Today, I'm going to take a critical look at Ampere's Law.
I'm going to run a current through a wire,
as we did before, but now I'm going to also put a
capacitor in that line and so we are charging a capacitor.
Here is that capacitor. And here is the wire.
We are running a current I. And as we are running this
current, clearly, we get a changing electric
field inside the capacitor. The electric field inside the
capacitor, sigma free divided by kappa epsilon zero,
which is also Q free divided by the area.
This is a circular plate capacitor.
Capital R, is the radius of this capacitor,
so we get pi R squared kappa epsilon zero.
But since I run a current the Q free is building up all the
time, and so the current per definition is dQ dT,
and so I now have ex- a changing electric field inside,
de dt, which is the current I divided by pi R squared,
kappa epsilon zero, because I simply take the
derivative of this equation, I get dQ dT,
and dQ dT is I. And only if the current is zero
is there no changing electric field inside.
So how does this affect the magnetic field?
Well, if I take here a point P1 at a
distance little R from the wire, if you fall away from this
capacitor it's hard to believe that Ampere's Law would not give
the right answer. And we will apply that very
shortly, Ampere's Law. It's on the blackboard there.
Suppose you are at the same distance from this line here at
point P2. Well, yeah, you've got to admit
there's an interruption of current now.
There is no current going through this space and so you
expect that the magnetic field here would be a little lower
perhaps than it is here. But not very much.
So the question is, how can we now calculate the
magnetic field here and there, now that we have this opening
in the wire. Well, Biot-Savart could handle
it but I wouldn't know how to do it
because if there's a current flowing like this there's also a
current going up on these plates, and one like so,
and I wouldn't know how to apply Biot-Savart.
In principle, yeah, but in practice,
no. How about Ampere's Law?
Well, let's give Ampere's Law a shot.
This is a cylindrical symmetric problem, so I choose a closed
loop, which of course itself is a circle with radius R,
and I apply -- I attach to this closed loop an open surface.
That's mandatory. And I give myself an easy time,
I make it a flat surface. So now I apply Ampere's Law.
You see it there on the blackboard.
Anywhere on that closed loop, the magnetic fields will have
the same strength, for reasons of symmetry,
and so we get B times two pi R equals mu zero times I pen,
and pen means the current that penetrates my open surface.
Well, that's I. I goes right through that
surface. And so the magnetic fields at
that point, P1 mu zero times I divided by two pi R.
We've seen this several times before.
Now I wonder about P2. Can I apply Ampere's Law for
point P2? Well, yeah, you can try.
So now I attach a closed loop to this point.
Circle again, radius little R,
and I use this flat surface and I apply Ampere's Law.
Well, I'm in for a shock, because B times two pi R is not
changing but there is no current that penetrates that surface.
And so I is zero, and so I have to conclude that
the magnetic field at point P2 is zero which is absurd.
Couldn't be. I can make the situation even
worse. I'm going to revisit point P1,
and here is my capacitor, and here is my point P1.
My current is flowing like so. Here's my closed loop.
According to Ampere's Law, int- closed loop integral B dot
DL. Why should I choose a flat
surface? I'm entitled to any surface!
I like surfaces like this. They are attached to a closed
loop, so I will choose that kind of a surface.
The surface now goes like so. [whistle] Right through the
capacitor plates, and I apply Ampere's Law,
so it's open here. B times two pi R,
the radius is little R. Mu zero times I,
but there is no I going through that surface.
Nowhere through this surface is a current poking,
because there is no current going between the capacitor
plates, so now I have to conclude that the magnetic field
at P1, which we first concluded was this, is now also zero.
So something stinks. So Ampere's Law is inadequate.
And so of course, Faraday and Ampere were both
perfectly aware of this. But yet it was Maxwell who
zeroed in on this and he argued that any open surface that you
attach to a closed loop should give you exactly the same
result, same answer. And so he suggested that we
amend Ampere's Law, and so he asked himself the
question, what is so special about in-between the capacitor
plates? Well, what is special there is
in-between the capacitor plates there is a changing electric
field. And Maxwell reasoned,
gee, Faraday's Law tells me that a changing magnetic flux
gives rise to an electric field, so he says maybe a changing
electric flux gives rise to a magnetic field.
And I want to remind you what an electric flux is.
Phi of e is the integral. In this case it would an open
surface of E dot DA. That is an electric flux.
With Gauss's Law that you see on the blackboard there,
we had a closed surface. I'm talking now about an open
surface. That is an open surface.
This is an open surface, and this is an open surface.
And so Maxwell suggested that we have to add a term which
contains the derivative of the electric
flux. And that's what I'm going to do
there now, walking over to Ampere's Law.
I'm going to amend it in a way that Maxwell suggested.
He adds a term here, epsilon zero kappa,
ddT, of the integral over an open surface,
attached to that closed loop of E dot DA.
This current, which is the one that
penetrates, remember, through the surface is really a
real current. This term here,
Maxwell called "displacement current.
I want to make sure that I have no slip of the pen,
because I hate slips of the pen.
That is correct. I have everything in place.
You may think now that we can start a party because all four
Maxwell's equations are now in place.
Not quite. We're going to make one small
adjustment after spring break, and that adjustment is going to
be made in this one, and then we'll have our party.
So now, I would like to use the new law and see whether we can
clean up that mess. So I'm going to revisit my
point P1 and I'm going to apply the new law by first having a
flat surface, that surface that we have here,
and then trying this surface. And I want to get the same
answer. If I use that surface,
do we agree that there is a current going through that
surface but there is no electric flux going
through that surface? So that second term,
that displacement current term, is zero for that flat surface.
So this answer is completely valid.
But now, I want to pursue this case.
And so I'll make a new drawing. We have here this point,
P1. This is my radius little R.
This is my surface going right through here.
Here's the current I, and here is my changing
electric field. And so I get B times two pi R,
mu zero. I pen is zero.
There is no current penetrating through this bag.
This is open here. So the first part is zero.
So I only deal with the second part, which is epsilon zero K,
kappa, displacement current. And now I have to put in there
d phi e dt. Phi E is very easy to calculate
because E and da right here- think of this part being flat.
Wherever you were inside the capacitor, if we assume that
there are no [inaudible] fields,
then there is an electric field only where you're inside the
capacitor, and so the electric flux is simply E times the
surface area, E and da are in the same
direction, so it is the electric field times this pi capital R
squared. And therefore,
if I want to know what the derivative is,
then I get this pi R squared which is that surface area and
now I need there de dt. And the de dt we have,
that is I divided by pi R square kappa epsilon zero.
I divided by pi R squared kappa epsilon zero.
So this is the area A, and this is de dt,
and this is the area of the part inside the capacitor that
has a flux going through it, cause outside here there is no
flux going through there, so there's no contribution.
There's no contribution here, either.
The electric field is only existent there.
That's my assumption. And so the whole thing here is
now d phi E dt. Well, let's look at our
results. I lose a pi,
I lose my R squared, I lose my kappa and epsilon
zero, and look what I get. I get mu zero times I.
That is truly amazing, so I find now that B equals mu
zero times I divided by two pi little R, which is exactly what
we had before. Hooray for Mr.
Maxwell, because now it doesn't matter anymore whether you take
the flat surface or whether you take the back surface.
You now get the same answer. In one case,
there is no contribution from the displacement current term,
and in the other case there is no contribution from the first
term, the real current. Let me make sure whether I'm
happy with my results. Yup, I think that's fine.
We can now also go one step further, and we can calculate
anywhere in between the capacitor what the magnetic
field is. I'll make another drawing of
the capacitor. It's right here.
I have this E field. I will not repeat that every
time. And here I have my point P2
now, which is inside the capacitor at a radius little R
from the center. And this is capital R,
circular plates. I have here my closed loop.
It's a circle, radius little R.
I apply now the new law, B times two pi R.
And there we go. We have a mu zero,
we have an epsilon zero, we have a kappa.
There's no current going through here,
so it's non-negotiable. I pen is zero,
right? That's not even an issue.
So we get mu zero, epsilon zero.
I get kappa. But now, the surface area right
here is not pi capital R squared, where there is a
changing electric field, but it is only pi little R
squared. I take a flat surface now.
And so now we multiply this by pi
little R squared, and then of course de dt is the
same, so we get our current I divided by pi capital R squared,
divided by kappa epsilon zero. And now you're again losing a
lot. You lose your epsilon zero,
you lose your kappa. I lose a pi.
And look, I have a little R here and
I have a l- little R square there.
So now we're going to get a result which is something that
you may actually have anticipated, namely that you get
a- a field inside the capacitor that is growing with R,
because if I make up my balance I get upstairs mu zero times I
but I get one little R upstairs. You see, you have R squared
here and you have R here. And downstairs I get two pi and
then I get a capital R squared, and I believe that's correct.
Let me check my notes. And yes, I'm happy with that.
And this is proportional with little R, whereas here falling
off one over R. And so I can now make a plot of
the magnetic field as a function of
little R when I'm inside the capacitor plates.
Little R, these are the magnetic fields,
and this is the radius of the capacitor plate.
It's going to be a straight line up to that point,
and then it will fall off as one over little R and you can do
your own work on that and it's very trivial to calculate to
demonstrate that when you go beyond the edge of the
capacitor that then it falls off as one over R,
just in the same way that point P1 is doing.
So now we have a tool to calculate the magnetic field
even inside capacitors while we were charging,
which we didn't have before. The strength here,
the maximum magnetic field here, you'll find by
substituting in there for little R capital R.
And when you do this, if this becomes capital R,
this becomes one over capital R.
If you had substituted in here for little R capital R,
you would've found the same result.
This part is not kosher. It can not be correct,
and I can not make it right for you.
And the reason why that part can not be kosher is because we
have made the assumption, which is wrong,
that there is no fringe field. And so we have assumed in our
calculations that the electric field
is only here and there, but it's zero here so that
there is nothing, no de dt here,
no changing magnetic, uh, electric flux.
And that's not true. So clearly, when you get close
to the edge, this is not correct.
And there's no way I can correct for that,
because the fringe fields will be different from capacitor to
capacitor and those calculations of course are not even very easy
to make. But Maxwell had introduced his
displacement current term. He was a very smart man.
He predicted that as a consequence of that term that
radio waves should exist. There was a time that we didn't
know that radio waves existed. He predicted their existence,
but not only did he predict their existence,
he even was able to calculate what their speed was going to
be. We call that the speed of
light. And we will do that in a few
weeks ourselves in eight oh two.
In 1879, which was the year that Maxwell died,
the German physicist Helmholtz asked once of his students,
Hertz- he was twenty-two years at the time, he was a junior- to
try to demonstrate that radio waves indeed exist.
Hertz declined, because he argued that the
equipment that was available at the time was not good enough.
But seven years later when new equipment had been developed,
he accepted the challenge and it took him two years,
but then he indeed was able to demonstrate that radio waves do
exist. Imagine what a victory that
was! Someone like Maxwell,
who predicts out of nothing that radio waves should exist,
and here comes someone who actually shows that they do
exist. Hertz died five years after his
great experiments. He was thirty-seven years old.
He was very young. Had he lived ten more years,
there is no doubt in my mind that he would've been awarded
with the Nobel Prize for physics, but the first Nobel
prize was only given in 1901, so he died just a little bit
too early. Maxwell also died very young,
age forty-eight. Why did Maxwell call that
strange term displacement current?
In the presence of a dielectric, if you put a
dielectric in there, the changing electric fields
will indeed cause a current in-between the plates,
because the polarization will change all the time.
You get a re-eras- re-arrangement of these induced
charges, so there is indeed a current, but in vacuum there
shouldn't be any current. Any electric field changing or
not changing will not cause a
current in vacuum. But Maxwell believed that
vacuum in a way behaves like any other dielectric,
just a special dielectric, happened to be a dielectric
with kappa equals one. And so he really believed that
there was an actual current going between the plates,
even though we now know of course that that is not the
case. So the name displacement
current was perhaps not a very lucky one, but the term is a
must, and it completes the theory of
electricity and magnetism. The name is obviously of no
consequence. After all, Shakespeare said it
himself, in Romeo and Juliet, what's in a name?
Remember, what's in a name? That which we call a rose by
any other name would smell as sweet.
Those were the words by Shakespeare.
I will abandon for now the displacement current,
but we will revisit it later when we
will deal with radio waves and with the propagation of
electromagnetic radiation, and I will return now to good
old Faraday, and I will return to electric generators that run
our economy. We've discussed that at length,
and I want to revisit that to you- with you.
Remember that if you rotate conducting loops in
magnetic fields. that you create induced EMFs,
currents, and that keeps our economy going.
Here is again one of those loops.
Conducting wire, and I don't care about the
direction of the magnetic field. If you want it this way,
that's fine. What matters is that we're
going to rotate it about this axis,
and as we rotate it about this axis we're going to get an
induced EMF. And that induced EMF,
which we derived I think it was last lecture,
as a function of time, will be a sinusoidal or a
cosinusoidal curve, and therefore,
will look something like this. I call this loop number one,
and so this is the EMF produced by loop number one.
But now I'm going to add two more loops which are not
electrically connected physically separate.
If you look from this direction you will see the following.
This would be your loop number one, because you're looking in
this direction and you would only see the conducting wire
like so. I have now a second one which
is rotated hundred and twenty degrees, and so in this picture
you will see it like so.
Look number two, and this is hundred and twenty
degrees. Physically hundred and twenty
degree rotated. And then I have a third one
which is again hundred and twenty degrees rotated.
It is like so. And so this angle here is also
hundred and twenty degrees and so this angle is hundred and
twenty degrees. And this is my look number
three. And so each one of those will
give an EMF that has this shape but they
are offset now in phase by a hundred twenty degrees.
And so they're all rotating in exactly the same way,
like so, and so the second one will give me an EMF if I try to
estimate that roughly, something like this,
so this is loop number two. It comes a little later in time
and number three will again be offset,
will look like this. Number three.
And what we- we call this a three phase current.
And a three phase current can produce a rotating magnetic
field. We will make one for you but
I'll first explain to you how that works.
So if the period of number one is sixty Hertz,
then the period of number two is
also sixty Hertz, and number three is also sixty
Hertz, but they're just offset in terms of the phase angle.
Suppose you're looking down onto a horizontal table,
so this is a horizontal table. And I have here a solenoid.
This is one and the same solenoid.
When the current runs clockwise here it will also run s- run
clockwise there. But it's open here.
Going to put something in there.
We call this number one. Then I have another one which
is rotated, physically rotated a hundred twenty degrees.
It's here. Also coils.
And I'm going to feed current number two through those coals
later, through those coils. This is number two.
And I have a third one and I'm going to run current number
three through those.
So here are coils, here are coils,
this is number three. And so one sees current number
one, two sees current number two, and three sees current
number three. At the moment that the current
through number one reaches a maximum, the current in two and
three are down by a factor of two.
You can check that [break in tape].
During my lecture I went a little bit too fast over the
part that is coming up now, so I'm going to redo it a
little slower to make it more clear.
When the current through loop one reaches a maximum,
let's say then that the magnetic field due to loop one
is in this direction. The current through this one
and the current through this loop are two times smaller.
You may want to check that. But it just so happens that the
vectorial sum of the magnetic field produced by loop number
two and by loop number three also happen to be in this
direction, so the net magnetic field is in this direction.
Let's now look one third of a period later in time.
Now, the current in loop number two reaches a maximum,
so its magnetic field is now in this direction,
and you guessed it of course, that it just so happens that
the vectorial sum of the magnetic field produced by the
other two loops is now also in this direction.
And if we now look again one third of a period later,
when the current through loop number three reaches a maximum,
then the magnetic fields will be in this direction and the
vectorial sum of the magnetic field of the other two loops
will also be in this direction. And look now what has happened.
In one complete period, the magnetic fields started out
like this. One third of a period later it
was like this, and one third of a period later
it was like this. So what we have created is now
a rotating magnetic field, and it rotates in one period
all the way around, three hundred sixty degrees.
OK, let's now go back to my original lecture.
[break in tape] rotates once around in the period of your
alternating current. If that is a sixty Hertz
current, then it will rotate around with sixty Hertz,
sixty times per second. And so if we put a,
a magnet in here, then this magnet will want to
go around [inaudible] wants to follow this rotating magnetic
field. And we call that a synchronous
motor. So the rotor of such a
synchronous motor itself would be a magnet
and it would rotate around with the frequency of your
alternating current. But you need a three-phase
current for that so that the magnetic field rotates.
I can also place in here -- this is again a horizontal
surface, you have it here, you're going to do it right
here. Here is that -- here are those
crazy loops with the three-phase current.
We can also put in here um conducting sphere,
or in my case I will use a conducting egg.
And when the magnetic field rotates around,
there's a continuous magnetic flux change with the surface of
that conducting sphere or egg, and so it's going to run cur-
eddy currents. Now, if you have an eddy
current going around, and you have a magnetic field,
then the magnetic field in the area current will cause a torque
on the current. In a similar way,
when we discussed earlier the idea of a motor that you were
going to build, there was a magnetic field and
there was a current and that caused a torque and the same way
you get a torque on the eddy current and so it starts to
torque up this conducting sphere.
And all the time there will be eddy current because the
magnetic fields keep going around, and so you're going to
get a torque which will always be in the same direction and
this conducting object will now start to rotate and we call
that an induction motor. Induction motors have no
brushes. How fast the induction motor
will go depends on the conducting object.
If it is a sphere, it will probably come very
close to sixty Hertz because a sphere has many possibilities
for eddy currents to run around, whereas if you take a ring,
and we will try that, if you try to spin a ring in a
rotating magnetic field then of course then of course the
various paths that are available for
eddy currents are very limited and only go around in the ring.
Many of the stationary tools that you find in people's
workshops and in the basements are induction motors.
A table saw and drill presses, also electric grass mowers are
induction motors. I want to demonstrate now to
you what three-phase currents can do,
and the first thing I'm going to do is show you that unit that
we have here which is the- which are the coils that I described,
through which we are going to run the three-phase current.
Must get my lights right. There you see it.
Coils are wound in a very strange way.
After class, you can come a little closer,
and so in here you would have a rotating magnetic field.
We use sixty Hertz, which rotates around sixty
times per second. And the first thing I'm going
to do is something wild, a little bit in style,
I suppose. I will put on top there a
cardboard cover with little magnets.
They're randomly oriented. There's no way that they can
ever rotate. They th- thee- are these little
magnets, flat, a lot of friction.
If I expose them to a rotating magnetic field,
then they will go nuts. I told you,
they were going nuts. You're not supposed to show
these to students, but OK.
Now here I have a conducting egg.
And this now has ample possibilities for eddy currents
to flow, and so now if I give these coils the
right current, a three-phase current,
it's spun up, the magnetic fields acts on the
eddy currents, and it starts to spin and I
have actually tried to measure the rotation rate.
It's only a little bit under thirty-six hundred RPM.
Thirty-six hundred RPM would be sixty Hertz.
It's very close to that. If I spin this object in the
direction in which the magnetic field is not rotating,
then it says sorry, no way.
It just rehearses, because the magnetic field is
going to slave it in the direction that it wants it to
go. So we're looking there at an
induction motor. I have here a ring.
Now a ring doesn't have as many possibilities for eddy currents
to run. Could only go around like this,
or like this, right?
But I can still make it spin probably if I do the right
thing. First of all,
I have to rotate it in the right direction,
which would be this one, I think.
There it goes. It doesn't go anywhere nearly
as fast as the egg because of the restrictive paths of the
eddy currents. But it rotates.
It's trying to follow that magnetic field to the best it
can, but its abilities are very limited.
And needless to say, if I try to spin it in the
wrong direction, that of course it will stop and
it has no way like the egg to
reverse its direction because of its peculiar geometry.
I owe you an explanation to the secret top.
If you haven't found one yourself yet.
Let me first come to a simple conclusion, and all of you must
have come to that conclusion. That top, when I showed it to
you during my exam review was spinning for more than an hour.
In fact, it was spinning the next day.
Energy has to come from somewhere, and so the only
conclusion that you could've drawn that the energy came from
inside the box, there must be something inside
the box. Clearly there must be a battery
in that box, and there is. But that doesn't tell you how
it works yet. And I can assure you,
I can a- a- admit that it took me quite a while before I fully
understand how it works. And I want to explain that to
you, and then I will demonstrate it to
you again. Remember what it looks like.
In the top itself is a magnet. So here is a top.
Let's say this is north and this is south and this is that
top. We're rotating it.
We're spinning it. Inside the box,
right at the center of the box, is a solenoid.
The switch and a nine-volt battery.
Inside this solenoid is also a little bit of iron.
We have not discussed that in our course.
It's not important for the explanation.
You'll later understand why there is also some iron in here.
It makes the magnetic fields so it's a little stronger.
This is right at the center of the- of the little platform on
which I was running this. It is a concave platform,
and here is a little plastic nod so
when the top hits it it bounces off.
Imagine for now that it's rotating in such a way that the
North Pole is approaching that solenoid, coming in from above.
What's going to happen now, in this solenoid,
in this coil, you are changing the magnetic
flux through the surface of this coil and so you're introducing
an induced EMF, an induced current.
And this current is sensed by a transistor which I have not put
in here, and the transistor throws the switch and now sucks
energy out of the battery and runs currents,
very high current through this coil, such that the top becomes
the south pole. Remember if you have a coil,
and you run current through here, that you get a magnetic
field like so. In this case,
this would be north pole and this would be south pole.
If you reverse the current, then this is south and this is
north. That magnetic field that comes
out there is fanning out in all directions three dimensionally.
It's going like this and it's fanning out like this.
So when it approaches this coil, there is a change in
magnetic flux. And this becomes a south pole.
The north pole is being attracted by the south pole.
I make you look at this from above now.
Here is the top seen from above, so it's spinning in this
direction. And let's say here is this
coil. This is the north pole and this
is the south pole. And I just discussed with you
that the current that's going to flow from the battery will make
this a south pole. The current can only flow in
that coil in one direction. That's just the way it's
designed. So whenever the current goes
it's always this becomes a south pole.
The north pole is being attracted by the south pole.
You'll notice it's going to be torqued up.
So far, so good. A little later in time,
looking from above, the north pole will be here and
the south pole will be there, it has rotated a little bit
further, and the coil is here. So now the north pole is
leaving. It's receding.
It's not approaching, it's receding.
If this were to remain a south pole, that would be disastrous
because south poles and north poles would attract each other.
You don't want that. Well, the transistor senses
that the EMF in the coil reverses direction.
It has to reverse direction, because if the north pole comes
in, the EMF is in one direction but when the north pole leaves
the EMF of course goes in the other direction.
You've got a reversal. And so what the transistor
does, it opens the switch, and so there is no north pole
here and there is no south pole here, and so the thing starts to
go around further. What happens now when the south
pole approaches that solenoid? OK, here is the situation that
the south pole is now approaching.
It's rotating in this direction.
And here is the coil. South pole is coming in.
From Faraday's point of view, there is no difference between
the north pole receding or the south pole approaching.
You should be able to reason that for yourself.
That's exactly the same thing, and so the transistor knows
that indeed the current is still in the wrong direction.
It keeps the switch open. It does nothing,
so as the south pole approaches no current through this coil.
We must remember, the current can only go in one
direction, can only make this a south pole.
It could have been designed in such a way that the current
could go in both directions.
It would have made it more expensive.
Just a matter of economy. So nothing will happen here.
But now, there comes a time that the south pole is leaving,
is receding, and so let us have here our
coil. A south pole receding is
exactly the same for Mr. Faraday as a north pole
approaching. And so now the EMF is in the
same direction in the coil as it was
here. And so now the transistor says
yippee, that's fine. I close the switch and I'm
going to run a current and so this becomes the south pole.
South pole and south pole repel each other, so now the thing
gets a kick again. So when the north pole
approaches, it pulls on the north pole, and when the south
pole recedes, it pushes on the south pole.
And so it is an induction motor which is only powered half per
full rotation, but a very,
very clever design. And I'm going to demonstrate it
to you again. I want you to see that as this
top approaches the center that actually, you can see it
starting spinning up. It really gets its energy when
it gets close to this coil. It also works,
doesn't matter in which direction you spin it.
That's also great. You can spin it clockwise or
counter-clockwise. Makes no difference.
And so, you're going to see that top
here, I think. There it is.
And this is probably the best way for you to see it.
We have here this box in which there is this very simple
circuit, very simple, and here is the top.
Has little bar magnet in it. I will try to spin it just a
little bit, to make you see that it actually spins up.
It may not be so easy for you to see, but I can s- ah,
you see it's really spinning up now.
And then it loses to friction, rotation rates.
It always comes back to the center because the surface is
concave, and then it gets to the center there and gets its kicks
again, gets spun up. And this can go on for as long
as your battery lasts, which is about a few days.
I can also rotate it counterclockwise.
It's not so easy, it's funny.
Have you ever tried to rotate a top counter-clockwise?
It's very hard! I don't know why that is,
because maybe because I'm right-handed.
I'll try. You see, I failed.
Ah, this is a nice one. I gave it a teeny-wee little
spin. It doesn't like it.
It stays near the center. Oh, doesn't like that.
It has to be a little bit away from the center.
Ah, I think, I think I've got it now.
Oh, no. Oh, no.
Too optimistic. Isn't it strange that it's hard
for a person to rotate something counterclockwise?
OK, I did it. Slowly coming in,
to friction now. And when it gets close to the
center, there it gets its kicks. Now it's spinning up.
Ah, you can really see it now. It's being spun up.
You see that? Really spun up.
I have another fantastic toy for you, which is also an
induction motor. And that one you're going to
see there, first want to explain to you how that one works.
That's a real beauty. It is an induction motor that
runs on a two-phase current. Here we have solenoids.
It's this, this baby here, big one.
And we're going to run sixty Hertz AC current through there,
and here we have one, also going to run sixty Hertz
AC through there. Here's the coil.
This one is easy to show. The other one,
very heavy. These two currents are ninety
degrees out of phase. Not hundred twenty,
but ninety. So it's a two-phase
current. So when the current is maximum
through this one, it is zero through this one.
When it is maximum through this one, it's zero through this one.
Let's look at the moment that the current is maximum through
this one. And let's say the magnetic
field is in this direction, which is created by this coil.
Then there is no current here. But one quarter of a period
later, this one has no current but this one does.
Let's assume that now the magnetic field from this is in
this direction. And so what you're going to see
now is that again, you have a rotating magnetic
field which goes like so. And if I put in here a can,
a paint can, we use a coffee can,
it's right here, and at the surface of that can,
so I will draw the can here, but it's really there.
At the surface of that can, you're going to have eddy
currents, because you have change of magnetic flux all the
time and these eddy currents with the magnetic field will
cause a torque on this can. And the torque will always be
in the same direction and the thing is going to rotate.
So it's another example of an induction motor.
It's a very cute one. And I want to show it to you
and for that you're going to see it there.
Needless to say that the can is a
very special can, Maxwell House coffee.
Of course. And you see that?
Maxwell House. All right, so let's see whether
we can get this to run. There it goes.
Nice example of an induction motor, and now I'm going to test
you. I'm going to ask you what
happens if I take this coil here,
which I can do, and flip over from here to
here. Who thinks that nothing will
happen? And you're all afraid of me
now, right? Who thinks that it will come to
a grinding halt? Grinding halt.
Who thinks that the direction of the motor will reverse?
Good for you. It's clear that when I flip
this one over, you can easily go through that
for yourself, that this magnetic field is
then not rotating this way,
but is rotating that way, and so clearly the motor will
reverse direction. I'm going to do that now.
Watch it. So it's torquing now in the
opposite direction. It's coming to a grinding halt.
You were right. The other people were also
right, because now it's reversing direction.
And you see there it goes. Another striking example of an
induction motor. Next lecture,
Friday, I'm going to elevate a woman.