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8.02x - Lect 21 - Magnetic Materials, Dia- Para- & Ferromagnetism

Jun 08, 2021
Yesterday we had two hundred and twenty-five engines and six of those engines were doing over two thousand RPM, which is a reasonable achievement. And the elite is here. These are the elite, the six highest. The winner is Yung Eun Lee, I spoke to her on the phone last night. If all goes well, she's here. Are you here? Where are you? There you go. Why don't you come over so I can congratulate you in person? I thought about the... the prize for a while, and I decided to give you something that's not particularly high-tech, but come here, give me a European kiss and another, in Europe, let's three.
8 02x   lect 21   magnetic materials dia  para  ferromagnetism
OK. Uhm, the prize I have for you is a thermometer that dates back to the time of Galileo Galilei. Come here. It was designed at the beginning of the 17th century. Uh, it doesn't require any knowledge of 802 to explain how it works. In any case, you need 801. It is not a digital thermometer. But it's accurate to about one degree Celsius and if you come here, you can tell, you look at these floats and the highest float indicates the temperature. It's seventy-two degrees here now. And I suggest you brush up on your knowledge of 801 so that maybe next week you can explain to me how it works.
8 02x   lect 21   magnetic materials dia  para  ferromagnetism

More Interesting Facts About,

8 02x lect 21 magnetic materials dia para ferromagnetism...

And, of course, tell your grandchildren. You might want to leave it here. It is very fragile. Uh, there's also some packaging material in here, so you can take it home without breaking it. So congratulations once again and of course... ...great. And you'll join us for dinner on April 13th with the other five winners. Thank you so much. There are two other very special people I want to mention. And one is a person who is not enrolled in 802, but he did extremely well and was very generous. He wasn't competing. His name is Daniel Wendel. His engine reached four nine hundred RPM.
8 02x   lect 21   magnetic materials dia  para  ferromagnetism
And then there was Tim Lo. Is Tim Lo in the audience? I hope he will be there at eleven. Tim made a motor, when I looked at it I said to myself, it will never work, but it is so beautiful. It was so artistic that we introduced a new award, a second award, for the most artistic engine and Tim Lo is definitely the one, by far, the best, the most beautiful and the most fantastic artistic design. So I bought him a book on modern art, what else could it be, for someone who built such a beautiful engine.
8 02x   lect 21   magnetic materials dia  para  ferromagnetism
It's here for those of you who want to watch it later. It is very difficult to show it on television because it is very delicate. It's like a bird cage that he built instead of just having loops like that, it's a bird cage. Is very pretty. I have the winning engine here and I'm going to show you the winning engine and I also want to teach you some physics, showing you the winning engine in a way that you may have never thought about. So this is the winning engine. And when we start this motor, the ohmic resistance of the current circuit is extremely low.
So the moment you plug it into your power supply, it will run a very high current. But the moment the motor starts rotating, a continuous change of

magnetic

flux occurs in these loops, so now the system will fight against itself and immediately cut off the current, which is another striking example of Faraday's Law. . I'll show you the current of this motor when I block the rotor so it can't spin. This is a six amp point. And you will see the moment I turn on the motor, that current drops enormously. A striking example of Faraday's law. So first I have to show you this current, so here you see the volt and a half and on the right side you see the current.
Now no current flows because the loop hangs in such a way that it does not make contact with the battery. And I'm going to try to do it... there it is. See the six amp dot on the right? The current is so high that due to the internal resistance of the power supply, the voltage also drops. But you saw the one point six, right? Now I'm going to run the engine. Look, the motor is running now and now look at the current. Currently, forty milliamps, thirty milliamps, fifty milliamps. It's forty times smaller than when I locked the rotor.
And this is one of the reasons why when you have a motor, whatever it is, it could just be a drill, you try not to block it suddenly, because it will run a huge current and it can really damage the motors. So you can see here how the current decreases by a factor of forty between running and not running. Alright. E

lect

ric fields can induce e

lect

ric dipoles in

materials

and in the case where the molecules or atoms themselves are permanent electric dipoles, an external electric field will try to align them. We've discussed that in great detail before when we talked about dielectrics.
And the degree of success depends entirely on the intensity of the external electric field and the temperature. If the temperature is low, there is very little thermal agitation, then it is easier to align those dipoles. We have a similar situation with

magnetic

fields. If I have an external magnetic field, this can induce magnetic dipoles in the material. And it induces magnetic dipoles at the atomic scale. Now, in the case where the atoms or molecules themselves have a permanent magnetic dipole moment, then this external field will try to align these dipoles and the degree of success depends on the strength of the external field and again on the temperature.
The lower the temperature, the easier it will be to align them. Then the material modifies the external field. Today I will often call this external field the vacuum field. So when you bring material into a vacuum field, the field changes. The inner field is different from the outer field, from the vacuum field. First I want to remind you of our definition of magnetic dipole moment. It's actually very simple how it is defined. If I have a current, a loop, it could be a rectangle, it doesn't have to be a circle and if the current runs in this direction, viewed from below clockwise and if this area is A, then the dipole moment magnetic is simply the current multiplied by the area A.
But we define A according to the... the vector A, according to the corkscrew rule on the right. If I come from below in a clockwise direction, then vector A is perpendicular to the surface and then points up. And so the magnetic dipole moment, for which we normally write mu, also points up. And so this is a vector A, which is this normal according to the corkscrew on the right. And if I have N of these loops, then the magnetic dipole moment will be N times larger. Then they will support each other if everyone is going in the same direction.
First I want to talk to you about diamagnetism. Diamagnetism. All

materials

, when you expose them to an external magnetic field, will oppose that external field to some degree. And they will generate, on an atomic scale, an electromagnetic field that will oppose the external field. Now you will say yes, of course, Lenz's Law. Mistaken. It has nothing to do with Lenz's Law. It has nothing to do with free electrons in conductors producing eddy current when there is a changing magnetic field. I am not referring to a changing magnetic field, but to a permanent magnetic field. So when I apply a permanent magnetic field, in all materials, a magnetic dipole moment is induced to oppose that field.
And there is no way we can understand that with 802. It can only be understood with quantum mechanics. So we won't make any attempt to do that, but we'll accept it. And so the magnetic field inside the material is always a little smaller than the external field, because the dipoles will oppose the external field. Now I will talk about paramagnetism. Paramagnetism. There are many substances in which the atoms and molecules themselves have a magnetic dipole moment. So the atoms themselves or the molecules, you can think of them as little magnets. If there is no external field, nor a vacuum field, then these dipoles are completely chaotically oriented and therefore the net magnetic field is zero.
So they are not permanent magnets. But the moment you expose them to an external magnetic field, this magnetic field will try to align them. And the degree of success depends on the strength of that field and the temperature. The lower the temperature, the easier it will be. And so if you had a magnetic field, let's say like this, this is your B field, this is your vacuum field, and you bring in paramagnetic material, then there's a tendency for the north pole to move a little bit. in this direction. And so these atomic magnets, on average, would try to pull the north pole a little bit in this direction.
Or, if I speak the language of magnetic dipole moments, then the magnetic dipole would try to go a little bit in this direction. If you remove the external field from a paramagnetic material, there is immediately complete and total chaos, so there is no permanent magnetism left. If you introduce paramagnetic material into a non-uniform magnetic field, it will be attracted to the strong side of the field. And this is very easy to... see how it works. Suppose I have a magnet here, and let this be the north pole of the magnet and this is the south pole.
And then the magnetic field is something like this. Notice here that it is not uniform. And I bring some paramagnetic material there. Let's say there is a single atom there. It is not to scale what I am going to draw. And here is that atom and this atom is now paramagnetic, it has its own magnetic dipole moment. And this magnetic dipole moment, now, would like to align itself in this direction to support the field. The field is trying to push it in that direction. Let's assume it's in this direction. So if we look from above, the current in this atom or in this molecule runs in this direction.
Seen from above, clockwise. So that would be the ideal alignment of this atom or this molecule in that external field. This loop of current will be attracted, it wants to go towards the magnet. Let's look at this point here. At that point, the current goes on the board. So here is that current I. And the magnetic field is like this, the external magnetic field is like this. So in which direction is the Lorentz force? It is always in the direction that I cross B. And I cross B... I cross B in this direction. That is the direction of the Lorentz force.
So right here there is a force on the loop in this direction. So right here there is a force on the loop in this direction, on the current loop. And so everywhere around this loop, there is a force pointing like this and therefore clearly there is a net upward force. And that is why this matter wants to go towards the magnet. Another way to look at this is that this current loop is itself a small magnet, so the south pole is here and the north pole there, because this is the direction of the magnetic dipole moment.
And the north pole attracts the south pole. That's another way of looking at it. That is the reason why magnets attract each other, why the north and south poles attract each other, and why the north and south poles repel each other. That's exactly the reason. It is the current that flows, it is the Lorentz force that causes the attraction or the repulsive force. The paramagnetic material is then attracted to a magnet. The essential thing is that this field is not uniform. And the diamagnetic material, of course, will be repelled, will be pushed out of the strong field, because in the paramagnetic material, in the diamagnetic material, this current will run in the opposite direction, because it opposes the external field while the paramagnetism supports it.
We have a third form and the third form of magnetism, actually the most interesting, is

ferromagnetism

. In the case of

ferromagnetism

, again we have that atoms themselves have permanent dipole moments. But now, for very mysterious reasons that can only be understood with quantum mechanics, there are domains that have dimensions of about a tenth of a millimeter, maybe three tenths of a millimeter, so the dipoles are one hundred percent aligned. And these dipoles, domains, which are in one direction, are uniformly distributed throughout the ferromagnetic material and therefore there may not be any net magnetic field. If I have here, if I try to sketch those domains, something like this, then maybe here all of these dipoles would be one hundred percent aligned in this direction, but for example here, they'll all be aligned in this direction.
And the number of atoms involved in that domain is usually ten to seventeen, perhaps even ten to twenty-one atoms. So if I now apply an external field, these domains will be forced to go in the direction of the magnetic field, and of course the degree of success depends on the strength of the external field, the strength of the vacuum field, and the temperature. The lower the temperature, the better it is, because then there is less thermal agitation, which of course adds a certain randomness to the whole process. So when I apply an external field, these domains as a whole can change.
Within the ferromagnetic material, the magnetic field can be thousands of times stronger than in the vacuum field. And today we will see some examples of this. If we eliminate the external field, in the case of paramagnetism, we again obtain total chaos of the dipoles. That is not necessarily the case with ferromagnetism. Some of those domains may remain aligned in the direction the external field was forcing them. If you very carefully remove that external field, undoubtedly some domains will recede, because of the temperature, there is always thermal agitation. Some can remain oriented and therefore the material, once exposed to an external magnetic field, canhave become permanently magnetic.
And the only way to remove that permanent magnetism might be to hit it with a hammer and then of course these domains will get very jittery and then randomize. Or you can warm them up and then you can also undo the orientation of the domains. The domains will remain, but then average not to produce any permanent magnetic field. So, for the same reason that paramagnetism is attracted towards the strong field, in case we have a non-uniform magnetic field, ferromagnetism will of course also be attracted towards the strong field, except in the case of ferromagnetism, the forces with which that ferromagnetism The material is attracted towards the magnet, much larger than in the case of paramagnetic material.
If I take a clip, you can do it at home, you can hang a clip on the south pole of your magnet or the north pole of your magnet, you all have magnets in your motor kit, so you can try it at home. . Take a paper clip and hang it on the magnets. It doesn't matter which side you hang it on, because the ferromagnetic material is always attracted to the strong field. If you hang some of those clips there and remove them very carefully and slowly, don't hit them with a hammer yet, you may notice that after removing them the clips have become magnetic.
In fact, you can try hanging them on each other, making a small chain. But let them fall to the ground a few times and that magendas... the magnetism will disappear. So what you have witnessed is that some of those domains remained aligned due to your external field. With paramagnetism, there is no way to hang paramagnetic material under most circumstances on a magnet. There is one exception. I'll show you the exception later today. And the reason is that the forces involved with paramagnetic material are generally only a small percentage of the weight of the material itself. So if you take a piece of aluminum and you have a magnet, the aluminum will not stick to the magnet.
There is a force. The aluminum will be attracted to the magnet, but the force is much less than the weight of the aluminum, so it will not be able to pick it up, unlike ferromagnetic material, which can be picked up with a magnet. So what I could demonstrate to you, on the one hand, I could take a bar magnet and show you that there are clips hanging from this. You could also show them that the aluminum doesn't hang from this. But that won't be very exciting. That's why I decided on another demonstration, in which my goal is to show you that the ferromagnetic material is attracted with enormous forces towards the strong magnetic field, as long as it has a magnetic field that is not uniform.
And the way I'm going to do it is with this piece of ferromagnetic material. And this piece of ferromagnetic material is quite heavy. And you're going to tell the class how heavy it is. Be very careful. What do you think? Wow! Good for you! Do it again! Sounds good...looks great. It's fifteen kilograms. Fifteen kilograms of ferromagnetic material. It is not a permanent magnet. There may be some permanent magnetism left, of course, because once you've exposed it to an external field, yes, there may be some permanent magnetism left. So now I'm going to keep this, let's first make sure that nothing happens to Galileo's thermometer.
So let's put this here. Look what the temperature is...oh man, it's rising. I must be sweating here. Seventy-four degrees, yes, seventy-four degrees now. Well, here is my magnet, which produces about three hundred and twenty gauss. But what counts is that the magnetic field is not uniform here and also here. So I'm going to turn on the magnet, I think I have to press a button here. And the first thing I'm going to do now is feed this magnet. So this is a solenoid. I put my hand here, my hand is paramagnetic, it's not being sucked.
It really isn't. I do not feel anything. The strength is... I can't even feel anything. But I'm not ferromagnetic, thank God. Now this. "Woosh", fifteen kilograms, just absorbed like this. And I'm very lucky that when he oversteps here he wants to come back, because he always wants to go to the stronger field. It doesn't matter if you have it here or there. The reason why is lucky, because if it weren't, this fifteen kilogram bar would fly out of here like a bullet. So the only thing you don't want to do when it goes in there is not break the current, because then it would come out like a bullet.
And I'm not going to do that, believe me. But I want to show you that... here it goes. It is an amazing ferromagnetic material. Oh! OK. So, the ferromagnetic material has enormous strength. If you have a field that has a strong gradient, that is very non-uniform, it is absorbed, attracted to the strong side. That's why it hangs on magnets. That's the basic idea. I have another demonstration. And another demonstration is to make you see the magnetic domains in a non-kosher way. But I'll tell you why it's not kosher. I have here a set of eight by eight magnetic needles, compass needles.
And you will see them there. And I will change the situation so that you have better light. And when I have an external magnetic field and I walk here a little bit and I just let it go, and I wait, you'll see areas where these magnetic needles are pointing in the same direction and you'll see areas where they're pointing in a different direction. . We'll just give it a chance. And that might make you think that this is the way domains form in ferromagnetic material. Oh, in fact we now have a situation where almost everyone is aligned in this direction and there is only one group here that is pointing in this direction.
I can change that, of course, by changing the magnetic field. Why isn't this really a kosher demonstration to convince you that dominions exist? Firstly, there is no thermal agitation, whereas in ferromagnetic material there is thermal agitation. Some may be oriented like this and some may be oriented like this, where here you only have two preferred directions. No quantum mechanics needed for that, just a matter of minimum energy considerations. And then, they are either pointed like this or like that, and that already shows that it is very different from ferromagnetism. But the reason we show it to you is that it still gives you an interesting idea of ​​the fact that it can have various orientations and that they come in groups.
That the groups stay united and not all go in the same direction. But like I said, it's not really a good way to explain why domains exist in ferromagnetic material. Ah, now you see again, you have some very neatly aligned here and some are in very different directions here. So the basic idea is there. It's a good demonstration, but it shows something that isn't really related to ferromagnetism. The demo that is one of my favorites, one of my absolute favorites, is one through which I can make you listen to the change of these domains. I have ferromagnetic material inside a coil.
I have a coil here... and I'm going to put ferromagnetic material here. And I have a speaker here... an amplifier too, I call it an amplifier. And this is a speaker. Let's first assume that there is no ferromagnetic material there. This is how I'll start the demo. And I approach this with a magnet and I go very fast. "Whooosh", what will happen? Faraday will say, "Yes, there is a change in magnetic flux and there will be an EMF in this coil." That means there will be a current in this coil, induced current. And it will be amplified and you will hear a hiss.
And you will hear that. However, if I go in very slowly, you won't hear anything, because d phi dt is so low, because the time scale of my movement is so large, that you won't hear any current. The induced current is negligibly small. Because remember that the induced current is proportional to the induced EMF and the induced EMF is proportional to the time change of the magnetic flux. So I can make that flow change very, very small if I introduce it very slowly. Now I will put the ferromagnetic material on and approach again very slowly. And now, there comes a time when some of those domains go "cluck," "cluck." But when the domains are reversed, there is a magnetic flux change within the material, so the magnetic flux change means d phi dt and is on an extremely short time scale.
And now you get an EMF, you get a current going through the wire and you hear a crackling sound through the speaker. And for every group of domains that change, you can hear that. And that's kind of amazing when you think about it, that ten to twenty atoms go "clucking" and that you can hear that. And this is what we're going to do here and I'll do it later, in several steps, so first you can hear the noise if I don't have ferromagnetic material and then... so here it is, here's the coil. A very small coil.
And here is a magnet. And I will come very quickly towards the coil. What you heard now is Faraday's Law. You simply have a change of magnetic flux in the coil. Oh, I shouldn't touch her. Now I enter very slowly and leave very slowly. You can't hear anything, d phi dt is too low. Now I put the ferromagnetic material. Put it inside the coil. And now I approach again, very slowly. There they go. Do you listen to them? Those are, those are domains that go. I'll go in with the other side. There you go, the domains.
Isn't it amazing? You hear how atoms change, groups of atoms. I'll turn it over again. Now they turn around. They don't like it, but that's their problem. This is called the Barkhausen effect. I find it really surprising that groups of atoms can be heard, ten to twenty atoms at a time, they turn around and when they do so, there is a change in magnetic flux within the ferromagnetic material, it is detected by the coil and a current is heard. . And if I do it quickly, these, these, these domains go crazy. Now they go crazy. Imagine you were a domain and I would treat you like this.
You say, "Cluck, cluck, cluck, cluck, cluck." But the fact that you can hear it is absolutely amazing, right? That's actually a good way to prove that these domains exist. If you did that with faramagnetic... paramagnetic material, you wouldn't hear that. So in all cases, whether we have diamagnetic material, paramagnetic material, or ferromagnetic material, the magnetic field inside is different than what the field would be without the material. And what would the field be without the material that we have called external field. I have called it a vacuum field. And in many cases, but not all, the next lecture I will discuss the issues that not in all, in many cases, but not all, the field within the material is proportional to the vacuum field.
And if that's the case, then you can write that the interior field is linearly proportional, so this is the interior field of the material, regardless of whether it is diamagnetic, paramagnetic or ferromagnetic, it is proportional to the vacuum field. I'll write void for this. And I call this constant of proportionality kappa of M. I... Our book calls it K of M. And it is called relative permeability. And now we can look at these relative permeability values ​​and we can immediately understand the difference between diamagnetic material, paramagnetic material and ferromagnetic material. Since in the case of diamagnetic material and paramagnetic material, the interior B field is only slightly different from the vacuum field, it is common to express kappa of M in terms of one plus something we call magnetic susceptibility, which is xi of M.
Because if it is very close to one, then it is easier to simply enumerate xi of M. And let's look at diamagnetic material. Note that these values ​​for xi of M are all negative, of course they have to be negative otherwise it would not be diamagnetic. It means that the inner field is slightly, a hair smaller than the vacuum field, because these induced dipoles oppose the external field, remember. It has nothing to do with Lenz's Law, but they still oppose it. And then you express it in terms of, um, magnetic susceptibility and then you have to take one minus one point seven times ten to the power of negative four to get kappa of M, which is very close to one.
If we now move on to paramagnetic materials, the minus signs become plus signs. Once again, the numbers are small. But the fact that it is positive means that inside the paramagnetic material, the magnetic field is a little bit, a hair larger than the vacuum field. But now, if we come to the ferromagnetic material, it is really absurd to ever list the value of xi of M, because xi of M is so large that one can forget about the one, so xi of M is approximately the same as kappa of M .And then these are numbers that are one hundred, one thousand, ten thousand and even greater than ten thousand.
That means that if kappa of M is ten thousand, you would have a field inside the ferromagnetic material that is ten thousand times greater than your vacuum field. In the next lecture I will tell you that there is a limit to how far you can go, but for now we will do it, we will leave it at this. So the paramagnetic and ferromagnetic properties depend on the temperature. Diamagnetic properties do not depend on temperature. So at very low temperatures, there is very little thermal agitation, so it is easier to align these dipoles, so the kappa values ​​of M will be different.
For ferromagnetic material, if you cool it, you expect the kappa of M to increase, so you will have a stronger field inside it. So it depends on the temperature. If you heat the material too much, it can completely lose its ferromagnetic properties. What happens at a certain temperature is that these domains break down, so the domains themselves no longer exist. They annihilate. And that happens at a very precise temperature. It's very strange. That's also somethingvery difficult to understand and for that you also need quantum mechanics. But at a certain temperature, which we call the Curie temperature, which for iron is one thousand forty-three degrees Kelvin, which is seven hundred and seventy degrees Celsius, suddenly the domains disappear and the material becomes paramagnetic.
In other words, if the ferromagnetic material would be hanging on a magnet and if you heated it above the Curie point, it would fall off. It would become paramagnetic, but paramagnetic material generally does not hang from a magnet because the forces involved are quite small. And the change is very abrupt and I am going to demonstrate it to you with a demonstration. I have a ferromagnetic nut. It's right there. You will see it very soon. And this nut, or washer, hangs from a steel cable and there's a magnet here. I don't know if this is the north or the south.
It doesn't matter. And here we have a heat shield. And so this washer is against the heat shield, because it's being attracted. He wants to go towards the strong magnetic field. It is ferromagnetic. Then you will be sitting here. And now I'm going to heat this above the Curie point, seven hundred and seventy degrees Celsius, and you'll see that it falls. And when it cools down again, it turns back on. Then I can make you see how the ferromagnetic properties disappear. And let me make sure I have the right settings. I see nothing. I see nothing.
But there it is. So here's this nut and here's this shield and the magnet is behind it, you can't see it, but it's right there. And then it goes against, right, it goes right towards the magnetic poles. Enter the strong magnetic field. The magnetic field is not uniform outside a magnet and is directed towards it. And now I'm going to heat it up. It will take a while, because seven hundred and seventy degrees Celsius is not that easy to achieve. The three most common ferromagnetic materials are cobalt, nickel and iron. Nickel has a Curie point of only three hundred and fifty-eight degrees Celsius, so if this were nickel... ooh.
If this were nickel...uh-uh. Oh, you like that, huh. I think I need a strong hand. Strong hand is coming. OK. I think I fixed it. I'm a big kid, I did it myself today. I lost my pen, but that's a detail. Okay, let's try it again. So I'm going to warm it up and mention that nickel has a Curie point of three hundred and fifty-eight degrees Celsius. So that's pretty low. This is seven hundred and seventy. Cobalt is at fourteen hundred degrees Kelvin, Curie point. Gadolinium is a very special material. Gadolinium is ferromagnetic in winter, when the temperature is below sixteen degrees Celsius, but is paramagnetic in summer, when the temperature is above sixteen degrees Celsius.
It's starting to get red hot now. Seven hundred and seventy degrees Celsius, some visible light is expected in the form of red light... here it goes. And I'll keep it warm, I'll keep the torch on it, so you can see that it's effectively no longer attracted to the magnet. And the moment you stop heating it, it will cool down very quickly. It will become ferromagnetic again and it will return. Just look at it. There it goes. Now it is ferromagnetic again. So the transition is extremely abrupt. Alright. OK that's fine. So paramagnetic materials, as I mentioned several times, generally cannot be hung from a magnet.
The force of attraction is that there is not enough of it. To hang on a magnet, the force must be greater than your own weight. And diamagnetic materials, of course, are completely ruled out because diamagnetic materials are always pushed toward the weak part of the field. Only paramagnetic and ferromagnetic materials experience a force toward the strong part of the field if the field itself is not uniform. Now there is a very interesting exception. And I want to draw your attention to this transparency here. Look here at the oxygen in an atmosphere. Oxygen at one atmosphere and three hundred degrees Kelvin has a value for xi of M that is two times ten to the power of negative six.
But let's now look at liquid oxygen at ninety degrees Kelvin. That value is eighteen hundred times greater than this value. Why is it so much higher? Well, liquid, in general, is a thousand times denser than gas in an atmosphere. So you have a thousand times more dipoles per cubic meter that can, in principle, align. And clearly you expect an immediate one-to-one correspondence between the density, how many dipoles there are per cubic meter, and the xi value of M. And then you see that this value is substantially larger. The reason it is more than a thousand times higher is that the temperature is also lower.
You go from three hundred degrees to ninety degrees and that gives you another factor of two, because when the temperature is lower, there is less thermal agitation and then the external field can align the dipoles more easily. And that's why you end up with a factor of eighteen hundred. Although this value for xi of M is extraordinarily high for a paramagnetic material, note that the interior field would only be point three five percent larger than the vacuum field, because if xi of M is three point five times ten to the power of negative three, That means that the interior field is only point three five percent larger than the vacuum field.
But this is enough for liquid oxygen to be attracted to a very strong magnet, as long as it also has a very irregular field outside the magnet. And so the force with which liquid oxygen is attracted to a magnet can be greater than the weight of the liquid oxygen. And so I can make you see today that I can have liquid oxygen hanging from a magnet. And that's what we're going to do here. Make sure you have the correct settings. Ah, this is it. So we're going to have some changes in the light. So there you see the two magnetic poles.
It is an electromagnet. And so we can activate the magnetic field at will. Here are the poles of the magnet. And the first thing I'll do is very boring. I'll throw some liquid nitrogen between the poles. Now I don't have the liquid nitrogen value there, but nitrogen is diamagnetic so it's not even a problem. The diamagnetic material is ejected from the strong field. So although the xi value of M will be very different for liquid nitrogen than for gaseous nitrogen, it doesn't matter. So he will certainly be expelled. That's the first thing I want to do, just to bore you a little.
Because I have to keep you on the edge of your seat before you see this oxygen, which will be floating there. So let's first turn on this magnet. I hope I did, yes I think I did. And here comes liquid nitrogen. Boring as hell, it just fails. Now comes the oxygen. Liquid oxygen. It's hanging there. I dare you, you have never seen a liquid hanging from a magnet in your life. You can tell your parents and, of course, your grandchildren. It's hanging there. I'll put a little more... I'll make sure I have the right thing, yeah.
Put a little more. There is liquid oxygen. When you cut off the power, it is no longer a magnet, of course it will fall. Don't worry, you'll get more. Who has ever seen a liquid suspended from a magnet in their life? It is paramagnetic, not ferromagnetic, but because the density is so high and it is so cold, the xi value of M is high enough that the force on it is greater than its own weight. If you do this with aluminum, there is no chance in the world. Aluminum can't hold up there, although aluminum, as you can see, is paramagnetic.
But two times ten to the power of negative five is too small and will not stick to a magnet. OK. You have something to think about. I will see you on Friday.

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