Why do electro-magnets not violate Conservation of Energy?

[Lamarr]

Think of two torus-shaped tubes.

Each tube is filled with electrically-charged ping pong balls.

The inside of the tube is smooth and friction-less.



So someone gives the ping pong balls inside a push, and the balls start moving in a circle.

The same thing happens in the 2nd torus.


Due to the movement of the charged balls, there is a current and a magnetic force is experienced by both tori.


So now both tori possesses some form of magnetic potential energy. It's as though energy was created from nowhere.

Can someone help me resolve this?

 

[Drakkith]

You had to give the balls a push, which gave them energy.

 

[Lamarr]

You had to give the balls a push, which gave them energy.

True, I gave the balls kinetic energy.


So the balls spin around in the friction-less torus-shaped tubes, and they don't stop moving, because no KE is lost.


But there is a force between the balls in one tube and the balls in the other tube. This force didn't exist before.

So magnetic fields can be created out of nowhere. Potential energy can be created out of nothing? But of course this cannot be.

 

[Drakkith]

True, I gave the balls kinetic energy.


So the balls spin around in the friction-less torus-shaped tubes, and they don't stop moving, because no KE is lost.

Perhaps. This sounds similar to a superconductor.

But there is a force between the balls in one tube and the balls in the other tube. This force didn't exist before.

So magnetic fields can be created out of nowhere. Potential energy can be created out of nothing? But of course this cannot be.

No, the fields were created by the movement of charges. They did not come from nothing and potential energy cannot be created from nothing. You added energy in the form of kinetic energy to the system. Because the balls are charged they will generate a magnetic field when they are in motion.

 

[Danger]

True, I gave the balls kinetic energy.

Please don't shout. Italics or bold are sufficient to emphasize a point.

 

[Drakkith]

Please don't shout. Italics or bold are sufficient to emphasize a point.

Just shield your eyes a little Danger!

 

[Lamarr]

Please don't shout. Italics or bold are sufficient to emphasize a point.

Nah, if not then the Font Size menu will be underused.

Besides I've seen people routinely use size 7. It's to help forum goers with bad eyesight lol.
Anyway, so the charges do create magnetic fields. But they don't loose any of their kinetic energy.

At the same time, magnetic forces act between the charges. And when there's a force there's potential energy.

But this potential energy seems to have come out of nowhere.Unless I'm missing something and the balls do lose their kinetic energy.

 

[Drakkith]

But this potential energy seems to have come out of nowhere.

Let me ask you this. Does the potential energy of a superconducting magnet come from nowhere?

 

[Danger]

Just shield your eyes a little Danger!

Easy for you to say. I'm photophobic; that huge mass of black sent my retinae into rebound shock.
Also, Lamarr... if you can manage to find frictionless ping-pong balls anywhere, you'll have a head start on a whole new version of the game.

 

[sophiecentaur]

But there is a force between the balls in one tube and the balls in the other tube. This force didn't exist before.

So magnetic fields can be created out of nowhere. Potential energy can be created out of nothing? But of course this cannot be.

Just creating a force doesn't imply any energy has been 'created' or transferred. There needs to be a force times a distance for that. Clearly, you are trying to make a simple model for an electromagnetic phenomenon, which may or may not be valid. But I think that your apparent paradox is not really there. If there is no actual distortion or movement (of the tubes) then I think all the energy transfer is into kinetic.

 

[voko]

1. The kinetic energy is not constant: the balls undergo acceleration, so radiate energy away. Recall that this very same consideration got quantum mechanics started.

2. When you pushed the balls originally, you had to give the balls more of a push than they had kinetic energy immediately after the push, because as soon as they started to move, the magnetic field they generated started to slow them down.

 

[sophiecentaur]

1. The kinetic energy is not constant: the balls undergo acceleration, so radiate energy away. Recall that this very same consideration got quantum mechanics started.

2. When you pushed the balls originally, you had to give the balls more of a push than they had kinetic energy immediately after the push, because as soon as they started to move, the magnetic field they generated started to slow them down.

I wonder at what frequency the energy would be radiated. I have a feeling that you would still need to apply QM considerations to this model and to associate some specific photon energy with the process. The Bohr model failed for this reason and I wonder how this model would fare. Would the photons correspond in some way to the period of circulation of the balls? Probably not.

 

[voko]

I wonder at what frequency the energy would be radiated.

This particular case is known as the synchrotron or cyclotron radiation, depending on the speed of the particle. The spectra are continuous, but the distribution of energy by frequency depends on the the frequency of the motion.

This is all quite well researched, with the synchotron radiation being a prominent laboratory X-ray source.

 

[krd]

Perhaps. This sounds similar to a superconductor.

The whole way superconductors are popularly described, gives the impression they're absolutely resistanceless. It's uncanny, but not surprising. But the way superconductors are described is as if they're breaking some fundamental law, when they're not.

Now...I'm going to blow your mind. With a controversial description I've just dreamed up. In the context of superconductors, a room temperature non-superconductor, experiences resistance as electromagnetic turbulence, due to thermodynamic effects.

The first law of thermodynamics is a lynch pin of the universe - no one beats it, ever.

 

[sophiecentaur]

This particular case is known as the synchrotron or cyclotron radiation, depending on the speed of the particle. The spectra are continuous, but the distribution of energy by frequency depends on the the frequency of the motion.

This is all quite well researched, with the synchotron radiation being a prominent laboratory X-ray source.

Memory is a wonderful thing. So is mine, sometimes - when it remembers to work! How could I not have remembered synchrotron radiation?

 

[krd]

This particular case is known as the synchrotron or cyclotron radiation, depending on the speed of the particle. The spectra are continuous, but the distribution of energy by frequency depends on the the frequency of the motion.

A Doppler shift of the entire spectra?


I've been wondering about that recently. The ambient thermal spectra in accelerators. It's at very low energies if you're not going anywhere - but once you move against it at high speed, I imagine the energy can rise steeply. Is this why the liquid helium cooling is used?

 

[voko]

A Doppler shift of the entire spectra?

That happens in the outer space, where remnants of supernovae produce massive synchrotron radiation. See the Crab nebula, for example.

The ambient thermal spectra in accelerators. It's at very low energies if you're not going anywhere - but once you move against it at high speed, I imagine the energy can rise steeply.

Please note it is NOT thermal. Well, there is thermal radiation as well, but what we are talking about here is not, and its spectrum is distinctly different from the black-body spectrum.

Is this why the liquid helium cooling is used?

As far as I know, it is used for the superconducting magnets. The radiation, while significant as compared with typical lab radiation sources, is not much compared to the massive structures of the accelerators, so I don't even think anyone takes its thermal effects into account. But I may be totally off on this.

 

[mfb]

LHC protons lose ~7keV per turn (source) - this is calculated with 7 TeV/proton. With the current 4 TeV, the radiation is suppressed by a factor of (4/7)^4=0.1. In order to evaluate the maximal effect, I will use 7 keV.

The design values for LHC operation are 1.1*10^11 protons per bunch and 2800 bunches. The tunnel length is ~27km, giving c/(27km)=11kHz revolution frequency. Therefore, each second, synchrotron radiation of 1.1*10^11 * 2800 * 7 keV * 11000 = 3800J is produced, corresponding to a total power of 3.8kW. This is some orders of magnitude below other values for the LHC power. The experimental magnets (not superconducting) require some MW, for example. Distributed over the full tunnel length, it corresponds to 140mW/m.

The number of protons is already above the design value (~1.4*10^11), but the other values are still below the design values, with the lower energy as most important factor.
@Lamarr: The induction of a magnetic field will reduce the kinetic energy of the ball.

 

[Lamarr]

1. The kinetic energy is not constant: the balls undergo acceleration, so radiate energy away. Recall that this very same consideration got quantum mechanics started.

2. When you pushed the balls originally, you had to give the balls more of a push than they had kinetic energy immediately after the push, because as soon as they started to move, the magnetic field they generated started to slow them down.

That sounds logical.

But people have started talking about synchrotron radiation, should we expect such radiation from an ordinary 3V copper wire circuit loop?


It just struck me that despite all that has been said and done, the true nature of electromagnetism still eludes everyone.

 

[Ibix]

[strike]Per Wikipedia, a 3A current in a 1mm copper wire yields an electron drift velocity of around 0.3mm/s. For a 1cm diameter loop, that gives a synchrotron frequency of around 0.01Hz. So the answer is yes, but not in any band we ever work with and not at any noticeable power.[/strike]

Edit: or maybe not. I think electrons in copper do not have a significant mean free path, so are unlikely to emit synchrotron radiation. Must think before I post...

 

[voko]

But people have started talking about synchrotron radiation, should we expect such radiation from an ordinary 3V copper wire circuit loop?

Things get tricky here. If we look at this from a purely classical point of view, then there is no elementary charge, so the charge carried by the current is spread completely uniformly along the loop. This means that there are no time varying sources anywhere, which means the resultant fields will also be stationary. So no radiation in a classical superconductive loop.

If we look at at semiclassically, that is to say assuming elementary charges (electrons) but assuming they still obey classical laws, we obtain that the radiation emitted by a single electron interferes with that of the others, and it is very nearly canceled out - which is to be expected because in the limiting case (above) it is exactly zero. At this stage to obtain any meaningful result we will need to introduce irregularities in the motion, which will connect us directly with the resistance of the medium, and then we might as well dismiss the whole issue because it is already known that electric current in resistive media produces heat, i.e., radiation. The accelerations that the electrons undergo when they collide with other electrons and ions are some much greater than those caused by the macroscopic curvature of any realistic loop that we can ignore the radiation caused by the shape of the loop completely.

It is important to keep in mind, though, that one (possible the most significant one) of the origins of thermal radiation produced by electric current is "synchrotron radiation", which here really means radiation due to acceleration during the above mentioned collisions. The photons thus produced then scatter many many times on electrons and ions, and the resultant spectrum becomes that of a black body.

 

[krd]

So no radiation in a classical superconductive loop.

I think next to no radiation in comparison to a typical room temperature conductor. I think there might be a little - it could be very very very little.

It is important to keep in mind, though, that one (possible the most significant one) of the origins of thermal radiation produced by electric current is "synchrotron radiation", which here really means radiation due to acceleration during the above mentioned collisions. The photons thus produced then scatter many many times on electrons and ions, and the resultant spectrum becomes that of a black body.

A way I've heard superconductors described - the charge carrying electrons are so close together they act as an electron condensate. Whereas in a typical conductor, there's more movement and jiggle. The electron cloud is more uneven and keeps shifting.