I was sticking to classical physics. If you want to be technical, string theory would tell you that there are no point particles.
Ahh, but a neutron is composed of charged particles, too. And of course, this conversation has nothing to do with the op, which was about classical physics. I will defer to you that electrically neutral, massive particles with nonzero spin all have magnetic dipole moments. I don’t remember that, but I haven’t had QM field theory in over 20 years.
It doesn’t matter whether only charged particles have magnetic moments, there are still magnetic fields not due to moving charges or changing electric fields.
I’m still not convinced magnetic fields do no work. Ring’s equation shows a magnetic field does no work on an electric charge, but that doesn’t address magnetic dipoles. Maxwell’s equations contain no source for a magnetic dipole, even though physically they exist, so looking to Maxwell’s equations may not be sufficient. Magnetic dipoles would have to be modeled as something else, which could obscure the physics (do I get the same answer to the OP modeling a magnetic dipole as a small current loop as I get modeling it as a pair of magnetic charges? Not likely).
A permanent magnet allowed to slowly rotate in a magnetic field can certainly do work, and it’s still not obvious to me that that work is only done through an electric field.
So if i Understand this explanation, if magnetic monopoles exist, then their mutual magnetic fields cold do work on each other whether or not they were electrically charged.
Yes. And if they have no electric moment or charge, electric fields could do no work on them.
It’s not the magnetic field doing the work, but rather, the electric field generated by the magnetic field that’s doing the work?
A. I don’t understand the difference between a magnetic field doing work and an electric field generated by a magnetic field doing work. In other words, the latter seems to me in my state of ignorance to be merely a special case of the former. Roughly: If A caused B and B caused C, then A caused C.
B. Is it supposed to be that even the apparent “work” of magnets smashing together and making a noise (as mentioned in the OP) is actually to be explained as being produced by an electric field generated by a magnetic field? Because if that’s the case, then it turns out I have no idea what a magnetic field is or does. I’d have counted this example as paradigmatically a magnetic phenomenon, and also by-the-way electric since the magnetic and electric are two aspects of the same force–but apparently I’m being told that the phenomenon is the result of an electric field and not a magnetic field? Then what’s a magnetic field do?
I guess I still don’t understand what’s different about magnetism in the example I presented earlier.
If I lift up a weight against the force of gravity, creating potential energy, I can then get work out of the weight as it falls.
If I compress a spring, creating potential energy, I can get work out of the spring if it is allowed to expand.
If I have a piece of iron attached to a strong magnet, and I pull the iron away from the magnet, I can envision getting work out of the iron as it moves back toward the magnet. Is not the magnetic force in this example a conservative force?
What am I missing?
ETA: Reading the wikipedia entry for conservative forces, I see that the magnetic force can be considered a conservative force in some contexts, but not in others.
robby, the difference is that there is no magnetic “charge”. When a magnetic field exerts a force on an electric charge, it does no work on it because the force is always perpendicular to the motion. It’s comparable to gravity’s effect on a marble rolling on a perfectly level surface–the force of gravity is always perpendicular to the marble’s motion, so gravity can’t speed it or slow it down (that is, do work).
A magnetic field also exerts a force on a magnetic dipole, and work can be extracted in that case. However, except for a few interesting particles, the magnetic dipole is actually the result of moving charges. So the work apparently done via magnetic fields is really being done on and by electric charges and fields. Of course, we don’t have to figure out all that extra complication, in most cases we can compute the work as if it’s being done by the magnetic field on the magnetic dipole. (In a way, it’s like using Newton’s gravitation to calculate the force of gravity instead of Einstein’s general relativity–a convenient approximation.)
Nitpicking myself: “moving charges” is also a simplification, since the dipole moment usually comes from the electronic orbital states.
Allow me to digress a bit, and see if I can’t clear up some of the confusion. Electric and magnetic fields are intimately related. In fact, within relativity it is easier to put them into the same mathematical entity, called the field strength tensor. If you think of a vector as a column of numbers that follow certain rules under rotations and other coordinate transformations, then you can think of tensors as two dimensional arrays of numbers following equivalent rules under coordinate transformations. You can think of the magnetic field as that part of the field strength tensor that does no work. For example, wikipedia defines the magnetic field as:
(it then gives the velocity cross magnetic field equation.)
Remember, this is the technical, physics form of work. A magnetic field will make a charged particle move in a circle, which is why there are huge magnets in particle accelerators. But that is not a physicists form of work, anymore than my desk is doing work holding up my computer, or I would be if I were holding my computer steady. A magnetic field is that part of the field strength tensor that imparts a force orthogonal to a charged particle’s trajectory, and the electric field is that part of the field strength tensor that imparts a force along a particle’s trajectory. So, by definition, a magnetic field can do no work.
As to what happens when you hold two magnets together, the real answer depends on the cause of the magnetism. I’m kind of surprised how hard it is to find something online, but there must be something. Unfortunately, I’m at work, so I can only sketch a path to the answer. There are two relevant factors: a changing magnetic field creates an electric field, and a magnetic field can displace charges so that even two neutral objects can attract each other electrically (picture shoving all the positive charges one way and the negative charges another - you can end up with a net attraction or repulsion, depending on how you do it). At some distance from each other, two magnets can not sense each other’s fields. You move them closer to each other, and the magnetic field has changed - therefore there is an electric field which can pull them together. At the same time, the magnets deflect each other’s electrons, which when acting on the bulk materials, can create an attraction or a repulsion. I don’t know which factor dominates, but I can see how both lead to electric fields doing the work.
Well, “a few interesting particles” includes electrons, and it’s the the electron’s magnetic moment that leads to ferromagnetism. Any “proof” that magnetic fields do no work that looks only at charges, and neglects the magnetic moment that real particles have, is flawed because it’s ignoring the source of ferromagnetism.
In the examples of a magnet attracting an iron bar, it’s the interaction between the magnetic field and the magnetic moment of the iron bar’s electrons that causes the attraction. In this case, and also for a magnet attracting another magnet, the magnetic field is doing work. No electric field needed.
It does indeed become simpler if you treat the electromagnetic field as a single object, rather than breaking it up into separate electric and magnetic parts. The only reason this isn’t usually done is that most folks are never taught how to use tensors.
I believe ZenBeam is correct for intrinsic magnets(as opposed to electromagnets). Ferromagnetism and Ferrimagnetism are due to the intrinsic magnetic dipole moment of an electron (a purely quantum affect). Magnetic fields can do work magnetic dipoles, and certainly the simplest solution would be the magnetic field is doing the work of attracting two bar magnets, as opposed to what I stated.
I wonder about electromagnets, though. In that case, the field is due to a current and not the elementary magnetic dipole nature of the electron. In this case, the magnetic fields will deflect the currents and I would think an electric field does the work.
Nitpick: muscles are not solid objects, and they DO expend energy when they’re holding something, even if there’s no motion (think of them as constantly moving a tiny tiny amount back and forth, with friction). So you are doing work when you hold up your computer (Only mentioning it because this is I think one of the common problems people have with learning the physics definitions of work).
Expending energy is not the same as doing work. There might be work done at a cellular level, but there is no work being done on the thing you’re holding. It’s gravitational potential energy is remaining constant.
Typical electromagnets have a metal core, and the field strength is mostly due to the core, not the current directly, so there it would still be mostly the magnetic field.
For air-core electromagnets, though (which interestingly, the strongest electromagnets are), that would have to be right (for work done to the electromagnet).
The issue is where the energy comes from. For instance, if you apply a magnetic field perpendicular to a current-carrying wire, you will get a magnetic force on the wire. If the force is enough to move the wire, then it certainly seems the force is doing work on the wire.
However, if the wire moves, then this also changes the shape of the circuit of which the wire is a part. And that changes the magnetic flux through the circuit, and this changing flux induces an electric field, which slows the flow of current. The energy you remove from the current is equal to the work that you did to move the wire.
So the magnetic field doesn’t lose any energy to the system; rather it causes energy to be transfered within the system. In that sense, it does no work.