explain how magnets work

[Eos of the Eons]

One thing I learned from that link is that Canada owns the magnetic north pole. But we'll let the rest of you use it, though. We're cool like that.

Ehhhh, who are you to speak for all Canadians

 

[EHLO]

I can see the April 1 headline now "Canada to place embargo on Magnetic North"...

 

[Big Al]

(Wait a tiny fraction of a second...)

What door?

What fridge?

Despite all the arguments about the relative strengths of the SNF and EM, take an atom like iron and try to fission that. You'd need some fearsomely energetic neutrons.

The point about large atoms like ununoctium or, indeed, uranium, is that the diameter of the nucleus is so large that the SNF is really struggling to hold it together - the range issue. You need to pack in a lot of extra neutrons to bind it, but that tends to make the size problem worse.

Of course, without this fine-balancing of SNF and EM, stars and therefore life would be impossible.

Uh-oh - here come the creationists! Man the battle stations! Get the anthropic principle ready on Tubes 3 and 4!

 

[Schneibster]

Well, the forces do not always balance out so equally. For large nuclei like, oh, Ununoctium, electromagnetism wins out. For small nuclei like hydrogen, the nuclear force wins.

EM starts to overwhelm the color force at about the size of thorium nuclei.

I'm not a physicist, but I know that the nuclear force does not follow a 1/r^2 curve the way electromagnetism does (and even electromagnetism doesn't follow that at very close range). So the "winner" is going to depend greatly on the exact distances we're talking about, which itself is going to depend greatly on how big the nucleus is and how it's arranged.

If you posit it's constant across the nucleus, and will just cover thorium, then it has to fall off at the seventh power of the distance. Neither of those is quite exactly correct, but it's close enough. Inside most nuclei except the heaviest, the color force so far overwhelms the EM force that EM might as well not exist for all the effect it has. Outside the nucleus, it's the opposite situation: the color force can't reach that far.

Part of the reason is because its symmetry is three-fold; there are nine possible combinations, but you only need eight gluons to cover them all, because the last one is just the combination of all eight. Another part of the reason is that it's subject to confinement because it's so powerful that if you try to pull two quarks apart from inside a meson, two more quarks will form from the energy you're putting into the field by pulling on them and promptly combine with the two you're trying to pull apart and turn them into mesons; so if you try to pull the quarks in a meson apart, you wind up with two mesons and a lot of wasted effort. Repeat until you get a clue and stop trying to beat the house odds.

I'd posit that it's why, after a certain point, extra neutrons will make a nucleus less stable.

Nope, it's not just neutrons, and you've got it backwards: it seems as if the more protons there are, the bigger an excess of neutrons you need to hold them together. So for example U-238 has 92 protons and 146 neutrons in it- an excess of 54, or more than 50% of the protons present. Go down to iron, and you get three isotopes: 56, 57, and 58; and one very nearly stable at 54, an alpha emitter with a half-life of more than 1E22 years, several million times the present age of the universe. Note that these need only 30 to 32 neutrons, for an excess of only four to six, some fifteen to twenty-five percent; and in fact, the nearly-stable iron-54 requires an excess of only two, less than 7%.

U-238's nearly stable; its half-life is over 4 billion years. Add one neutron, it becomes unstable and decays by beta emission with a few-day half-life into Neptunium-239, and a very short time later that decays by beta emission into Plutonium-239, which is fissile like U-235 is. Get up to about element 108 or 110, which have those numbers of protons of course, you get to a point where no matter how many neutrons you stuff in there the half life is like nanoseconds. Might be a bit higher than that, 112 or some such, but not much.

The nuclear force falls off faster than the electromagnetic, and therefore a bigger nucleus is not held together so strongly as a small one. That's just a guess (and I realize there are many complicating factors) but I think the basic gist of it is true.

- Dr. Trintignant

Well, basically, yes- but remember that that seventh-power falloff indicates a seventh-power buildup, too- and that means that just inside the outside edge of the nucleus, the color force's ratio to the EM force is higher than EM's to gravity. And if you want to know how weak gravity is, it can't even pull a little bitty magnet off a fridge with the WHOLE FREAKIN EARTH. If gravity were as strong as EM, you would die from a momentary exposure to the tides from the gravity of a baseball flying by within sight.

In fact, it's even worse than that. You did some math down there, I see. You made a mistake, or else Wikipedia gave you a wrong starting point. One of the things you might want to look up is the ratios of the forces; the ratio between EM and gravity can be found by comparing the gravitational constant with its equivalent for the EM force, which is called the "fine structure constant," and they're two of the constants that currently have no explanation in the Standard Model. That ratio is about 137:1.752E-45. That's about forty-seven orders of magnitude. I'm sure you can see that not merely your body but the entire Earth would be at great hazard from a baseball if gravity were as strong as EM. Gravity only gets as strong as it does because there's no antigravity.

Now, the thing about the color force that makes it asymptotic is that its beta function is negative; that means that its coupling constant varies a great deal with a tiny change in distance, unlike gravity and EM, both of which have essentially stable coupling constants outside the nucleus (EM starts to self-interact at nuclear distances and gets complicated like the color force is, and nobody knows what gravity does- to know that we need a quantum mechanics for gravity, which we don't have). So that's at least part of the problem; you need the beta function to figure out how to describe how the coupling constant varies, so you can figure out what value to use for it at different distances and characterize how it falls off.

Good luck; I'm too lazy to get that involved.

 

[Cuddles]

When people say that the strong force is stronger than gravity, what they really mean is that the force constant is larger. Just as the gravitaional constant (G) is smaller than the electic constant (k), the equivalent for the strong force is much larger than both. The actual strength of the forces depends very much on the exact situation. Since the strong force decays exponentially it is only really stronger at very short distances, while the electomagnetic force decays much slower and is actually much stronger in most situations. In fact, on most scales gravity is not only the strongest force, but is actually the only one, since all the others will be close enough to zero that it makes no sense to even consider them. For the strong an dweak forces this is simply because they decay faster than the other two forces, for electromagnetism it is because it is so strong that opposing charges always end up near each other, so at long range their effects cancel out.

Interestingly, this is part of the reason that the strong force decays so fast. If you take, for example, an electron and a proton. Close to them there are very strong forces. As you move further away, the distance between them becomes very small in comparison to the distance to you, and so you now see the combined field, which cancels essentially to zero. The same is true for the strong force. The actual things the force acts on are quarks and gluons, not protons and neutrons. Inside a proton there are very strong forces between the quarks, but outside the proton you no longer see the individual fields, you see the combined field of all the things inside. The situation is a little more complex than just a proton and an electron, but the effect is the same. The force essentially "leaks" out of the particles so that there is still some force that binds nucleons together, but it is nowhere near as strong as the actual force between two monopolar sources. The same effect allows neutral atoms to form molecules.

 

[Dr. Trintignant]

EM starts to overwhelm the color force at about the size of thorium nuclei.

Interesting--I would have guessed iron, since that's what I've always heard has the least energy in the nucleus per nucleon. That's pretty far off from thorium, though.

Inside most nuclei except the heaviest, the color force so far overwhelms the EM force that EM might as well not exist for all the effect it has.

Makes sense. I wouldn't mind seeing a chart of the forces holding nuclei together for each of the elements and their isotopes.

two more quarks will form from the energy you're putting into the field by pulling on them and promptly combine with the two you're trying to pull apart and turn them into mesons; so if you try to pull the quarks in a meson apart, you wind up with two mesons and a lot of wasted effort.

Ha. Mother Nature can be tricky sometimes...

Nope, it's not just neutrons, and you've got it backwards: it seems as if the more protons there are, the bigger an excess of neutrons you need to hold them together.

Indeed, I realized my error after that post and corrected myself. My error was in forgetting that the nuclear force applies to protons and neutrons (almost) equally.

Might be a bit higher than that, 112 or some such, but not much.

Beyond that is the hypothetical "island of stability", I guess. I don't fully understand that but it seems to be somewhat analogous to electron shells.

You did some math down there, I see. You made a mistake, or else Wikipedia gave you a wrong starting point. One of the things you might want to look up is the ratios of the forces;

Actually, there I was doing a comparison between the nuclear and EM force--while there's certainly the possibility of error, my result seems to fit with the other evidence. At the claimed typical internucleon spacing (1.3 fm), EM is actually more powerful than nuclear (assuming my calcs were correct). It seems that's the reason neutrons are needed in the first place--they "dilute" the EM force while keeping the nuclear force.

That's about forty-seven orders of magnitude. I'm sure you can see that not merely your body but the entire Earth would be at great hazard from a baseball if gravity were as strong as EM.

Incredible, isn't it? One day I'll have to figure out how it is that capacitors don't simply implode. 2 F capacitors are easily available at 2 V; that is one Coulomb. At 1 m plate spacing that would be 8.988e9 N; at typical capacitor plate spacing it would be far greater. The dielectric must be under tremendous stress unless there's something else going on.

Gravity only gets as strong as it does because there's no antigravity.

Indeed. It's a good thing that like charges do not attract each other. I'm not sure the universe could work were that the case.

EM starts to self-interact at nuclear distances

So I've read. I believe what I've heard is that electrons act like fuzzy splotches of charge, despite there being no evidence of internal structure. So at very short distances, there's no longer a 1/r^2 falloff.

Good luck; I'm too lazy to get that involved.

Thanks again for the great information. As I mentioned, I'm no physicist, but I enjoy this stuff greatly. Recently I've been reading the Feynman Lectures on Physics and have found it to be a fascinating and appealing approach to the subject (far more interesting than my physics classes in college).

- Dr. Trintignant

 

[Yllanes]

Just two short points:

On the relative strength of the EM and nuclear forces. The electrostatic energy of a uniformly charged sphere of total charge Ze and radius R is

[latex]
\footnotesize
\[
E=\frac35 \frac{Z^2 e^2}{R} = \frac{3}{5} \frac{ \alpha \hslash c}{R}
\]
[/latex]

This formula gives a reasonably good estimate of the coulombian repulsion of protons in a nucleus. At the same time, a nucleus of A = N+Z nucleons has a radius of about 1.25 A^1/3 fm. hbar c = 197.3 MeV·fm and alpha = 1/137 so

[latex]
\footnotesize
\[
E(MeV)\simeq\frac35 \frac{197 Z^2}{137 \cdot1.25 A^{1/3}}
\]
[/latex]

You can use this formula to guess the amount of electrostatic repulsion in a given nucleus. Compare with the total binding energy. For example, for ₂₆⁵⁶Fe the atomic mass is m_Fe = 55.934942 u = 52 103.5103 MeV. The mass of a proton is 938.280 MeV and the mass of a neutron 939.573 MeV, so the total binding energy is (neglecting electron binding energy)

B = 26*938.280 + 30*939.573 + 26*0.511 - 52 103.5 = 492.25 MeV

while the electrostatic repulsion is

E ~ 122 MeV

so the EM force is a real player even for this relatively light nucleus.

Beyond that is the hypothetical "island of stability", I guess. I don't fully understand that but it seems to be somewhat analogous to electron shells.

One of the simplest models for nuclear structure is the shell model, in which neutrons and protons fill two independent systems of orbitals in a similar way as what happens with atoms. This model is much more crude for nuclei than for atoms, but it predicts many interesting properties. From high school chemistry one knows that the ionisation energy peaks at the amgic numbers Z=2, 10, 18, 36, 54 (noble gasses). This is because the last electron in these atoms just finishes filling one shell. The next atom will have one extra electron, which would have to jump to a new shell, so there is a big change in the ionisation energy. The same thing happens with nuclei, although the shell ordering is different. We have magic numbers 2, 8, 20, 28, 50, 82, 126. When the number of protons or neutrons is one of those, the nucleus is particularly stable (some nuclei are even doubly magic, such as ²⁰⁸Pb). Also, nucleons tend to pair, so even-even nuclei (even N and Z) are specially stable and odd-odd nuclei very rare (the unpaired proton and neutron tend to pair with each other). This explains why, when finding new, bigger artificial atoms there are gaps in the periodic table. The next magic number would be 184, so there could be a superheavy 126 protons and 184 neutrons doubly magic nucleus. I can elaborate on this but I don't think it is too relevant to this thread.

 

[Art Vandelay]

Magnetism is simply an artifact of viewing the four-dimensional EM tensor in a three-dimensional frameworl.

baron's link is a good one. But, if you want a very condensed version, there are four known forces in the universe: strong, electromagnetic, weak, and gravity. I listed them in order of strength. Note that electomagnetic is stronger than gravity.

That sort of statement doesn't make sense to me. They're in completely different units. Gravity is in force per mass squared, electricity in force per charge squared. How can you compare them? That's like saying that a kiligram is a lot bigger than a centimeter.

 

[Art Vandelay]

Somethings we just don't know. Unless, I'm wrong and someone wants to let you and I in on the secret. I wouldn't hold my breath.

[nitpick]me, not I[/nitpick]

 

[Yllanes]

That sort of statement doesn't make sense to me. They're in completely different units. Gravity is in force per mass squared, electricity in force per charge squared. How can you compare them? That's like saying that a kiligram is a lot bigger than a centimeter.

The sort of comparison usually done with these things is to form adimensional constants related to each of the interactions and compare them. For EM we have e²/(hbar c) = 1/137.036. For the weak interaction, g·m²·c/hbar =1.026·10^-5 (g is the so called beta minus decay strength constant, g = 0.88 ·10^-4 MeV fm³). These constants can be ranked as he said,

• Pion-nucleon (strong force) strength: 1
• Electromagnetic strength: 1/137
• Weak (beta decay) coupling strength: 10^-5
• Gravitational coupling strength: 10^-39

Alternatively, you can consider the ratio in the intensity of the gravitational attraction between two protons and their electrostatic repulsion. These constants do not mean that one interaction is always the winner, but they are useful.

 

[Topspy]

Probably worth describing the relativistic correction to the electric force that results in magnetism in more detail, if we're going to "explain how magnets work."

Suppose there are two electrons just sitting there. They will act on each other by their electric charges of one unit each, with a force that is inversely proportional to the square of their separation; double the separation, the force is quartered; halve the separation, the force is quadrupled. Now force is mass times acceleration; so we see that it is doubly dependent upon time.

Now suppose that the electrons are both moving by at a substantial fraction of the speed of light. Note that from our point of view, they will experience time dilation; that is, we will see time as passing more slowly for them than for us. I have described elsewhere the spacetime rotation that results in this. If the force is doubly dependent upon time, you can see that this will result in a perception on our part that the force between the electrons is reduced. One way to explain this reduction in force is to posit another force that is acting in opposition to the original force; but since the electrons must be moving for us to see this force, its vector is not directly opposed to the vector of the original force. In fact, it acts at an angle to the original force, because of the movement of the electrons. We call this force, "magnetism." It acts always on moving charges, and always at an angle to the electric force; since the electric force moves at the speed of light, we see the angle as a right angle, both to the direction of movement, and to the direction of the electric force.

OK, so what's a magnet? The simple answer is, magnets form when materials have a net unbalanced charge in their electron shells. The spin of the electrons results in the relativistic effect we call magnetism, and the lack of balance results in residual force that is not canceled by the existence of equal and opposite force. A more detailed explanation is available at the linked article above.

My, my. I'm not sure if you are speaking 'tounge in cheek' or not. At first glance this seemed logical - given that I admire your superior knowledge of these things. However: "Now suppose that the electrons are both moving by at a substantial fraction of the speed of light" - is this a condition for magnatisim? If so, does that mean that magnetic materials (i.e. magnets) all have electrons moving at speeds close to light, while non-magnetic materials don't? I've never heard of a relatavistic explanation of magnatism untill now.... please expand.

 

[Topspy]

or Magnetsim. Pardon my spelling ( if correct THIS time.)

 

[Topspy]

Friction holds the magnets up. The force of friction between two surfaces is more or less proportional to how hard the force is that holds them together. Because magnets attract themselves to the refrigerator pretty well, there is more friction between a magnet and a refrigerator door than there is between a non-magnetic object and a refrigerator door. The friction balances out the force of gravity.

Glue is something different, although similar on a fundamental level.

OMG. Yikes!

 

[Ben Tilly]

My, my. I'm not sure if you are speaking 'tounge in cheek' or not. At first glance this seemed logical - given that I admire your superior knowledge of these things. However: "Now suppose that the electrons are both moving by at a substantial fraction of the speed of light" - is this a condition for magnatisim? If so, does that mean that magnetic materials (i.e. magnets) all have electrons moving at speeds close to light, while non-magnetic materials don't? I've never heard of a relatavistic explanation of magnatism untill now.... please expand.

He was not speaking tongue in cheek - he's serious.

To answer your question, magnetism is not always dependent on charged particles moving near the speed of light. At any speed there is a relativistic correction, so if electric particles are moving, there will always be magnetism. Since the electromagnetic force is so strong, it isn't hard to get appreciable magnetism even from relativistic corrections to slow motions. (The motion of electrons in electromagnets is something like centimeters per second. But enough charge is moving to cause a significant magnetic field.) But as a thought experiment, it is easier to visualize what happens "near the speed of light" for people who have learned a little special relativity.

But yes, all magnetism that we know of is tied to moving charged particles. However all substances have moving charged particles - so whether or not it is magnetic is tied to subtle details about the internal structure of the material.

Cheers,
Ben

 

[Schneibster]

Thanks, Ben. To put it another way, Topspy, magnetism is the correction for the fact that a charge is not attracted to or repelled from where another charge is now, but where it was when it emitted the virtual photon that the particle interacted with; in other words, the correction for the fact that the electromagnetic force that couples charges does not act instantaneously across intervening space.

 

[Topspy]

Thanks, Ben. To put it another way, Topspy, magnetism is the correction for the fact that a charge is not attracted to or repelled from where another charge is now, but where it was when it emitted the virtual photon that the particle interacted with; in other words, the correction for the fact that the electromagnetic force that couples charges does not act instantaneously across intervening space.

Hmm. An EMF that is responding to the void left by a photon? I vaguely remember the 'right-hand rule' from my electronics classes, so some of this rings a bell. To put a temporal aspect to it ( in this way ) will make my head hurt for a few days. I must ponder..... in the meantime, anymore clarifying remarks would be welcome - but I will be gone for a few days.... thanks.

 

[Schneibster]

Not EMF. That's voltage. Electromagnetic force. It's a different thing, it's the force that charges feel when they interact with other charges.

 

[H3LL]

Jesus holds them on.

This is why small magnets are not very good as they can slip through the holes in his hands.

.

 

[Topspy]

Not EMF. That's voltage. Electromagnetic force. It's a different thing, it's the force that charges feel when they interact with other charges.

now I'm upset. NOT emf? that DOES stand for 'electromagnetic force' does it not? And, what is voltage if not the force charges feel when they interact with other charges? Potential difference is my understanding, which is another way of saying ...... EMF.

 

[Dilb]

now I'm upset. NOT emf? that DOES stand for 'electromagnetic force' does it not? And, what is voltage if not the force charges feel when they interact with other charges? Potential difference is my understanding, which is another way of saying ...... EMF.

Actually, the EMF is electromotive force, a holdover from the early days of electricity. The EMF is the voltage, which is a potential. Taking the slope of a potential gives you a force, so the EMF isn't really a force; and that's why it's a holdover.

The electromagnetic force, on the other hand, is a force.