Yesterday we had two hundred
and twenty-five motors and six of those motors went faster
than two thousand RPM, which is a reasonable accomplishment. And the elite is here. These are the elite, the six highest. The winner is Yung Eun Lee,
I talked to her on the phone last night. If all goes well, she is here. Are you here? Where are you? There you are. Why don't you come up so that I can
congratulate you in person. I thought about the-- the prize for a while, and I decided to give you something that is not
particularly high tech, but come up here, give me a European kiss
and another one, in Europe, we go three. OK. Uhm, the prize that I have for you is a thermometer
which goes back to the days of Galileo Galilei. Come here. It was designed in the early part
of the seventeenth century. Uh, it doesn't, uh, require any knowledge
of 802 to explain how it works. If anything, you need 801. It's not a digital thermometer. But it's accurate to about one degree centigrade
and if you come here, you can tell, you look at these floaters and the highest floater
indicates the temperature. It's now seventy-two degrees here. And I suggest that you brush up
on your knowledge of 801 so that perhaps next week
you can explain to me how it works. [laughter] And of course tell your grandchildren
about it. You may want to leave it here. It's very fragile. Uh, there is also some package material here,
so that you can take it home without breaking it. So congratulations once more and of course... [applause] ...terrific. And you will join us for dinner on the thirteenth
of April with the other five winners. Thank you very much. There are two other people who are very special
who I want to mention. And one is a person who is not enrolled in,
uh, 802, but he did extremely well, and he was very generous. He was not competing. His name is Daniel Wendel. His motor went forty-nine hundred RPM. And then there was Tim Lo. Is Tim Lo in the audience? I hope he's going to be there at eleven o'clock. Tim made a motor, when I looked at it,
I said to myself, it'll never run, but it's so beautiful. It was so artistic that we introduced
a new prize, a second prize, for the most artistic motor and Tim Lo definitely
is the one, by far the best, the most beautiful,
the most terrific artistic design. And so for him I bought a book
on modern art, what else can it be, for someone who built
such a beautiful motor. It is here for those of you
who want to see it later. It's very hard to display it on television
because it's so delicate. It's like a birdcage that he built instead
of having just, loops like that, it's a birdcage. It's very nice. The winning motor I have here and I'm going
to show you the winning motor and I also want to teach you some,
some physics by demonstrating the winning motor to you in a way that you may
never have thought of. So this is the winning motor. And when we start this motor, the ohmic resistance
of the current loop is extremely low. So the moment that you connect it with your
power supply, a very high current will run. But the moment that the motor
starts to rotate, you have a continuous magnetic flux
change in these loops and so now the system will fight itself
and it will immediately kill the current, which is another striking example
of Faraday's Law. I will show you the current of this motor
when I block the rotor so that it cannot rotate. It's about one point six amperes. And you will see the moment that I run the motor,
that that current plunges by a huge amount. Striking example of Faraday's Law. So I now have to first show you this current,
so here you see the one and a half volts and on the right side you see the current. There is no current flowing now because the loop
is hanging in such a way that the, that it makes no contact with the battery. And I'm going to try to make it--
there it is. Do you see the one point six amperes
on the right? The current is so high that due to the internal
resistance of the power supply, the voltage also plunges. But you saw the one point six, right? Now I'm going to run the motor. See, the motor is running now
and now look at the current. Current now, forty milliamperes,
thirty milliamperes, fifty milliamperes. It's forty times lower
than when I blocked the rotor. And so this is one of the reasons why when
you have a-- a motor, whichever motor it is, it could be just a drill, you try not to block
it all of a sudden, because an enormous current will run
and it can actually damage the motors. So you see here how the current
goes down by a factor of forty between running and not running. All right. Electric fields can induce electric dipoles
in materials and in case that the-- the molecules or the atoms
themselves are permanent electric dipoles, an external electric field will make an attempt
to align them. We've discussed that in great detail before
when we discussed dielectrics. And the degree of success depends entirely
on how strong the external electric field is and on the temperature. If the temperature is low,
you have 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 in material magnetic dipoles. And it, uh, induces magnetic dipoles
at the atomic scale. Now in case that the atoms
or the molecules themselves have a permanent magnetic dipole moment, then this external field will make an attempt
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 is to align them. So the material modifies the external field. This external field, today I will often call
it the vacuum field. So when you bring material into a vacuum field,
the field changes. The field inside is different from the external
field, from the vacuum field. I first want to remind you of our definition
of a magnetic dipole moment. It's actually very simple how it is defined. If I have a current, a loop, could be a rectangle,
it doesn't have to be a circle and if the current is running in this direction,
seen from below clockwise and if this area is A, then the magnetic dipole
moment is simply the current times the area A. But we define A according to the-- the vector A,
according to the right-hand corkscrew rule. If I come from below clockwise,
then the vector A is perpendicular to the surface and is then pointing upwards. And so the magnetic dipole moment,
for which we normally write mu, is then also pointing upwards. And so this is a vector A, which is this normal
according to the right-hand corkscrew. 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 they're
all in the same direction. I first want to discuss with you diamagnetism. Diamagnetism. All materials, when you expose them
to an external magnetic field, will to some degree oppose that external field. And they will generate, on an atomic scale,
an EMF which is opposing the external field. Now you will say, yes, of course, Lenz's Law. Wrong. It has nothing to do with Lenz's Law. It has nothing to do with the free electrons
in conductors which produce an eddy current when there is a changing magnetic field. I'm not talking about a changing magnetic field,
I'm talking about 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 that we can understand
that with 802. It can only be understood
with quantum mechanics. So we'll make no attempts to do that,
but we will accept it. And so the magnetic field inside the material is always a little bit smaller than--
than the external field, because the dipoles will oppose the external field. Now I will talk about paramagnetism. Paramagnetism. There are many substances whereby
the atoms and the molecules themselves have a magnetic dipole moment. So the atoms themselves or the molecules,
you can think of them as being little magnets. If you have no external field,
no vacuum field, then these dipoles are completely
chaotically oriented and so the net el-- magnetic field
is zero. So they are not permanent magnets. But the moment that 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 on the temperature. The lower the temperature, the easier it is. And so if you had a magnetic field, say, like so--
this is your B field, this is your vacuum field-- and you bring in there
paramagnetic material, then there is the tendency for the north pole
to go a little bit in this direction. And so these atomic magnets, then,
would on average try to get 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
of a paramagnetic material, immediately there is complete, total chaos,
so there is no permanent magnetism left. If you bring paramagnetic material
in a non-uniform magnetic field, it will be pulled towards
the strong side of the field. And this is very easy to--
to see how that works. Suppose I have a magnet here-- and let this be the north pole of the magnet
and this the south pole. And so the magnetic field
is sort of like so. Notice right here it's very non-uniform. And I bring some paramagnetic material in there. Let's say, think of it as just one atom there. It's not to scale, what I'm going to draw. And here is that one atom
and this one atom now is paramagnetic, has its own magnetic dipole moment. And this magnetic dipole moment, now,
would like to align in this direction to support the field. The field is trying to push it in that direction. Let's suppose it is in this direction. So if we look from above, the current then
in this atom or in this molecule is running in this direction. Seen from above, clockwise. So that would be ideal alignment of this atom
or this molecule in that external field. This current loop will be attracted,
it wants to go towards the magnet. Let's look at this point here. That point, the current is going in the blackboard. So here is that current I. And the magnetic field is like so,
the external magnetic field is like so. So in what direction is the Lorentz force? It's always in the direction I cross B. And I cross B--
I cross B is in this direction. That's the direction of the Lorentz force. So right here, there is a force on the loop
in this direction. So therefore 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 that is pointing like this and so there clearly is a net force up. And so this matter wants to go
towards the magnet. Another way of looking at this is that this
current loop is all by itself a little magnet, whereby the south pole is here
and the north pole is 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's the reason why magnets attract each other,
why north and south pole attract each other and why north and north poles repel
each other. That's exactly the reason. It is the current that is flowing,
it is the Lorentz force that causes the attraction
or the repelling force. So paramagnetic material
is attracted by a magnet. Essential is that this field is non-uniform. And diamagnetic material, of course,
will be repelled, will be pushed away from the strong field,
because in paramagnetic-- in diamagnetic material, this current will be running
in the opposite direction, because it opposes the external field
whereas paramagnetism supports it. We have a third form and the third form
of magnetism, it's actually the most interesting,
is ferromagnetism. In the case of ferromagnetism, we again have
that the atoms have themselves permanent dipole moments. But now, for very mysterious reasons which
can only be understood with quantum mechanics, there are domains which have the dimensions
of about a tenth of a millimeter, maybe three tenths of a millimeter,
whereby the dipoles are hundred percent aligned. And these dipoles, domains,
which are in one direction, are uniformly distributed throughout
the ferromagnetic material and so there may not be any
net magnetic field. If I have here, if I try to make a sketch
of those domains, something like this, then perhaps here all these dipoles would all be
hundred percent aligned in this direction, but for instance here, they will all be aligned
in this direction. And the number of atoms involved in such a
domain is typically ten to the seventeen, maybe up to ten to the twenty-one atoms. So if now I 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 on the temperature. The lower the temperature, the better it is,
because then there is less thermal agitation, which of course adds a certain rando--
randomness to the whole process. So when I apply an external field,
these domains as a whole can flip. Inside the ferromagnetic material, the magnetic
field can be thousands of times stronger than it is in the vacuum field. And we will see some examples of that today. If you remove the external field,
in the case of paramagnetism, you have again complete chaos
of the dipoles. That's not necessarily the case
with ferromagnetism. Some of those domains may stay aligned
in the direction that the external field was forcing them. If you very carefully remove that external field,
undoubtedly some domains will flip back, because of the temperature,
there is always thermal agitation. Some may remain oriented
and therefore the material, once it has been exposed to an
external magnetic field, may have become
permanently magnetic. And the only way you can remove that permanent
magnetism could be to bang on it with a hammer and then of course these domains
will then get very nervous and then they will randomize themselves. Or you can heat them up and then you can
also undo the orientation of the domains. The domains themselves will remain,
but then they average out not to produce any permanent magnetic field. So for the same reason that paramagnetism
is pulled towards the strong field, in case that we have
a non-uniform magnetic field, ferromagnetism of course will also be pulled
towards the strong field, except in the case of ferromagnetism,
the forces with which ferromagnetic material is pulled
towards the magnet, way larger than in case
of paramagnetic material. If I take a paperclip,
you can do that at home, you can hang a paperclip on the south pole
of your magnet or the north pole of your magnet, you all have gotten magnets in your motor kit,
so you can try that at home. Take a paperclip, hang it on the magnets. Doesn't matter on which side you hang it, because ferromagnetic material is always pulled
towards the strong field. If you hang a few of those paperclips on there
and you very carefully and slowly remove them, don't hit them with a hammer yet, you may actually
notice that after you remove them that the paperclips themselves
have become magnetic. You can actually try to hang them on each other,
make a little chain. But drop them on the floor a few times
and that magendas-- magnetism will go away. So what you have witnessed then is that some
of those domains remained aligned due to your external field. With paramagnetism, there is no way that you
can hang paramagnetic material under most circumstances on a magnet. There is one exception. I will show you the exception later today. And the reason is that the forces involved
with paramagnetic material in general are only a few percent
of the weight of the material itself. So if you take a piece of aluminum
and you have a magnet, aluminum will not stick to a magnet. There is a force. Aluminum will be attracted by the magnet,
but the force is way smaller than the weight of the aluminum,
so it won't be able to pick it up, unlike ferromagnetic material,
which you can pick up with a magnet. So what I could demonstrate to you,
for one thing, I could take a bar magnet and show you that paperclips
are hanging on this. I could also show you that aluminum
is not hanging on this. But you won't find that very exciting. And therefore I decided on a different
demonstration, whereby my goal is to show you
that ferromagnetic material is pulled with huge forces towards
the strong magnetic field, provided that I have a magnetic field
which is non-uniform. And the way I will do that is with this piece
of ferromagnetic material. And this piece of ferromagnetic material
is actually quite heavy. And you are going to tell the class
how heavy it is. Be very careful. What do you think? Wow! Good for you! [laughter] Do it again! Sounds go--
looks great. [laughter] It's fifteen kilograms. Fifteen kilograms of ferromagnetic material. It is not a permanent magnet. There may be a little bit of permanent magnetism
left, of course because once you have exposed it to
an external field, yes, there may be some
permanent magnetism left. So now I'm going to hold this, let's first make sure
that nothing happens to Galileo's thermometer. So we're going to put this here. See what the temperature is--
oh man, it's going up. I must be sweating here. Seventy-four degrees, yeah,
seventy-four degrees now. OK, so here is my magnet, producing about
three hundred twenty gauss. But what counts is that the magnetic field
is non-uniform here and also here. And so I am going to turn on the magnet,
I believe I have to push a button here. And the first thing I will do is now
power this magnet. So this is a solenoid. I put my hand in here, my hand is paramagnetic,
it's not being sucked in. Really it isn't. I feel nothing. The force is--
I can't even feel anything. But I'm not ferromagnetic,
thank goodness. Now this one. "Woosh", fifteen kilograms,
just sucked in like that. And I'm very lucky that when it overshoots
here that it wants to go back, because it always wants to go
to the strongest field. Doesn't matter whether you have it
here or there. The reason why that's lucky,
because if that were not the case, this fifteen kilogram bar would go
like a bullet coming out of here. So the one thing you don't want to do
when it goes in there, you don't want to break the current,
because then it would come out as a bullet. And I'm not going to do that,
believe me. But I want to show you that--
there it goes. It's amazing,
ferromagnetic material. Aargh! OK. So ferromagnetic material,
there's enormous force. If you have a field that is-- has a strong gradient,
that it's very non-uniform, is sucked, pulled towards 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 sort
of see in a non-kosher way magnetic domains. But I will tell you why it's non-kosher. I have here an array of eight by eight
magnetic needles, compass needles. And you're going to 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 march over here a little and I just let it go, and wait, you will see areas whereby these
magnetic needles point in the same direction and you will see areas where they point
in a different direction. We'll just give it some chance. And so that may make you think
that this is the way that domains-- are formed in ferromagnetic material. Oh, in fact we have now a situation that almost
all are aligned in this direction and there's only a group here
that is pointing in this direction. I can change that, of course,
by changing the magnetic field. Why is this not really a kosher demonstration
to convince you that domains exist? First of all, there is no thermal agitation,
whereas in ferromagnetic material there is thermal agitation. Some may be oriented like this
and others like that, where here you only have
two preferred directions. You don't need quantum mechanics for that,
simply a matter of minimum energy considerations. And so they either are pointed like this
or they are pointed like that and so already that shows you that
it's very different from ferromagnetism. But the reason why we show it to you is it
still gives you an interesting idea of the fact that you can have various orientations
and that they come in groups. That the groups stick together
and are not all in the same direction. But as I said, it is not really a good way
to explain to you why there are domains in ferromagnetic material. Ah, now you see again, you have some nicely
aligned here and others are in very different direction here. So the basic idea is there. It's a nice demonstration, but it shows you something that really
is not related to ferromagnetism. The demonstration that is one of my favorites,
one of my absolute favorites, is one-- whereby I can make you listen
to the flip-over of these domains. I have ferromagnetic material inside a coil. I have here a coil-- and I'm going to put ferromagnetic
material in here. And I have here a loudspeaker--
an amplifier as well, called it an amplifier. And this is a loudspeaker. Let's first assume there is no
ferromagnetic material in there. That's the way I will start the demonstration. And I approach this with a magnet
and I go very fast. "Whooosh", what will happen? Faraday will say, "Yeah, there's a magnetic flux
change 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
some sissing noise. And you will hear that. If, however, I come in very slowly,
you won't hear anything, because d phi dt is then so low, because the time
scale of my motion is so large, that you won't hear any current. The induced current is insignificantly small. Because remember 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 flux change very, very small
if I bring it in very slowly. Now I will put in the ferromagnetic material
and I will approach it again very slowly. And now, there comes a time
that some of those domains go "cluck", "cluck". But when the domains flip over, there is a
magnetic flux change inside the material and so the magnetic flux change means d phi
dt and it's on an extremely short time scale. And so now you get an EMF,
you get a current going through the wire and you hear a cracking noise
over the loudspeaker. And for every group of domains that flip,
you can hear that. And that's an amazing thing
when you think about it, that some ten to the twenty atoms
go "cluck" and that you can hear that. And so this is what we're going to do here
and I will do it then in, in several steps, so that you first can hear the noise
if I don't have ferromagnetic material and then-- so here is the,
here's the coil. A very small coil. And here is a magnet. And I'll come very fast towards the coil. [cloink] What you heard now is Faraday's Law. You simply have a magnetic flux change
in the coil [cloink] oh, I shouldn't touch it. [cloink] Now I come in very slowly
and go away very slowly. You hear nothing, d phi dt is just too low. Now I put in the ferromagnetic material. Put it inside the coil. And now I approach it again, very slowly. [cracking noise] There they go. You hear them?
Those are, those are domains that go. I'll come in with the other side. [cracking noise] There it goes, the domains. [cracking noise] Isn't that amazing? You hear atoms switch,
groups of atoms. [cracking noise] I'll turn it over again. Now they flip back. They don't like it,
but that's their problem. [cracking noise] This is called Barkhausen effect. I find it truly amazing that you hear
groups of atoms, ten to the twenty atoms at the time,
they flip over and when they do, there is a magnetic flux change
inside the ferromagnetic material, is sensed by the coil
and you hear a current. And if I do it fast, uh, these, these,
these domains go haywire. They go nuts now. [loud cracking noise] Imagine that you were a domain
and I would treat you that way. [loud cracking noise] You go, "Cluck, cluck, cluck, cluck, cluck" [loud cracking noise] But the fact that you can hear it
is absolutely amazing, isn't it? [buzzing sound] So that's actually a nice way of demonstrating
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 or paramagnetic material or ferromagnetic material-- uh, the magnetic field inside is different
from what the field would be without the material. And what the field would be without the material
we've called external field. I've called it vacuum field. And in many cases, but not all,
next lecture I will discuss the issues of not all, in many cases but not all cases, is the field inside the material
proportional to the vacuum field. And if that is the case, then you can write
down that the field inside is linearly proportional, so this is the field inside the material,
regardless of whether it's diamagnetic or paramagnetic or ferromagnetic,
is proportional to the vacuum field. I will write down vacuum for this. And this proportionality constant
I call kappa of M. I-- Our book calls it K of M. And it's called the relative permeability. And so now we can look at these values
for the relative permeability and we can immediately understand now
the difference between diamagnetic material, paramagnetic material
and ferromagnetic material. Since in the case of diamagnetic material
and paramagnetic material, the B field inside is only slightly different
from the vacuum field, it is common to express kappa of M in terms
of one plus something which we call the magnetic susceptibility,
which is xi of M. Because if it is very close to one,
then it is easier to simply list xi of M. And let's look at diamagnetic material. Notice that these values for xi of M
are all negative, of course, they have to be negative,
otherwise it wouldn't be diamagnetic. It means that the field inside 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 oppose it nevertheless. And so you express it in terms of the, um,
magnetic susceptibility and so you have to take one minus one point seven
times ten to the minus four to get kappa of M, which is very close to one. If now you go to paramagnetic materials,
the minus signs become plus. Again, the numbers are small. But the fact that it is plus means that inside
paramagnetic material, the magnetic field is a little, a hair larger
than the vacuum field. But now if you go to ferromagnetic material,
it is really absurd to ever list the value for xi of M, because xi of M is so large that you can forget
about the one and so xi of M is about the same as kappa of M. And so you deal there with numbers that are
a hundred, a thousand, ten thousand, and even larger than ten thousand. That means that if kappa of M
is ten thousand, you would have a field inside ferromagnetic
material that is ten thousand times larger than your vacuum field. Next lecture I will tell you that there is
a limit to as far as you can go, but for now we will,
we will leave it with this. So paramagnetic and ferromagnetic properties
depend on the temperature. Diamagnetic properties do not depend
on the temperature. So at very low temperatures,
there is very little thermal agitation and so you can then easier
align these dipoles, and so the values for kappa of M
will then be different. For ferromagnetic material, if you cool it,
you expect the kappa of M going up, so you got a stronger field inside. So it's temperature-dependent. If you make the material very hot, then it can lose completely
its ferromagnetic properties. What happens at a certain temperature,
that these dosmain-- domains fall apart, so the domains themselves no longer exist. They annihilate. And that happens at a very precise temperature. It's very strange. That's also something that is
very difficult to understand and you need quantum mechanics
for that too. But at a certain temperature,
which we call the Curie temperature, which for iron is a thousand forty-three
degrees Kelvin, which is seven hundred seventy
degrees centigrade, all of a sudden the domains disappear
and the material becomes paramagnetic. In other words, if ferromagnetic material
would be hanging on a magnet and you would heat it up above the Curie point,
it would fall off. It would become paramagnetic, but paramagnetic
material in general doesn't hang on a magnet, because the forces involved are quite small. And the change is very abrupt and I am going
to show that to you with a demonstration. I have a ferromagnetic nut. It's right there. You will see it very shortly. And this nut, or washer, hanging on a steel cable
and there is here a magnet. I don't know whether this is north or south. It doesn't matter. And here we have a thermal shield. And so this washer is against the thermal shield,
because it's being attracted. It wants to go towards the strong magnetic field. It's ferromagnetic. So it will be sitting here. And now I'm going to heat this up
above the Curie point, seven hundred seventy degrees centigrade
and you will see it fall off. And when it cools again,
it goes back on again. So I can make you see ferromagnetic
properties disappear. And let me make sure
I have the proper settings. I see nothing. I see nothing. But there it is. So here is this nut and here is this shield
and the magnet is behind it, you can't see it, but it's right there. And so it goes against it, right,
it goes just towards the magnetic poles. It goes into the strong magnetic field. The magnetic field is non-uniform outside
a magnet and it goes towards it. And so now I'm going to heat it. [sound of blowtorch] It will take a while, because, um, seven hundred
seventy degrees centigrade-- is not so easy to achieve. The three most common ferromagnetic materials
are cobalt, nickel and iron. Nickel has a Curie point of only three hundred
fifty-eight degrees centigrade, so if this were nickel-- ooh. If this were nickel-- uh-uh. [laughter] Oh, you like that, huh. I think I need a strong hand. A strong hand is coming. OK. I think I fixed it. I'm a big boy, I did it myself today. I lost my pen, but that's a detail. OK, let's try again. So I'm going to heat it up and I was mentioning
that, um, nickel has a Curie point of three hundred fifty-eight
degrees centigrade. So that's quite low. This is seven hundred seventy. Cobalt is fourteen hundred degrees Kelvin,
Curie point. Gadolinium is a very special material. Gadolinium is ferromagnetic in the winter, when the temperature is below
sixteen degrees centigrade, but it is paramagnetic in the summer, when the temperature is above
sixteen degrees centigrade. It's beginning to be red-hot now. Seven hundred seventy degrees centigrade,
you expect some visible light in the form of red light--
there it goes. And I will keep it heating,
I will keep the torch on it, so that you can see that indeed
it's no longer attracted by the magnet. And the moment that I stop heating it,
it will very quickly cool. It will become ferromagnetic again
and it will go back. Just watch it. There it goes. So now it's again ferromagnetic. So the transition is extremely sharp. All right. Uh, OK. So paramagnetic materials,
as I mentioned several times, in general cannot hang on a magnet. The attractive force is there's not enough. To hang on a magnet, the force has to be
larger than its own weight. And diamagnetic materials is of course
completely out because diamagnetic materials are always pushed
towards the weak part of the field. It's only paramagnetic materials and ferromagnetic
materials that experience a force towards the strong part of the field
if the field itself is non-uniform. Now there is one very interesting exception. And I want to draw your attention to this,
um, transparency here. Look here at oxygen at one atmosphere. Oxygen at one atmosphere and three hundred
degrees Kelvin has a value for xi of M which is two times ten to the minus six. But now look at liquid oxygen
at ninety degrees Kelvin. That value is eighteen hundred times
larger than this value. Why is that so much higher? Well, liquid, in general, is about thousand times denser than gas at one atmosphere. So you have thousand times more dipoles
per cubic meter that, in principle, can align. And so clearly you expect an immediate
one-to-one correspondence between the density, how many dipoles you have per cubic meter
and the value for xi of M. And so you see indeed that this value
is substantially larger. The reason why it is more than a factor
of thousand 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 so the external field
can align the dipoles more easily. And so that's why you end up with a factor
of eighteen hundred. Even though this value for xi of M is extraordinarily
high for a paramagnetic material, notice that the field inside would only be point three
five percent higher than the vacuum field, because if xi of M is three point five times
ten to the minus three, that means that the field inside is only point three five percent higher than the vacuum field. But that is enough for liquid oxygen
to be attracted by a very strong magnet, provided that it also has a very non-uniform field
outside the magnet. And so the force with which liquid oxygen
is pulled towards a magnet can be made larger 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 are going to do here. Make sure I have the right setting. Ah, this is it. So we're going to have
some changes in the light. So there you see the two magnetic poles. It's a electromagnet. And so we can turn the magnetic field on at will. So here are the poles of the magnet. And the first thing I will do is very boring. I will throw some, uh, liquid nitrogen
between the poles. Now I don't have the value for liquid nitrogen
there, but nitrogen is diamagnetic, so it's not even an issue. Diamagnetic material is pushed away
from the strong field. So even though the value for xi of M
will be very different for liquid nitrogen than it is for gaseous nitrogen,
it doesn't matter. So certainly it will be pushed out. So that's the first thing I want to do,
just to bore you a little bit. Because I have to keep you
on the edge of your seat before you're going to see this oxygen,
which will be hanging in there. So let's first power this magnet,
I hope I did that, yes, I think I did. And here comes the liquid nitrogen. Boring like hell, just falls through. Now comes the oxygen. Liquid oxygen. It's hanging in there. I challenge you, you've never in your life
seen liquid hanging on a magnet. You can tell your parents about it--
and of course your grandchildren. It's hanging there. I'll put some more in-- make sure
I have the right stuff, yeah. Put some more in. There is liquid oxygen. When I break the current, it's no longer a magnet,
it will fall of course. Don't worry, you'll get more. Who has ever in his life seen a liquid
hang on a magnet? It's paramagnetic, it's not ferromagnetic, but because the density is so high
and because it's so cold, the value for xi of M is high enough that
the force on it is larger than its own weight. If you do this with aluminum,
not a chance in the world. Aluminum will not hang in there,
even though aluminum, as you can see there, is paramagnetic. But the value two times ten to the minus five
is way too small and it will not stick to a magnet. OK. You have something to think about. I will see you Friday.
