I’m somehow trolling myself over magnets. Physical theories suggest magnetic fields can do no work. The magnetic force is always perpendicular to velocity, so the integral is always zero. I’m sure physical theories are correct, but two things are bothering me greatly.
Two questions.
Place two magnets in proximity, and release them. They come together, and make a noise. Where did this noise come from, if the magnetic force does no work?
Suppose water is magnetic, or take a flow of iron filings whose weight is equal to the water flow. Take a typical waterwheel. Gravity pulls the water down on the wheel, the wheel turns, and is used to do some work. Now, with our magnetic water, place a huge magnet underneath the waterwheel. Exactly the same work is done, since the magnetic force can do no work? What?
But these two scenarios are really blowing my mind. Any help is appreciated.
Gravity is – so far as we’re concerned – the same as magnetism. When we capture the force of water moving down a slope to create electricity, we’re using gravity. If we had a giant magnetic planet (without gravity) with a river of iron dust being pulled down a slope by the magnetic pull, we’d be able to capture some percentage of the force to create electricity. So obviously, magnetic force can be used to create energy.
The problem is that it’s a one-shot deal. If there was a great, cosmic rubber band that was already pre-stretched waiting for us to come along and utilize the force it had, that’d be great. But if we have to stretch the rubber band ourselves, we certainly can’t get more energy out of it than we put in to stretch the band. Unless you know of a set of magnets that are already all set up to have their force harvested, we can’t create a situation where we can harvest energy from them where we don’t use the same amount or more energy to put things into place to begin with (probably).
Save that gravity doesn’t have a positive (repulsive) pole (or at least, not as far as we know, though some emergent theories of quantum gravity suggest that gravity is not a fundamental force but it is dependent on several fundamental interactions governed by couplings between degrees of freedom). Both gravity and electromagnetic forces are classically considered to be conservative, and so while you can put energy into or take it out of the system by injecting kinetic energy or changing potentials by moving the charges and masses, the properties of the fields themselves don’t change.
For a mechanical analogue, consider a racquetball court in which someone has thrown a bunch of perfectly linearly elastic balls with considerable momentum (assume no loss of energy to the boundries, acoustic losses, et cetera). The balls will bounce off the floor, walls, and ceiling without any change in energy or momentum. They’ll also bounce into one another, and may transfer energy between one and another via impulse transfer (impact); however, since both energy and momentum are conserved in our hypothetical system the energy level remains the same, and of course, the “field strength” of the interactions between balls (i.e. their elasticity) doesn’t change and thus force transfer is dependent only on the relative vectors of the momentum of the balls. If you throw another ball into the mix, you increase the energy of the system, but the the innate energy of the ball–the energy it stores per unit deformation–remains the same.
Any distantly separated electric opposite charges or masses have an innate energy stored in their coupling. Even if they’ve never met since the moment of the Big Bang, the “tensile” attraction between them is part of the overall potential energy budget of the Universe, so when they come together, that energy is converted to kinetic, acoustic, thermal, or other forms of energy.
Stranger, so what you’re saying is that, though I can in principle use a magnet to do work, that’s only from a limited perspective. In fact the work was originally done setting up the device (e.g., the sun evaporating my magnetic water), which is then later extracted.
This is the kind of question I love to see, since it shows that someone is, on the one hand, reading their textbooks, but on the other hand, also isn’t just blindly accepting what the textbook says. In this case, the textbook is correct: Magnetic fields, unlike gravity or electric fields, indeed do no work. So how does one account for situations like the one you describe? The key is that magnetic fields don’t exist in isolation: Magnetic fields can generate electric fields, and vice versa, and in every case where it looks like a magnetic field is doing work, it’s actually an electric field generated by the magnetic field that’s doing the work.
And this makes a lot of sense when you consider, say, rotating an iron bar by turning on an electromagnet. It’s really hard to see in, ah, more mundane situations.
The force of gravity, force of magnetism, and force of an ideal spring are all examples of so-called “conservative” forces. You can use these forces to store energy by doing work, and later (in the ideal case) get this work back, but none of them can ever do any net work.
For example, you can do work by lifting a weight against gravity, creating gravitational potential energy. You can get this energy back by releasing the weight, which converts the potential energy into kinetic energy. The same thing happens when water falls over a water wheel. The water had to be lifted up in the first place, either by a pump, or by evaporation (in which case the energy to evaporate the water came from an external heat source, such as the Sun).
In similar fashion, you can store elastic potential energy by compressing a spring. When the spring is allowed to expand, the elastic potential energy is converted to kinetic energy.
Finally, if you pull apart two magnets that are stuck together, you do work to separate the magnets. This work is converted into magnetic potential energy, which you can get back if you release the magnets and allow them to go back together, converting the magnetic potential energy into kinetic energy.
In none of these examples is any net work done. Either you had to do work in the first place, which you are merely getting back, or something external had to do work on your system.
Again, magnetism is different from gravity or a spring. Nothing can ever do net work; that’s the law of conservation of energy. But you can do work with gravity or a spring, if you’ve put energy into it somehow, but despite appearances, you can’t do the same with magnetism.
The fact that magnetic fields do no work has nothing to do with conservative forces or anything else other than what Chronos said
dW = F dot dl = Q(v X B) dot v dot dt = 0
When two magnets are pushed apart or drawn together all the magnetic field does is redirect the internal electric fields that are creating the magnetic field. The actual work is done by the electric fields.
Electric fields are created by point sources, for classical situations either electrons or protons, or their kin (muons, for example).
Classically, gravitational fields also have point sources - any object with mass.
Magnetic fields have no such point sources and are only created by moving charged sources, or changing electric fields. It is not possible to have a magnetic field without an electric field. (Chronos, you might be glad to know that one of my “Electricity and Magnetism” textbooks, circa the 70s, explicitly asked in the question section at the back, "If magnetic fields can do no work, how do electromagnets pick up a car?)
To see how subtle it gets, consider two bar magnets facing so as to repulse each other. Both are electrically neutral, so there would appear to be no electric fields, so their respective magnetic fields must be the source of the attraction, right? Wrong. Magnetic fields only exert forces on charged particles, so the magnetic field wouldn’t seem to be able to exert a force, either! I’m sure wikipedia or one of the online physics tutorials contains a better explanation of what is happening, with pictures, than I can give, but the basic idea is that electrons working as a group create an effective current and it is the electric charges within the material that actually do work.
Not surprising; I think pretty much everyone uses Griffiths’ book for undergrad E&M. I would have gone looking for the cite once I got to the office, if Ring hadn’t beaten me to it.
Something about this was niggling me and I finally realized what it was. Magnetic fields can also exert force on magnetic dipoles. In many cases, that dipole is composed of moving charges and electric fields. But not always.
There are elementary particles that have a magnetic moment. Electrons, muons, etc. They have charge, so it’s tricky to separate the work done on the charge vs the magnetic moment. However, neutrinos have no charge but still have a magnetic moment. With difficulty, one could extract work from a magnetic field using neutrinos.
If one wanted to take charge out of the picture altogether, we could produce the magnetic field with neutrinos only. The cross section of two neutrinos via magnetic interaction must be extremely small, though.
No magnetic dipole moment has ever been measured for neutrinos, and the upper bounds are billions of times weaker than the dipole moment of the electron.
Yes, but if they have mass, and it looks like they do, then they have a magnetic moment, even if it’s currently unmeasurable.
Are there any other chargeless elementary particles with a magnetic moment? The Z boson maybe?
Of course, unless one is willing to work out the internal details, the neutron is a chargeless particle with a magnetic moment, so one could reasonably talk about the work a magnetic field does on it.
If I understand correctly*, the problem wasn’t that you can’t talk about potential energy for magnetism the same way you can talk about potential energy for gravity and in discussing elastics. You can; so long as you have conservation of energy (and you always do), you can define potential energy from it.
The problem was that this didn’t actually address what the OP was talking about; with gravity and so on, you can extract that potential energy and use it to do work, whereas, when one looks at the basic law governing a magnetic field’s effect upon a charged particle, one finds that it is unable to do work (in the same way as, at least classically, a planet in circular orbit is moving under the influence of gravity, but gravity is not actually performing work upon it; the force is perpendicular to the velocity at all times, so the force causes no change in speed). But this seems paradoxical in light of the fact that one can use magnets to perform work. That is the problem which the OP was posing, which is rather more subtle than simply being confused about potential energy.
(*: Naturally, please correct me if I don’t. The extent to which I no longer know anything about physics (I actually never took any science classes after high school) is one of my main intellectual regrets/embarrassments.)
