You have ten days left for your motor, so that's a nice project
for Spring Break. I'll give you some hints.
Keep the friction of your rotor as low as you can.
You can't use any oil, of course; that's not allowed.
Balance your rotor to the best you can.
And try to avoid that the rotor begins to bounce,
begins to vibrate, because when it vibrates it
loses contact with the current when it needs it so there's no
torque. How will we test your motors?
We do it with a stroboscope, and I've decided to demonstrate
to you how we're going to do that.
That's probably the best thing to do.
We have a disk, and we're going to rotate the
disk at thousand RPM. Let's assume that is your
motor. And we're going to strobe it
with a strobe light until it stands still.
In this case, I have set the strobe so that
it will stand still, roughly, and the strobe is now
going at five hundred RPM, and the motor is going at
thousand RPM. So this clearly is not the
rotation rate of your motor. In fact, your motor goes twice
around between the blinks. And we'd have no way of knowing
that, so we double the frequency.
I'm trying to double it now, double the frequency of the
blinking of the strobe light. And now it stands still again.
So now we may think that your motor is going thousand RPM,
but we don't know yet. Maybe it's going three thousand
R- two thousand RPM. Maybe three thousand RPM.
So what are we going to do now, we're going to double the
frequency. And so we go now with the
strobe light to two thousand RPM.
And what we see now is we see a double image.
So two thousand RPM is out, and any multiple of two
thousand RPM is out. So four thousand RPM is out,
six thousand, and eight thousand is out.
But what is not yet out is three thousand and five thousand
and seven thousand. So we would have to test for
that. On the other hand,
I told you already that this motor is going thousand RPM,
so there's no sense us testing that now.
But during the actual contest, of course, we will continue all
the way until we are convinced that we have the right RPM for
your motor. And so that's the way we will
do it. We will put a little bit of
white paint on one side of your rotor, so that's the way it will
be done. Of course, if your motor is
highly unstable in terms of rotation rates,
it will not be easy to get a right correct number.
I want to talk with you about the heart.
The heart, our heart has four chambers.
Looks sort of like this. The left atrium and right
atrium. Maybe this is why it's -- this
is why it's called the heart. And here is the left and the
ri- and the right ventricle. And here is the aorta.
The sole purpose of the heart is to pump blood.
About five quarts per minute, which is seventy-five gallons
per hour, which is seventy barrels per day,
which is about two million barrels in seventy-five years.
And it pumps about seventy times per minute.
If the blood to your brain stops for about five seconds,
you lose consciousness. So it's five skips of the
heartbeat, and you're down on the floor.
And four minutes later, permanent brain damage.
The way the heart works is absolutely mind-boggling.
Extremely complicated. Nature had one billion years to
design it, but nevertheless it's impressive.
Each heart cell is a mini chemical battery,
and it pumps ions in or out as it pleases.
In the normal state, each heart cell is minus eighty
millivolts on the inside relative to the outside.
There are some cells which are called pacemaker cells.
They are located in a very small
area, about one square millimeter, near the atrium,
the right atrium, and they change their potential
from minus eighty millivolts to plus twenty millivolts.
Now why they do that is a different story,
which I will not address. Once they go to plus twenty
millivolts, the neighboring cells follow,
and a wave propagates over the heart.
I'll make you a drawing shortly.
So the wave first moves over the atrial chambers and then
over the ventricle chambers.
And when the cells are at plus twenty millivolts inside
relative to the outside, they contract.
So they form a muscle. The whole heart is one big
muscle. And after about two tenths of a
second, the cells return to minus eighty millivolts,
and this wave goes from below to above.
And then the whole thing waits again for another message from
the pacemaker cells. Takes about one second,
and then the whole process starts all over.
Now I want to be more precise. Here is one heart cell.
So this is about ten microns in size.
And this cell has eighty millivolts with respect to the
outside. So that means it has repelled
positive ions, and so the inside is negative.
And there is no E field here outside, because if you put a
Gaussian surface around here, there is no net charge inside.
But there is, of course, a electric field
across the walls here, from plus to minus.
Now the depolarization, which is the change to the plus
twenty millivolt state starts, and it starts from above.
And I will assume now that it is not plus twenty but zero
millivolts, and it's easier to see.
If we have this cell, and the wave is,
say, halfway down, and this is now zero
millivolts, then there is no longer minus charge here and no
longer plus charge here, because zero millivolts
relative to the outside world. So there is no electric field
across here anymore. [unintelligible].
In other words, what the cell has done,
it has moved positive ions back in.
But here the situation is still as it was before,
so this is still at your minus eighty millivolts.
And if you look now, you have here a minus layer on
top of a positive layer. Positive here,
minus on top. And that creates an electric
field, which has roughly the shape of a electric dipole.
It has this shape. So as the wave goes through the
cells, only then do they create a dipole.
And we call this the depolarization.
A little later in time, when this wave has passed,
the whole thing is plus twenty millivolts.
I chose zero here, but it really goes to plus
twenty. This is just easier to explain.
So that means that now the inside is plus,
so positive ions are now inside, negative ions are
outside, and the E field here is again zero.
Now there is the repolarization wave,
which comes from below, when it goes back to minus
eighty millivolts. And I will again do the same
trick that I did before; I will just assume the wave is
halfway, that it is not minus eighty but that it is zero
millivolts. So there are no charges here,
but the charges here are unchanged.
So what do you have now here? You have a minus layer on top
of a plus layer. So you have exactly what
you had before. So again you get an electric
field, [unintelligible] electric dipole field,
which has again the same shape. So what's going to happen is
the depolarization wave is going to run down, leaves behind here
the cells at plus twenty millivolts, when they are
contracted, so this part of the heart has already pumped,
and it moves down. And only the cells where the
depolarization occurs, that's only the ones on the
ring, contribute to that electric dipole field.
If there is no wave, which is sizeable fraction of
the heart, of the cycle, there is no wave,
then there is no electric dipole field.
And when the repolarization goes in the other direction,
when the heart relaxes because the cells go back to minus
eighty millivolts, then again there is an electric
dipole field, but only from the cells through
which the repolarization wave moves.
And you can very easily see that the electric dipole fields
of all these cells here support each other.
So you get a dipole field from the heart.
And so if I make you look at your heart -- so this is you,
this is your body, your legs, and this is your
arms, and here is your heart, and there goes this
wave. And so here is your electric
field that is generated while the wave is going,
either depolarization down or repolarization up.
But if there is an electric field, there's going to be a
potential difference between different parts of your body.
You look here at your belly button, and you follow this
electric field line at your head,
there is an E field. The integral E dot D L gives
you a potential difference. And so now you see that
there're going to be potential differences between the various
parts of your body. And that's the idea behind an
electrocardiogram. Typically there are twelve
electrodes attached to arms, legs, head, and chest to get as
much information about the heart as we can.
And the maximum potential difference between two
electrodes, in general, is not more than about
two to three millivolts. I'd like to show you a healthy
heart cardiogram, of a healthy person.
I have that here. The time here is about one
second, and from here to here is about one millivolt.
The P wave -- we call this the P wave -- that
is observed when the atrium is being depolarized,
so when the depolarization wave goes over the atrium.
A little later it goes over the ventricle, and you get a larger
potential difference because there is more muscle in the
ventricle. So that's why this R wave is
higher. The T wave is the
repolarization, when the wave goes back over
the ventricles. The dipole field is in the same
direction, remember. That's the T wave.
It's not known, at least it wasn't known
recent- until recently, what causes the U wave.
I talked to a heart expert about this, Professor Cohen at
MIT, and I was surprised to learn that it's not known what
the U wave is about. Not everyone's cardiogram looks
as healthy as this one. There is a terrible disease,
which four hundred thousand people die of per year in the
United States, which is known as ventricular
fibrillation, also known as sudden death.
The ventricles fire without any message from the pace wave,
pacemaker wave, and there is random,
non-synchronous depolarization. So the heart doesn't pump
anymore, in five seconds you lose consciousness,
on the floor, and in four minutes you,
um, have permanent brain damage.
In hospitals, heart patients are being
monitored, and as soon as it's noticed
that there is something wrong like this, so severe as the
fibrillation, ventricular fibrillation,
then they apply electric shock treatment.
So you have to be fast, you only have a few minutes
before you get brain damage. And three thousand volts is
applied, one amperes, for about a tenth of a second.
Large plates are being used on each side of the chest.
And this, of course, is enough to kill the patient.
But it makes little difference, because the patient would have
died anyhow.
Heart patients can also get synchronization problems and
then they implant a pacemaker that's a circuit.
And this pacemaker takes over the role from the pacemaker
cells. When the heartbeat rate falls
below a certain rate, the artificial pacemaker takes
over. About ten milliamperes for half
a millisecond, and it does it sixty times per
minute. And so it triggers,
then, the depolarization wave. These pacemakers are
susceptible to influences from the outside world,
and one person's pacemaker stopped, for instance,
every ten seconds due to a radar sweep from a police car.
It's also possible that you get a built-in defibrillator,
in other words, a system that gives you
electric shocks when sudden death might otherwise occur.
So it senses that something is wrong, that the ventricle is
going into fibrillation, and then it applies,
all by itself, six hundred fifty volts,
about five and a half milliseconds,
up to five to ten amperes. And that's not enough to kill
the patient, and the whole idea is sort of a wake-up call to the
heart to get it back into synchronization,
to get this depolarization wave being synchronized again.
So clearly I would like to show now a heart cardiogram of a
student, and I prefer to have a healthy
one to avoid some difficulties. You feel strong?
You a healthy person? You don't mind volunteering?
Tight pants, we have to do something about.
OK, why don't you sit down. [laughter].
Well, there's nothing I -- come in.
We'll, we'll, we will, we'll,
we'll find a way. All right, so we have to attach
-- we don't have twelve electrodes, we only use three.
And the first one -- that's why I was worried about your
tight pants. Can you roll them up a little?
OK. Oh, this one goes here.
Let's hope that it makes good contact.
Now the others go on your arm, and we need very good
electrical contact, and therefore we put some
conducting grease on there. It will make it a little -- it
will make it a bit of a mess, but we'll give you a chance
later to clean up. So let's first put this one --
you're relaxed, right?
Yes, of course. So can you roll up your sleeve
there? Very good.
And mayb- oh, oh, and maybe you can put this
over your arm, yeah, over your -- yeah,
that's good. High up.
Oh man, boy, you have muscles.
[laughter]. All right, just relax.
If it hurts a little, oh well, that's the way it is.
[laughter]. We need, we ne- we need good
contact. OK, now your other arm.
Again, a little bit of gooky stuff.
Oh, you need another rubber band, so put it around your arm
high up. That's good,
yeah. All right.
So now it's very important that you relax, because when you
start moving, the other muscle cells will
also produce electric dipole fields.
And that we don't want, because then that will be
overpowering. All right.
I'm going to take -- make you take a look at this.
Yeah? Everything OK?
So I'm going to change the light situation so that you can
see shortly there what's coming up.
Oh, man. What a da- oh gee,
look at this. Oh, gee.
Oh, look! I see your -- I don't see your
P wave. [laughter].
But you have an amazing T wave, right -- no,
no, you have an amazing R wave! It looks like your R wave is in
the wrong direction. [laughter].
You feel OK though, right?
Yeah, I can't see your P wave. Well, maybe some people survive
without P waves. [laughter].
It's a certainly an unusual, an unusual heart,
but if you tell me that you are healthy,
then I'll take your word for that.
I think it would be nice if you show class now,
why don't you just stand up for a while, let your other muscles
begin to act, and y- they will see then --
just stand up. You will see -- move a little
bit your arms. Move your arms.
You see? Now you get the electric dipole
field from the other muscles in the body [laughter] which
contract. This is even more interesting
than your heart, man.
[laughter]. All right.
Sit down again and let's take it off.
And then you can clean up. Looks good.
Yeah. Heart cardiograms are not so
easy to interpret. But I think you're looking
fine. And you feel all right,
right? That's important.
So thank you very much for volunteering,
very courageous. [applause].
Yeah, make sure you clean that stuff off, huh.
It's water-soluble, so it's not so bad.
What is your name, by the way?
Danny. You were great,
Danny. [laughter]. And now I want to talk about Now I want to talk about
Aurora Borealis. If we have a magnetic field and
we have a charged particle, let's say make it plus,
and the velocity of that charged particle is in this
direction, then the force on that charged
particle, the Lorenz force, equals Q times V cross V.
I'm going to decompose this velocity now into one component
parallel to the magnetic field and into a component
perpendicular to the magnetic field, so the vectorial sum of
these two is V. And so I can rewrite this as Q
times V parallel plus V perpendicular
crossed with V. But V parallel crossed with V
is zero, because the angle is either zero degrees or hundred
eighty degrees, so the sine of the angle is
zero. And so the force is exclusively
determined by this term. It's by the perpendicular
component. And so what is going to happen,
this charged particle is going to circle around.
But then it continues to go in this direction with that
velocity V parallel. And so you are going to see a
path like this. Well, by this radius R of that
circle, that radius i- I still remember it from the lecture
when we discussed that, that was M V divided by Q B,
but the V now is of course the perpendicular component divided
by Q B, and then in this direction it continues unaltered
with the velocity which is the parallel
component. Magnetic field of the earth,
it's not a straight line but is curved, and so charged particles
can spiral around the magnetic field and follow the magnetic
field lines, and they come down on Earth where the magnetic
field lines enter, which is near the magnetic
poles. The sun emits a plasma.
Plasma is highly ionized electrons and protons.
We call that the solar wind. Sometimes it's strong,
sometimes it's weak. And when it reaches the Earth,
it ionizes the upper atmosphere of the Earth,
and then it produces light. The light is very faint,
can only be seen at night. And that light is called
Aurora, and we here call it Northern Lights,
but I'm sure that people in the southern hemisphere,
they call it Southern Lights. When the sun is very active,
it can be breathtaking, really absolutely fabulous.
The Aurora can change very fast, on time scales of seconds
to minutes. And it is, of course,
strongest near the magnetic poles, and so you r- rarely ever
see it in Boston. It can have very bright colors,
red, green, white is the most common.
And the color that you will see depends on the energy of the
charged particles as they come in.
But it also depends on whether the nitrogen molecules in the
atmosphere or the oxygen molecules are being excited.
Also depends on at what height, what height in the atmosphere
the ionization occurs. I've seen it quite a few times
in my life. I did hiking in the Adirondack
where I saw it. I've seen it from Calgary in
Canada. But whenever I fly to Europe,
and flights are always at night, I always ask for a window
seat on the left side of the plane,
and that's the reason. So that I can look to the
north, and a few times have I seen spectacular Aurora from the
plane. I want to show you some slides.
If you visit the eight oh two website I made some links for
you to some fabulous slides of Aurora.
But now I want to show you a few that I have here.
Can I have the first slide? This is, um,
white Aurora, and like a nice curtain.
Not so uncommon. Can change on time scales of
minutes to seconds. As I said, you can only see it
at night. It's very faint.
The next slide? You see another remarkable
example of Aurora, white Aurora.
Strange shapes, very unpredictable.
And the moving, it's like looking at a movie
when you actually see Aurora. The next one is red Aurora,
like a wonderful curtain coming down.
For reasons that are not so easy to understand,
maximum light comes from a ring which is, which has a radius of
about five hundred kilometers from the magnetic pole.
And the next slide shows you a picture taken from a satellite
which is three Earth radii away from the Earth.
This is taken in ultraviolet light.
And you see beautiful this, this ring.
So this radius is roughly five hundred kilometers,
and here is one of the magnetic poles.
I don't know whether it's the North Pole or the South Magnetic
Pole. And the next slide shows you
something similar. If you look only at these four,
they are taken twelve minutes apart, again in UV,
and you see here a crossbar. I don't know how to explain
that crossbar. It's called Theta Aurora.
Obviously why theta goes without saying,
right. Amazing.
And this is sort of -- these are twelve minutes apart,
so that gives you also an idea how fast this can change.
Over here it's very dark and here it's very bright.
So the changes are quite dramatic. And now I want to talk about Now I want to talk about
superconductivity. Superconductivity was
discovered by a Dutch physicist. His name was Kamerlingh Onnes.
And he discovered that if you cool mercury to something like
four degrees Kelvin -- he used liquid helium for that,
in fact he actually discovered how to make liquid helium.
That was the incredible thing. And then he used the liquid
helium to cool down substances, among them mercury,
and he discovered that mercury would lose completely all its
resistivity. So the electrical resistance
would go down to zero. And he got the Nobel Prize for
that in nineteen thirteen. You can only understand
superconductivity with quantum mechanics, and even quantum
mechanics has a major problem nowadays to understand all the
phenomenon about superconductivity.
The problem started in nineteen eighty-six,
when two scientists in Zurich, Muller and Bednorz,
discovered that certain alloys can be made superconducting at a
temperature as high as thirty-five degrees Kelvin.
And theorists earlier had proven that it was impossible to
ever get superconductivity at thirty-five degrees Kelvin.
And so this was such a splash in the community that these guys
got the Nobel Prize within one year.
In nineteen eighty-seven they got the Nobel Prize.
I don't think there's any other example that I recall whereby a
discovery was made and within one year the Nobel Prize was
awarded. And theorists still cannot
explain today fully why there is what's called high-temperature
superconductivity. The record today,
I checked that yesterday with Professor Lee at MIT,
the record is now hundred thirty-five degrees Kelvin.
So certain alloys can be made superconducting at hundred
thirty-five degrees Kelvin. And since you probably know
that liquid nitrogen has a temperature of
seventy-seven degrees Kelvin, anyone can now play nowadays
with superconducting subjects, materials, even high schools,
because liquid nitrogen is very easy to come by.
If you make power lines out of superconducting material,
there would be no loss of energy.
People are thinking about that. You can imagine how costly it
might be, but in principle you could transport electric energy
without any loss, without any omega losses.
No I squared R, because R is zero.
Also, if you have zero resistance in
a material, you can run extremely high current through
it, and you can therefore get very strong magnetic fields.
Using superconducting coils, you can get very strong
magnetic fields, and these colliders that we
talked about earlier, these atom-smashers like we
have at Fermilab and in Geneva, they are going to make use of
superconducting coils to get magnetic fields as high as six
tesla or so, or even higher.
No electric field can exist in a superconductor.
And you can very easily see that, because if there were an
electric field -- if this is a superconductor and there is an
electric field, say, in this direction,
there would be a potential difference over the
superconductor. And Ohm's Law,
V equals I R, tells you then immediately that
if this is not zero but if this is zero that I would go to
infinity. So you cannot have any electric
field in a superconductor. If I approach a superconducting
disk or material with a magnet -- say this is the north pole
and this is the south pole, so we have an electric field
configur- a magnetic field configuration roughly like so.
If I approach this superconducting material,
then the EMF generated in here because of Faraday's Law,
because there's a change in the magnetic flux coming off,
that EMF must remain zero, because you cannot have an
electric field inside a superconductor.
And this, of course, is I R.
So R is also zero. So I now can have any value,
completely legitimate. So you can have a huge current
inside the superconductor, but no EMF.
And so as you approach with this
magnet, eddy currents are going to run inside the superconductor
in such a way that D phi D T, the flux change in here,
is always zero. And so these eddy currents will
flow to never allow any magnetic flux, because there was no
magnetic flux to start with when the magnet was high up,
so there can never be any change.
And so the eddy c- currents create a
magnetic field themselves which, if you vectorially add
them to this magnetic field, will always make sure that
there is no net magnetic field inside the superconductor.
And so if you now make a drawing of the,
of the two fields, the one that is produced by the
eddy currents and the one that is produced by the magnet,
when the magnet comes very close -- so here is north and
here is south, and here is your superconductor
-- then the superposition of those
two fields then, effectively comes down to the
effect that this magnetic field is completely repelled -- that's
another way of looking at it. You get a squeezed field here.
But that is the superposition of two magnetic fields,
one produced by the eddy currents and one from the,
the magnet. And whenever you have here such
a squeezed magnetic field, there is magnetic pressure.
We know why there is magnetic pressure, because north and
north poles repel each other, but we never expressed that in
terms of a quantity. And the magnetic pressure
equals B squared, which is the magnetic field
strength, divided by -- is it two?
Yeah, two mu zero, divided by two mu zero.
I'll get back to this a little later in the lecture.
And this is pressure, so this is in newtons per
square meter.
This is not entirely new, this idea of pressure,
because you may have seen at people's desks nice conversation
piece. You have here a,
a magnet, and you have here a magnet, and this is a,
a wooden stick. There's a hole in here and
there's a hole in here. This is north pole,
south pole, north pole, south pole, and they repel each
other. That's magnetic pressure.
It's the same thing. And if you drew the magnetic
field configurations here, go like this,
that's the magnetic field from this magnet and this would be
the magnetic field from that magnet.
We get the same idea. You get magnetic pressure
there. If I rotate this magnet here,
so th- first of all, the magnet is repelled,
which is in a way a form of levitation, and we're
going to show you that. The magnet is just pushed up by
the superconductor is the way you can look at it.
But if you start rotating it, for instance,
around with the south pole here or the south pole there or the
north pole there, the eddy currents will
instantaneously adjust to always repel that magnet.
So even if you rotate it, it would still hang there,
levitated, rotating. What is not so easy to
understand is why the whole thing
is so very stable. As you will shortly see,
it's quite stable. So I'm going to show you there
this superconducting idea. I first have to top it off with
some liquid nitrogen, so let me do that when we still
have full lights. Oh boy.
Good. So I have to top it off.
And this disk, which is about an inch in
diameter, going to be superconducting.
I can even tell you what kind of material it is.
It is a copper oxide mixed with yttrium and barium,
and it becomes superconducting at ninety degrees Kelvin.
And liquid nitrogen is seventy-seven degrees.
So we're going to put a small magnet on top,
which we will levitate. For that, we're going to have
the following light situation. And of course you want to see
it also, don't you. And you want some lights.
So there you see the disk, which is -- should be
superconducting now. And here comes my little
magnet. So there is no magnetic flux
going through there. It itself is not a magnet.
But now I'm going to come close with a magnet,
and the eddy currents go nuts in there, and it just floats on
top. It's amazing,
isn't it. So this is magnetic levitation,
and you can rotate it around, and the eddy currents adjust
instantaneously. And there it is.
Now you've all seen it, clear enough.
OK, let me get the -- rescue my magnet.
Imagine in the days of Kamerlingh Onnes it took four
degrees Kelvin to have anything superconductive,
and now you can do it as easy as that.
There are other forms of magnetic levitation.
One going to be very promising in our economy,
we hope, and that is magnetic levitation can be used for
trains. If you have a magnet and you
move it fast over a conducting surface,
then you also get levitation. You have to move it though,
whereas there you don't have to move it.
See, if you let that magnet just go, if you don't move it
anymore, then there is an eddy current going on,
but the eddy current never dissipates any heat.
There is no I squared R because R is zero.
So you never lose the eddy current.
That's different with what is coming now.
Now I have a, a magnet.
Here is north and here is south.
So we have a magnetic field sort of like this.
And I'm going to move it over a plate, over a conducting plate,
and I'll put the plate here. And as it comes over this
conducting plate, the magnetic flux through that
plate will change. Mr.
Faralow s- Mr. Faraday says -- actually,
it's Mr. Lenz who says,
"I don't like that." And so they're
going to run an eddy current in here, and the eddy current will
undoubtedly go in this direction as it comes over here.
And this current ring now will produce a magnetic field in this
direction. And look what you have.
You have again this is the north pole of this eddy current
and this is the south pole. North pole repels north pole.
And so if this has a high enough speed so that the change
of the magnetic flux,
the D phi D T is high enough, the train can float.
Tens of tons of weight can be made to float.
And the reason why in this case the train has to keep going,
that if the train stops the eddy current will die out.
There's no longer the D phi D T but there is resistance in this
conductor, and so you get only dissipation.
You get I squared R. You get heat in here.
And so then the train will just plunge down.
And that's not the case with the
superconductor because you don't dissipate any heat in the
superconductor because the superconductor has no
resistance. So the idea is the same,
but you see now why you have to keep this one going and why
there you don't. And so again you get a squeezed
magnetic field, like you have there,
and so you get magnetic pressure.
Japan and Germany are really the leaders in the world in the
technology of, uh, maglevs -- that's what
these trains are called.
United States is trying to catch up.
There's an enormous reduction in friction if you can have a
train that is not in contact with the rails.
In fact, speeds have been recorded up to three hundred
forty miles per hour. Both Germany and Japan have
test trains, prototypes, in operation.
United States has made a commitment to build a maglev
train to go from Washington, DC, back and forth to
Baltimore, should be ready in the year two
thousand seven. The cost per mile at about
thirty million dollars per mile. Now that make strike as high,
but keep in mind that if you build a four-way highway,
that's also thirty million dollars per mile.
So it's no more expensive than a four-way highway.
And again, when you visit the eight oh two website,
I made several links to maglev sites.
I advise you to take a look. Now there is a third form of
magnetic levitation whereby we don't need any speed and we
don't need any superconductors but we use AC,
we use alternating current. And that's also easy to see
now. Here is such a coil,
and we run AC through it. So at one particular moment in
time, let's say the magnetic field is like so,
and maybe is increasing. And then of course the magnetic
field turns around, up, down, up,
down, because it's AC. Now I have here a conducting
plate, and I put this above this plate.
But now I have this continuous magnetic field change,
so I have a continuous change of magnetic flux in that plate.
So as this magnetic flux, as the B field down is
increasing, you're going to get an eddy current running in this
direction, which will create the magnetic field in that
direction. And you're back where you were.
You again have north pole, north pole, south pole,
south pole. So again, the eddy current in
the conducting plate is responsible for a magnetic
field, and the two repel each other.
So a little later in time, the magnetic field strength
will decrease. When that happens,
the eddy current will reverse direction, and the two will
attract each other. And so you will think now it
seems quite reasonable that half the time they will attract each
other and the other half of the time they
will repel each other. That, however,
is not the case. There will be a net repelling
force. And why that is,
I will explain to you during the next lecture.
But I want to demonstrate it now.
I have here such a coil, about an area of about one
square foot. I can simply run hundred ten
volts, sixty hertz AC. I switch th- turn this on.
This goes into hundred ten volt outlet, and I increase the
current. It starts to float.
No high-speed train, nothing superconducting.
What do you think will happen when I turn it over?
Excuse me? Of course it will float again.
The ed- the eddy currents adjust themselves at any moment
in time, and they will always make it float.
So this is another interesting form of magnetic levitation.
So we have the superconducting way, whereby there is no
dissipation in the disk, so those currents
never die out. Then you have the case of the
train, if I call that the train, the magnetic levitation,
whereby you have to keep the speed going, because if you
don't have the speed then you don't have enough magnetic flux
changes in the surface, and so you don't have the eddy
currents. The eddy currents would die,
you get heat dissipation. And then there is the third
case here, whereby you simply have a
changing magnetic field in the coil with AC,
which then creates the changing eddy currents.
So now we come to the levitation of a woman.
How do we levitate a woman? Well, the secret must be in
that equation. V is B squared divided by two
mu zero. We have a coil which is about
one square foot, so the area of that coil is
about oh point one square meters.
And so our goal was that we should be able to lift,
let's say, a two hundred pounder, to give ourselves a
little bit of leeway. And so we calculated that if
the magnetic field, B, is about fifteen hundred
gauss, which is about oh point one five tesla,
that we would get very close. We know that mu zero is four pi
times ten to the minus seven in SI units.
And so you can calculate now what the force is on this area.
The force is of course the pressure times the area,
assuming that the magnetic field is uniform.
And so you're going to get that this force is going to be B
squared, which is oh point one five squared,
divide by two, divide by four pi,
times ten to the seventh, multiplied by the area,
which is oh point one square meter, and you find that this is
about nine hundred newtons. Ninety kilograms,
as I said, a two hundred pounder.
Then we tried to get this magnetic field,
and believe me, Marcos and I and Bill,
we really tried, but there was a problem,
because we needed enormously high currents to get these
magnetic fields. And at these very high
currents, our circuit breakers would go every time.
So we called up the physical plant, and they said,
"Yeah, what do you expect, man?
You need several hundred amperes.
You think we can get seven hundred -- several hundred
amperes out of this system? You have to redesign MIT for
that." So it was very disappointing for us.
So the best we could do was the strongest current that we could
generate, we could only get a magnetic field of about three
hundred and fifty gauss, which is four times lower.
And the tragedy has it that the magnetic pressure goes with B
squared, so that makes it sixteen times lower.
So the two hundred pounder now becomes a twelve pounder.
But that's the reason why when some women wrote me very nice
email yesterday because they volunteered, why I had to say,
"Thanks, but no thanks." But I want to keep my
promise. I said I was going to levitate
a woman, and I will. And here she is.
[laughter]. And as far as we know,
it is a woman.
[laughter]. OK, give her some room.
She deserves -- we ready for that?
And there she goes. I levitated a woman.
[laughter]. Have a great Spring
Break. [applause].