to read it let me know and I'lll dig up the reference.

Pete

 

[da_willem]

It is not the magnetic field doing work in the example you gave. As I recall, it is another force in the system that is doing the work. It may appear to you that it is the magnetic force doing work but it is actually another force (force of conductor on charge I think) that is doing work. There was an article on this topic in AM. J. Phys. If anyone wants to read it let me know and I'lll dig up the reference.

Pete

I would definitely want to read some more on this subject, so if you could...

 

[da_willem]

A good example is the moving wire with a current under a magnetic static field. The magnet loose no energy (just momentum). The wire starts moving in order to keep the orbital momentum of the electrons compatible with the current path in the wire and the magnetic field. Now, because the wire starts moving, it takes its energy from the electrons and not from the magnetic field.

Seratend

So the kinetic energy of the wire remains constant because as it accelerates the current decreases by just the right amount to allow for the increase in velocity of the wire?

 

[seratend]

So the kinetic energy of the wire remains constant because as it accelerates the current decreases by just the right amount to allow for the increase in velocity of the wire?

I will say it depends on the current behaviour (the source of energy transferred to the electrons by an external source) (if the current is externally forced to be constant or not, etc ...). Note that the wire develops the so-called Laplace force, a reaction to the electric force created by the wire to keep its neutrality (property of the wire) due to the update of the electrons orbital momentum. This force allows the transfer of the energy between the electrons of the current and the wire (and not between the magnetic field and the wire). When we look at the wire and not the electrons path, we just got the classical dynamical equations (due to the neutral property of the wire and the different time scales).

Seratend.

 

[pmb_phy]

I would definitely want to read some more on this subject, so if you could...

See

Work done on charged particles in magnetic fields, Charles A. Coombes, Am. J. Phys. 47(10), Oct. 1979

I thought I had two but I must have been thinking about something else.

Pete

 

[da_willem]

See

Work done on charged particles in magnetic fields, Charles A. Coombes, Am. J. Phys. 47(10), Oct. 1979

I thought I had two but I must have been thinking about something else.

Pete

Thanks, it looks like this is going to answer my questions, I'll get right to it!