Would Magnetic Monopoles Violate Conservation of Energy?

[Mr Skeptic]

So I know that some theories allow for magnetic monopoles, and that including them would make Maxwell's Equations pretty and symmetrical. However, it seems to me that because we have true magnetic dipoles (ie they are not made of two magnetic monopoles) that having magnetic monopoles in addition would allow you to generate infinite energy as follows:

 

Put a magnetic dipole somewhere, and guide a magnetic monopole in a closed loop along one of the dipole's magnetic field lines. Since at all times the monopole will be moving in the direction of the force it will gain energy. But where does this energy come from? The magnetic dipole as a fundamental property of things like electrons can't necessarily be destroyed, and presumably a magnetic monopole couldn't be destroyed either by an analogue to the law of conservation of charge.

 

The same reasoning would apply if it were possible to make a true electric dipole, one not made with electric monopoles. We could equally work with this case if such electric dipoles exist.

[Sha31]

Magnetic monopoles would not be some new particles, but just like magnetic dipoles they would be an effect of motion of electric charges, also known as electron and positron.

 

Charge spin produces magnetic dipole moment, but those two poles are not two new "magnetic particles", just two additional fields, and only one particle, one charge, is "producing" all these fields.

 

There is another kind of motion next to spin, that is spatial displacement, be it along a straight line or circular, it again produces magnetic field. However, as it happens, different kinds of motion produce different kinds of magnetic fields. You say this magnetic field of moving charge has no poles, I say it has one pole, the place where the field is strongest, the charge itself, again. Whatever the case, if magnetic monopoles exist they would not be some new type of particles, because magnetic fields are just an effect of motion of electric charges. Particles to look at for magnetic fields are always electron and positron.

[Mr Skeptic]

I'm talking about real magnetic monopoles, the ones that the second of Maxwell's Equations says don't exist. Sha31, keep your made up fantasies to your own thread please. Or to yourself, as this is a forum for science.

[swansont]

Put a magnetic dipole somewhere, and guide a magnetic monopole in a closed loop along one of the dipole's magnetic field lines. Since at all times the monopole will be moving in the direction of the force it will gain energy.

 

Here's the flaw in your scenario: the particle won't follow the flux lines. The direction of force and direction of velocity are not the same thing, and the field is curved. The particle would have a radial component to its velocity, and be moving away from the wire, toward a weaker field. It would gain a finite amount of energy, and this would look like a load on the circuit providing the current — that's where the energy comes from.

[Mr Skeptic]

Here's the flaw in your scenario: the particle won't follow the flux lines. The direction of force and direction of velocity are not the same thing, and the field is curved. The particle would have a radial component to its velocity, and be moving away from the wire, toward a weaker field.

 

That's why I said to guide the monopole. However, the same but with more complicated math will apply for several different closed loops. Just so long as you don't move the monopole against the field. Or if you like, pass the monopole through loops of wire, which should slow the monopole and generate an electric current.

 

It would gain a finite amount of energy, and this would look like a load on the circuit providing the current — that's where the energy comes from.

 

Hm, I understand that, but what if you use a fundamental particle as the source for your magnetic field? An electron's spin, for example. That can't be reduced, so the energy can't come from there (or do I seriously misunderstand something?).

[Sha31]

Put a magnetic dipole somewhere' date=' and guide a magnetic monopole in a closed loop along one of the dipole's magnetic field lines. Since at all times the monopole will be moving in the direction of the force it will gain energy. But where does this energy come from?

[/quote']

 

You don't need a monopole to ask question about energy and work done by magnetic force. You only have to remember that FORCE does the work, not FIELDS. Direction of magnetic field is not (always) the direction of the magnetic force, so magnetic force can indeed do work. -- The same thing you can ask about gravity and magnetic dipoles.

 

a.) Bowling ball drops to ground, it moves in the direction of gravity force.

Does it gain energy? Where does this energy come from?

 

b.) Two magnets stick together, moving in the direction of magnetic force.

Do they gain energy? Where does this energy come from?

 

 

I'm talking about real magnetic monopoles...

 

The same reasoning would apply if it were possible to make a true electric dipole' date=' one not made with electric monopoles. We could equally work with this case if such electric dipoles exist.

[/quote']

 

"true electric dipole"? "real magnetic monopole"?

 

- You expect there will be some new type of particle for electric dipoles?

- You think, for some reason, magnetic field of moving charge has no poles?

- You expect there will be some new type of particle for magnetic monopoles?

 

Electric fields are electric fields, charges aka electron and positron, and that's it.

Magnetic fields are EFFECTS of motion, due to charge spin and spatial displacement.

 

 

Electric dipoles exist as well. It's nothing more but pair of opposite electric fields "stuck together", which happens when positron and electron interact. They keep trying to stick together, but due to their magnetic fields, instead of orbiting, they end up spiraling around each other in some linear direction, describing helical trajectory or double helix. This is also known as transverse electromagnetic wave, em radiation or photon and can be experimentally demonstrated with what is called "Pair annihilation". Inverse process, "Pair production", does the opposite, it splits this electric dipole (photon) into two monopole electric fields, positron and electron.

 

http://en.wikipedia.org/wiki/Pair_production

http://en.wikipedia.org/wiki/Pair_annihilation

Edited December 5, 2009 by Sha31

[npts2020]

Sha31; a: The bowling ball got its energy from being carried to whatever height it gets "dropped" from.

b:Why do you think the magnets "gain" any energy or field strength beyond what their sum would be anyway?

[Mr Skeptic]

Please ignore Sha31. He is not interested in facts, and he makes up his own definitions.

[Sha31]

Sha31; a: The bowling ball got its energy from being carried to whatever height it gets "dropped" from.

 

Ok. You say ball lost energy that it previously gained from being carried up. So' date=' isn't that just the same as when you start with two permanent magnets that are already stuck together and you have to do some work and invest energy to move them apart? Consider this. Piece of asteroid, or something, is on it way towards Earth and its velocity vector points 1,000km north above. However, as it closes by it gets attracted and its trajectory curves, so it ends up colliding with the planet. Where does this energy come from?

 

 

b:Why do you think the magnets "gain" any energy or field strength beyond what their sum would be anyway?

 

I didn't say that, did I? Those were my questions. My only statement was that two questions, about gravity and magnetic dipole forces, are the same as for magnetic monopole, or maybe even any other force. Anyway, I think current theory explains this situation so that magnets, as they move closer together, gain kinetic energy and lose potential energy, hence energy gets conserved, similar to what you said about bowling ball and gravity. This can be understood as that energy comes from the differences in field potentials.

 

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Please ignore Sha31. He is not interested in facts, and he makes up his own definitions.

 

Ignorance will not help you to learn. Since you can not articulate your argument you should at least let other people think for themselves. I told you facts. What part do you not believe? Do you want some more reference or more explanations? What part do you not understand?

Edited December 5, 2009 by Sha31
Consecutive posts merged.

[Mr Skeptic]

Well, could you at least stop implying that every scientist for the past century has the IQ of a toddler? We all know what the magnetic field of a moving charge is, we all know what a magnetic monopole looks like, and we will quickly recognize one if we see one.

 

If you think you are some kind of Einstein because you are the only person who thinks a moving electric monopole is a magnetic monopole and every single scientist for the past century is either wrong or dumber than you, then you've got a problem.

 

Yes, we all understand that when you make up your own definition then the moving electric monopole fits your definition of a magnetic monopole. We don't care, because your definition is wrong.

 

Now go away, make your own thread about what you think magnetic monopoles are. This one is about whether magnetic monopoles as described by Maxwell's Equations modified to include magnetic monopoles, would violate the law of conservation of energy.

 

Ignorance will not help you to learn. Since you can not articulate your argument you should at least let other people think for themselves. I told you facts. What part do you not believe? Do you want some more reference or more explanations? What part do you not understand?

 

Ignorance is a prerequisite for learning. Arrogance is what you get when you fail to realize your own ignorance, and will prevent you from learning. What we don't believe is your definition of a monopole. I understand everything you said, including your incorrect definition. Go look up a definition for a monopole. Provide a reference. In a different thread. If you don't make your own thread I will make one for you and choose what I think is an appropriate title for it.

 

Now, back to posts #1 and #5.

[swansont]

Hm, I understand that, but what if you use a fundamental particle as the source for your magnetic field? An electron's spin, for example. That can't be reduced, so the energy can't come from there (or do I seriously misunderstand something?).

 

An electron is free to move, though, and also the spin orientation can change. You would have potential energy contained in the configuration in which you started.

 

One interesting behavior is that I think that a monopole would be repelled (though not radially) by a current in a wire, regardless of the "charge" on the monopole or direction of the field.

 

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Let's keep the discussion to the question posed in the OP and related topics, please. Questioning the sincerity of a user, and bringing up behavior from a different thread is out of bounds. Please let the staff handle moderation duties.

Edited December 5, 2009 by swansont
Consecutive posts merged.

[Mr Skeptic]

An electron is free to move, though, and also the spin orientation can change. You would have potential energy contained in the configuration in which you started.

 

Well, I don't doubt that there would be potential energy in the system. My suggestion is that the potential energy is essentially infinite due to the energy gained moving the monopole in a closed loop. An easier way to state that is that there is no potential energy minimum in the magnetic monopole-electron system. No way to arrange them so that they remain at rest (or in a stable orbit).

 

I'm not sure I can prove that but here goes. As I understand it, at any point in a magnetic field, the direction of that field is the direction a north magnetic monopole would be accelerated if it were at rest. Since the field lines always form closed loops, wherever in the field it is it could be moved in a closed loop and gain energy. Since at an energy minima there would be no force on it, nowhere in the field can be the energy minima.

 

One interesting behavior is that I think that a monopole would be repelled (though not radially) by a current in a wire, regardless of the "charge" on the monopole or direction of the field.

 

For a straight wire you mean? Yeah, that would make sense. It would spiral away.

[swansont]

Well, I don't doubt that there would be potential energy in the system. My suggestion is that the potential energy is essentially infinite due to the energy gained moving the monopole in a closed loop. An easier way to state that is that there is no potential energy minimum in the magnetic monopole-electron system. No way to arrange them so that they remain at rest (or in a stable orbit).

 

I'm not sure I can prove that but here goes. As I understand it, at any point in a magnetic field, the direction of that field is the direction a north magnetic monopole would be accelerated if it were at rest. Since the field lines always form closed loops, wherever in the field it is it could be moved in a closed loop and gain energy. Since at an energy minima there would be no force on it, nowhere in the field can be the energy minima.

 

 

But the particle won't move in a closed loop on its own. You'd have to have another force present, and that's where the extra energy comes from. Remember, an object moving around a circle needs an inward radial force, not a tangential force.

[Mr Skeptic]

But the particle won't move in a closed loop on its own. You'd have to have another force present, and that's where the extra energy comes from. Remember, an object moving around a circle needs an inward radial force, not a tangential force.

 

Well, what I was thinking was passing the monopole through coils of wire. It should induce a current in them, providing electricity and an opposing magnetic field. The idea is for the monopole to be moving slowly enough that it could be considered to be approximately at rest, so that it would follow the field lines on its own.

 

To simplify things, the electron could be held in place, perhaps in a permanent magnet.

[swansont]

Well, what I was thinking was passing the monopole through coils of wire. It should induce a current in them, providing electricity and an opposing magnetic field. The idea is for the monopole to be moving slowly enough that it could be considered to be approximately at rest, so that it would follow the field lines on its own.

 

To simplify things, the electron could be held in place, perhaps in a permanent magnet.

 

Any current induced by the monopole and its motion would indeed induce an opposing field, which would slow the monopole down. No violation there.

[Mr Skeptic]

Any current induced by the monopole and its motion would indeed induce an opposing field, which would slow the monopole down. No violation there.

 

Yes, but what happens when the monopole slows down? The current and consequent magnetic field that are induced will be lessened. The magnetic field of the electron will be unaffected. As I said, anywhere in the magnetic field the magnetic monopole gets accelerated. The coils are just to transfer the energy out of the system.

[swansont]

Yes, but what happens when the monopole slows down? The current and consequent magnetic field that are induced will be lessened. The magnetic field of the electron will be unaffected. As I said, anywhere in the magnetic field the magnetic monopole gets accelerated. The coils are just to transfer the energy out of the system.

 

You appear to have several conditions under discussion: the behavior of a monopole in a coil, the behavior in a coil with an externally supplied current, and an electron, whose function is not clear to me. And previously we were talking about a magnetic monopole near a long current-carrying wire. Perhaps you could clarify.

 

My previous post described a monopole traveling down the axis of a coil. Once the monopole stops, it stops. There is no external field to induce any motion.

 

If you have a current in the wire, the monopole keeps feeling a force, but this will show up as a load on the circuit. Energy comes from that external supply.

[Mr Skeptic]

OK, what I mean is a magnetic monopole in a magnetic field, a magnetic field generated by fundamental particles, not induced by an electric current. My example of this was an electron, as AFAIK an electron's magnetic field cannot be destroyed. A permanent magnet would function as well but only if it will not get demagnetized. I did not state it, but I was using a north magnetic monopole. Assume that the coils are attached to the permanent magnet so any force between the coils and magnet will not result in the transfer of energy (other than very small amounts due to stress).

 

In this situation, wherever the monopole is, it will be accelerated in the direction of the magnetic field lines. Is this correct?

 

Now, so long as the monopole is moving in the direction of the field it will be gaining energy. It doesn't have to exactly follow the field lines for this. Is this correct?

 

Now that the monopole is moving, passing it through coils of wire will induce a current in the wire. This will generate an opposing magnetic field that will slow the monopole. The net result is the transfer of energy away from the system, in the form of electricity. Is this correct?

[npts2020]

Why would a monopole not reach equilibrium at some point? I mean would it not come to rest at the part of the field it is moving through where the highest opposite charge is?

[swansont]

OK, what I mean is a magnetic monopole in a magnetic field, a magnetic field generated by fundamental particles, not induced by an electric current. My example of this was an electron, as AFAIK an electron's magnetic field cannot be destroyed. A permanent magnet would function as well but only if it will not get demagnetized. I did not state it, but I was using a north magnetic monopole. Assume that the coils are attached to the permanent magnet so any force between the coils and magnet will not result in the transfer of energy (other than very small amounts due to stress).

 

In this situation, wherever the monopole is, it will be accelerated in the direction of the magnetic field lines. Is this correct?

 

Yes, it will be accelerated in that direction, but that does not mean its trajectory will follow the field line.

 

Now, so long as the monopole is moving in the direction of the field it will be gaining energy. It doesn't have to exactly follow the field lines for this. Is this correct?

 

Yes. There will be potential energy in the system, and it will be converted into kinetic energy.

 

Now that the monopole is moving, passing it through coils of wire will induce a current in the wire. This will generate an opposing magnetic field that will slow the monopole. The net result is the transfer of energy away from the system, in the form of electricity. Is this correct?

 

Yes.

 

You will have to do work to put the particles in their starting positions. That's the limit of how much energy you will get out when you do these things.

[Mr Skeptic]

You will have to do work to put the particles in their starting positions. That's the limit of how much energy you will get out when you do these things.

 

OK, lets say we move the monopole in from a direction perpendicular to the north-south axis of the magnetic field, so that its motion is perpendicular to the field lines. How much potential energy does it gain (assume any specifics that you need to).

[swansont]

I expect the potential energy will look something like -mp cos(theta)/r^2, where m is the magnetic charge and p is the dipole moment. The dipole will feel a torque and align with the monopole's field. You'll do work in realigning the dipole.

[Mr Skeptic]

Hm, by holding the dipole in place I meant also holding its alignment in place. If both the monopole and dipole are held onto but the dipole is allowed to rotate, then the south pole of the dipole will align to face the north monopole, and it would act as only an attractive force.

 

Was my assumption that we could hold a dipole in place and in a certain alignment wrong? My best guess for doing that would be using a permanent magnet.

 

On the other hand, if the alignment of the dipole cannot be held in place and alignment, let me suggest a different scenario. Both the dipole and the monopole are placed near each other in a vacuum. If we assume that the monopole may pass through the dipole, then what we get is the monopole more or less vibrating in place and the dipole spinning rapidly and also vibrating. Ie, the north monopole gets attracted to the south end of the dipole, passes through it, then gets repelled away by the north end of the dipole, also causing the dipole to rotate. Some energy will be transported away via electromagnetic waves. Now my questionable assumption is that the monopole may pass through the dipole. I don't know what particle type is proposed for magnetic monopoles, so I don't know whether they could in fact pass through each other.

[swansont]

In principle, you could hold in place. But in practice, you'll do work — the dipole wants to rotate. If it was a physical dipole, you'd be requiring an infinitely rigid material, which violates relativity, so I'm suspicious that this requirement is unphysical.

 

Another problem is that by bringing the charge in, even under these conditions, you have a time-changing field; it's not static, and you can't just look at electro- and magnetostatic equations. A time-varying magnetic field creates an electric field, and you have to account for that. If you do it slowly, the term may be small, but it also takes a long time to do it. I think you will still end up doing work.

 

This has to be true of electric charges and dipoles as well, because with magnetic monopoles Maxwell's equations become symmetric. So if magnetic monopoles violated conservation of energy so simply, electric charges would, too.

[Mr Skeptic]

In principle, you could hold in place. But in practice, you'll do work — the dipole wants to rotate. If it was a physical dipole, you'd be requiring an infinitely rigid material, which violates relativity, so I'm suspicious that this requirement is unphysical.

 

I don't think it has to be perfectly rigid, just enough to hold the alignment mostly in place. I'm pretty sure I don't want to hold it in place with a magnetic field though, as then I may really need to drag around the monopole.

 

Another problem is that by bringing the charge in, even under these conditions, you have a time-changing field; it's not static, and you can't just look at electro- and magnetostatic equations. A time-varying magnetic field creates an electric field, and you have to account for that. If you do it slowly, the term may be small, but it also takes a long time to do it. I think you will still end up doing work.

 

Well, vacation starts in a few weeks so I will examine the problem more thoroughly then. I agree that I may have left out a significant factor, which is why I was asking.

 

I had been assuming in particular that moving a magnetic monopole perpendicular to magnetic field lines would not require any work. Thinking about this a bit more this may be a poor assumption. I need to double check that too. If this doesn't hold then I'd definitely need to pass straight through the dipole to get this to work.

 

Unfortunately, I am much more familiar with the static equations than the dynamic ones, so that could be a problem too.

 

This has to be true of electric charges and dipoles as well, because with magnetic monopoles Maxwell's equations become symmetric. So if magnetic monopoles violated conservation of energy so simply, electric charges would, too.

 

Yeah, I said that at the start. So I am also claiming that there are no permanent electric dipoles that are not made of monopoles (eg, a fundamental particle that has an electric dipole). If you make a dipole out of two monopoles, the field between the two monopoles will be very strong in the opposite direction as the larger but weaker field outside of that area. Another way of saying it, the field lines do not form closed loops for the electric field. So dipoles made of monopoles are OK.

 

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Now, I was considering that the magnetic dipole (an electron) could be held in place in a permanent magnet, which would simplify things as with a magnet you can definitely pass through it (drill a hole through first), whereas if forces other than electromagnetism are involved the monopole could bounce off the dipole. The reason I didn't want to start off with that is because I don't know if it would get demagnetized. I know rubbing a magnet in the opposite direction with another magnet can demagnetize it for example.

 

Uh, if I had a magnetic monopole would it be attracted to a ferromagnetic material?