We see last time that using Biot and Savart's formula that
if you have a current going straight into the blackboard
perpendicular to the blackboards that we get a magnetic field at
a distance R. The magnetic field tangentially
to the circle, B here,
B here, and then the strength of that magnetic field equals mu
zero times I divided by two pi R.
If you walk around this circle, just walk around,
and you carve up this circle in little elements DL,
and you calculate the closed circle integral,
so the closed circle of B dot DL, so everywhere locally you
dot B with DL, the B and DL are in exactly the
same direction everywhere, then you would find that this
obviously is B times two pi R. But B times two pi R equals
also mu zero times I. This DL here has nothing to do
with this DL here. Don't confuse the two.
This DL is a small amount of length in the wire that goes
into the blackboard which carries a current.
This DL is simply your DL when you walk around this current
wire. It doesn't matter at what
distance you walk around. You always get mu zero times I.
You see it right in front of your eyes because B is inversely
proportional to R. And it was Ampere who first
recognized that you don't have to walk around in a circle to
get the answer mu zero I, but that you could walk around
in any crooked path as long as it is a closed path,
something like this. And now you have here the local
B, which of course is
perpendicular to this radius and here you have your local DL and
if now you go around, closed circled any path,
it doesn't have to be a circle, dot DL that now becomes mu
zero times I, which is known as Ampere's Law,
and I then is often given an index and closed.
It is the current which is enclosed by that path.
It is actually easy to prove this using Biot and Savart's
formalism. This is almost a third
Maxwell's equation. We already had two out of four.
This is almost number three, not quite.
We're going to amend it in the future.
What is ill-defined a little bit in this equation is what we
mean by enclosed, and I'm going to define that
now so uniquely that there is never any
misunderstanding. If I have a very strange
looking closed path that I have chosen, that's the path I walk,
I have to attach to that closed loop a surface,
an open surface. That's mandatory.
You can make it flat. That's fine.
You're free to choose it. You can also make it sort of a
plastic bag so it's open here. You can put your hands in here,
and here, like a hat. Any surface is fine,
but you must attach to that loop a surface,
so here I have some paths that you could be walking,
and this would be perfectly fine open- open surface.
Could be flat, but it could also be open,
so it's like a hat. And now I can define uniquely
what it means by- what it means by this I enclosed,
because if now I have a current that goes through this surface
and pokes out here, then I have a current
penetrating the surface and that is uniquely defined,
and if I have another one coming in through the surface,
for I two, this is penetrating that surface.
By convention, if you go clockwise around,
we follow the same notation that we had before,
in the right-hand corkscrew notation,
the connection between magnetic field and current.
If you go around clockwise seen from this side,
so you go clockwise, then I one as I have it here,
the new equation would have to be larger than zero.
I two is then smaller than zero.
But if you decided to go counterclockwise,
which is perfectly fine, Ampere's law doesn't at all
dictate in which direction you have to march around,
then I one would be negative and then I two would be
positive. So we follow the right-hand
corkscrew notation. And so if you want to amend now
Ampere's Law to do me a favor, but you don't do books a favor
because all the books use the word enclosed.
I would like to see this replaced by penetration.
It is the penetration of the surface of the current that is
uniquely defined. But a current enclosed by a
loop is ill-defined. Because where possible,
when we apply Ampere's Law, we will try to find easy passes
around circles sometimes, sometimes rectangles,
and since you are free to choose the surface that you
attach to the loop if you can get away with it you use a flat
surface, but you can not always get away with a flat surface.
So the recipe is as follows. You choose your closed loop.
Any loop is allowed. It may not help you very much
if you choose the wrong loop. Any loop is allowed.
You then attach an open surface to that loop.
And I penetrate is now the current that penetrates through
that surface, according to this convention.
And the direction of rotation is free to you.
How you go around to pass is your choice, but that defines
then the sign of the penetrating of the curve,
of the- of the current, according to the right-hand
corkscrew. So now we can,
for the first time, calculate the magnetic field
inside a wire that draws a current using Ampere's Law.
I have here a wire that has a radius capital R and a current
is coming to me, I, and let's assume that the
current is uniformly throughout the wire, so it has a uniform
current density. And I would like to know what
the magnetic field is everywhere.
The cylindrical symmetry, I want to know outside the wire
and I want to know inside the wire.
Let's first look at radius which is larger than R,
and so here we have the cross-section of that wire,
radius R. The current I is going through
this surface. I now have to choose a closed
path. Since we have cylindrical
symmetry it is clear that we would
choose the circle, with radius little R,
so we can be sure that the magnetic field strength is the
same everywhere because of reasons of symmetry.
Since the current is coming towards me and I am free to
choose in which direction I'm going to march,
I know that the magnetic field is in this direction,
so I might as well also march in this direction so that my DLs
are all in this direction. I don't have to do that.
I could march the other way around, but if I march
counterclockwise then both terms left and right of Ampere's Law
will be positive. I now have to attach an open
surface to my path. Well, this will be,
the blackboard will be, that open surface.
And so now I apply Ampere's Law, so I get B times two pi
little R, because DL and B are in the same direction so it's a
trivial integral. That now equals mu zero times
I, which now penetrates my
surface. Uniquely determined,
all these currents from this wire that comes to me penetrates
my surface, so times I, and so B equals mu zero times I
divided by two pi R, and that's the same result that
we found last time, when we applied Biot and
Savart. So that's no surprise that you
see this, because now we have a way of
finding the magnetic field also inside the wire,
so here we have the wire again, the cross-section,
current coming out of the blackboard, and now I want a
radius which is smaller than capital R and of course my
closed pass again for reasons for symmetry is going to be a
circle with radius R. And my surface that I attach is
a flat surface, and so here I go,
B times two pi little R equals mu
zero times- ah, now I have to be careful,
because now not the full current I is now penetrating my
surface, but it is only a fraction that penetrates the
surface, and the fraction that penetrates the surface is now
little R squared divided by capital R squared times I.
You see, because the total current comes through the radius
capital R, but I only have now a circle with radius little R.
And so I lose one R here and so we get a very different result.
You get now that the magnetic field equals mu zero times I is
now linear in little R divided by two pi capital R squared.
And this grows linearly with R, whereas this falls off as one
over R. And if you substitute in this
equation R equals capital R, which then would be the
magnetic field right at the surface of
the wire, you find exactly the same result here.
Little R becomes a capital R. If little R becomes a capital
R, you lose one capital R, you get the same result.
And so if you make a plot of the magnetic field as a function
of little R, then it looks like- like so, so this is little R,
this is capital R, and this is the magnetic field
strength because we know that it is tangentially
to the circles. It would be straight line and
then here it falls off as one over R, and the maximum value
here is the value that you find there if you substitute little R
equals capital R. I will now show you that we
can, using Ampere's Law, also come very close to
calculating the magnetic field inside what we call
solenoids. Solenoids is like a slinky
current that goes around in a spiral, one loop after another.
I want to remind you that if we had a loop, a nice current loop
coming out of the blackboard here, and the current going into
the blackboard so there's a circular wire but I only show
you the cross-section. I want to remind you that the
magnetic field as we discussed last
time, would be clockwise here, would be counterclockwise here.
In the middle, remember, it was like this.
And then in-between it was like so.
That was sort of the magnetic field configuration in the
vicinity of a loop through which we have a current going.
But now imagine that you put another loop here,
current again coming out of the blackboard going into the
blackboard, and another one, and so on, several.
What do you think is going to happen with these magnetic field
lines which now diverge? They're going to be sucked in
here. This loop also wants the field
lines to come through its circle, so to speak,
and this one too, and so you're beginning to get
a near-constant magnetic field and the more tightly these loops
are wound, the more accurately will your magnetic field be
approximately constant, and I have some
transparencies which will show that in more detail.
Here we have a figure from your book.
You see five windings, a spiral.
If you look from the left, the current is going in
clockwise direction, and so the magnetic field is
going from this side to that direction.
And when you look here you see that the magnetic field is
approximately constant inside,
and outside these current loops, outside the solenoids --
we call them solenoids -- magnetic field is extremely low.
And if you start winding these loops very tightly,
then you get a configuration looks like this.
You get an almost perfect constant magnetic field inside
the solenoids and the magnetic field outside the solenoids is
extremely weak. And now I would like to
calculate with you using Ampere's Law
what that magnetic field inside such a solenoid would be.
And we have to make a few assumptions.
Let this be my solenoid, and the length of the solenoid
is capital L. A current I is going through
like so. I, and I assume that if I look
from the left side that the windings are wound clockwise,
so I know that the magnetic field is then in this direction.
I make the assumption that the magnetic field outside the
solenoid is approximately zero. I will show you later with a
demonstration that that's a pretty good approximation.
And so the question now is, what is the magnetic field
there. And I assume I have N loops,
N windings, capital N. So now I have to choose a path.
I have to apply Ampere's Law. I choose a pass,
and you may be surprised the path I'm going to take.
This is the path I choose. It's a rectangle.
And the length of this side inside the solenoid is L.
And I think of this as four different passes.
Number one, number two, number three,
and number four. Let's first look at number two.
We have assumed that the magnetic field is practically
zero, so clearly if you go to integrals, you'd go around,
then the contribution here must be zero.
If the magnetic field is zero, then the integral B dot DL is
zero, so that's easy. But if you look at one and
three, there is no magnetic field, very small magnetic field
outside. The magnetic field inside is in
this direction. But DL is like this if I march
like this, and B is like this so there's ninety degree angles and
so the dot product is zero. And so the only paths that
contribute to my closed-loop integral of Ampere's Law is only
path four, and that tells me then that B times little L --
because B is constant, I have assumed that it is
constant, and I integrate it over a length little L.
Now I have to agree on my surface.
What surface am I going to choose to attach to that closed
loop? Well, why not using a flat
surface just like the blackboard?
Now, I have to calculate the current that penetrates that
surface. The current that penetrates
that surface, I have to know how many times
this winding pokes through that surface.
If the length of my rectangle is little L and is if the length
of the solenoid is capital L, and if there are N windings on
capital L, this is the number of times that the current pokes
through that surface, uniquely defined.
I have a surface now. There is no such thing as I
enclosed. There is I penetrating,
through that surface. It's a soap film,
and I poke straight through it, and I do it so many times that
I poke through it,
and then I have to multiply this by mu zero,
and then I have my I, but each time that it pokes
through I have current I. And so what you see now is that
B equals mu zero times I times N divided by L,
and so that is our prediction for approximating the constant
magnetic field inside a solenoid, and this actually is a
very good approximation as long as L,
the length of the solenoid, is substantially larger than
the radius of the solenoid. The radius would be the radius
of these loops. I'll work out a numerical
example which is aimed at a demonstration that comes
shortly. We have here a solenoid whereby
N is about twenty-eight hundred and
L is about sixty centimeters, that is oh point six meters,
and I'm going to run through there a current which I really
don't know yet but is going to be close to four and a half
amperes, we will see when we do the demonstration.
And so I can calculate now what the magnetic field is going to
be. So the magnetic field strength
is going to be four pi times ten to the minus seven,
because that's what mu zero is, and then I have to multiply it
by twenty-eight hundred.
I have to multiply it, divide it by point six,
and then I multiply it by the current, four point five,
and when I do that I find about point oh two six Tesla.
Point oh two six Tesla, that is about two hundred and
sixty Gauss. And when we do the experiment,
the current will be a little different but you will see that
indeed the field will be very close
to two hundred and sixty Gauss. Why is it that the magnetic
field is not proportional to the number of loops,
but proportional to the number of loops per unit length?
You may say well, if I have one loop I have a
certain magnetic field, two loops I have twice that
magnetic field, ten loops I have ten times that
magnetic field. Well, imagine that we start a
solenoid [inaudible] seven. And so here is [inaudible]
seven, and here is that solenoid.
There it goes, all the way,
thousands and thousands and
thousands and thousands of loops, and we end up here in
twenty-six one hundred. Look at this loop.
Think of it at the first loop. Creates a magnetic field.
What is the shape of that magnetic field?
Well, it is a current loop and as we discussed last time,
the magnetic field that one loop produces is like a dipole
field. So do you really think that
here in twenty-six one hundred we can sense the magnetic field
that is produced by this one dinky toy loop?
Practically nothing! It falls off so rapidly,
the magnetic field, that we don't notice it- notice
it here. So it's immediately obvious
that the magnetic field is not proportional to how many loops
you have. If, however,
you put all those loops on top of each other,
then of course you can add the magnetic fields.
And so it is natural that you get
how many windings you have pre unit length.
So now I want to first show you the magnetic field configuration
of a very loosely wound loop, seven windings,
and I will do that by sprinkling magnetites,
this iron file, in the vicinity.
We've done this before for other current configuration.
Now we'll do it for this solenoid with seven windings,
and I'm going to run a few hundred amperes through there,
have to first get this car battery .
All right. And so we put some iron files
on here and what I want you to see now is that the magnetic
field inside, even though it's very loosely
wound, begins to look nicely uniform and that there's almost
no electric- er, magnetic field outside.
Look at this, isn't that wonderful?
Isn't that incredible? You see how these iron files
line themselves up very nicely horizontally inside the loops
and when you look outside the loop here or there,
where we assume the magnetic field was about zero,
you don't see the iron file being where we ended in any
preferred direction, which indicates that the
magnetic field is very low. Now, I want to show you what
magnetic field we can get with this baby, which is exactly what
I had here on the blackboards.
It has twenty-eight hundred windings, and we're going to run
a current which is something like four point five amperes,
but I'm going to tell you what that current is,
because I have a current meter there for you and I also have a-
a meter which indicates the magnetic fields.
The lower one is the current meter, and the maximum current
that you see there at the three would
be six amperes. And the upper one is calibrated
in such a way that if it is full scale, you would have three
hundred Gauss, so it's three,
it's three hundred Gauss. And I can -- I have a probe,
a magnetic probe -- we never discussed how that works.
We call it a Hall probe, and this Hall probe allows me
to measure the magnetic field in the vicinity of this solenoid.
It's even sign sensitive. If the magnetic field is like
this, it would go to the right. If the magnetic field is like
this, it would go to the left. And so this allows us,
then, to be actually quite quantitative and evaluate the
magnetic field near the opening of the solenoids.
Then we can go in there and we can also probe the outside.
So I'm running now a current. Let's look at it,
that's the bottom meter. So that is about four point
eight amperes. I assumed it was four point
five. It's a little higher.
And here comes this probe, and I'm now about a foot away
from the entrance,
and you see nothing. And I come closer to the
entrance and the magnetic field begins to show.
Nowhere nearly constant yet. I'm now entering one hundred
Gauss. I'm going in deeper.
Two hundred Gauss. Even deeper.
And deeper, and now I have about two hundred and forty
Gauss and notice, as I go in farther,
it doesn't increase. It's more or less constant.
Amazing, that it's more or less constant.
And when I come out here, I move it back and forth about
twenty centimeters. If I came in from the other
side, you would simply see a reversal in the sign,
which is not so interesting, so you see two hundred forty
Gauss with the other direction because this probe is
sign-sensitive. I can now also show you that if
I come on the outside of the solenoid, you see nothing.
So indeed, our assumption that the magnetic field is very low
outside a tightly wound solenoid was a very good
assumption. Very well.
You've been asked, and the deadline is Friday four
p. ., to explain the behavior of
the Kelvin water dropper. And I decided to give you a
little bit of help on that. Most of you may already have
figured it out, but those who haven't probably
won't figure it out between now and Friday anyhow,
so I might as well tell you. That water dropper,
called the Kelvin water dropper, is an amazing battery.
We've seen it before. We know what it's doing,
but I will go over that again. We have here buckets A and B.
Water comes down from above, water runs through.
You see the water there, it runs out.
And we collect these water drops
here in bucket D, it's a conductor,
and this water is collected in bucket C, is also a conductor,
and the paint can A is connected to C.
That's crucial. And the paint can B is
connected with D. And here there are two bowls,
which I can bring close together.
I run water, and after a while I see a spark
here. I can even see a spark when the
distance is something like six millimeters,
which would be about potential difference of about twenty
kilovolts. How does it work?
Well, water has a pH of seven. And that means one in ten to
the seven molecules is ionized. So I have OH minus,
and I have H plus. And the- Those are going to be
the current carriers. The ions are doing the work
here, are doing the job. Let us make an enlargement
here of can A. And can A, let us assume that
purely by chance, it has a little bit of positive
charge on it. It could be negative,
but I'll just assume it's positive for now.
In either case it will work, you will see.
Just by chance, like you have a little bit of
net charge. You're not completely neutral.
And so this can has a little bit of positive extra charge.
Now here is the drop from the spout.
What's going to happen? Through induction,
through polarization, you get a little bit of excess-
excess negative charge here and a little bit of excess positive
there, because the positive repels each other and the
negative is being attracted. So the H plus goes a little bit
up and the OH minus comes a little bit down.
But now the drop breaks, and there goes the drop.
So it's a little bit negative. So now a little bit of negative
drops come down and so this becomes negative.
But this is connected with B, so B becomes negative.
But what do you think is going to happen now with the drops
that fall through B? They are going to become
positive, because if B is negative then of course this
will be reversed, the bottom will be positive,
the top will be negative, and so those drops now that are
going to fall through are going to be positive.
So C becomes positive. But C is connected with A,
so A becomes more positive, and so A can do even a better
job now on these water drops, and polarize them even more,
and so you get a runaway process.
And the whole system feeds on itself until the potential
difference here becomes so high that you exceed the three
million volts per meter, and there you get the breakdown
and you see a spark. Now, you can think of a
continuous stream of water as a stream of individual drops,
so it also works if you just have a
regular stream of water going down.
Who is doing the work here? Someone has to do the work.
You have a battery. The battery's being charged,
and then it is discharged to the spark.
Who is doing the work? Any idea?
Have you thought about that? Yeah?
Gravity. Very good.
It's gravity that is doing the work.
We can see that very easily by identifying the current that is
flowing and the electric field. How is the current flowing?
If negative charge is going down, would we all agree that
the current is going up? If positive charge is going
down, do we agree that the current is going down?
This side of the spout, here, will be slightly positive
and this is slightly negative, because the H plus is more
abundant here than there, and so we're going to get a
current through the water, in this direction.
Current has a reasonable conductivity,
because it's ionized one out of ten to the seven molecules,
and so once in a while if you see a spark here,
then you get a current there, but that's intermittent of
course. How about the electric fields?
Well, electric fields we know go from plus to minus,
so that's easy. We can put the electric fields
just in like that. Electric field must here be in
this direction. Electric fields here goes from
plus to minus. C is to plus charge,
B is minus charge, and so the electric field is in
this direction. Electric field is from plus to
minus. This is plus,
this is minus, so the electric field is in
this direction. Electric field is from plus to
minus. The can A was positive,
remember? So the electric field is from
plus to minus. So that's the electric field
configuration. But now look what's happening.
Here, the E field and the current are in the same
direction. That's fine.
Here the E field and the current are also in the same
direction. That's great,
but now look at these poor negative ions.
These negative ions don't want to go in the direction of E.
Negative charge wants to go against the direction of E.
But gravity says, "Sorry, you can't do it.
I force you down. And so these negative drops are
forced by gravity to go down. Look at this positive charge.
These poor water drops which are positively charged go
against the electric field. They don't want that.
Positive charges want to go with the
electric field. Gravity says,
"Sorry, it's too bad. I force you down.
And so gravity is doing the work, so to speak,
against the will of the charges.
And then the battery charges up and charges up until the
potential difference becomes so high there that you see a spark,
and you deal with potential differences of something like
twenty kilovolts. Remember last time,
and you will see that again today,
that as the water goes through and as the system charges up,
that you begin to see that the water which starts running like
so, begins to spread out. It fans out.
You can hear it by changing the sound, but you can also see it,
and I'll make you see it again today.
Why is that? Well, that's immediately
obvious. If this can is positively
charged but if the water is negatively charged,
the negative charge wants to go through the positive can,
and so it spreads out. So it's clear that by the time
that you reach almost a spark,
that that water will spread out quite substantially and you will
see that. And then when there is a
discharge, it will start running again narrow stream,
and then slowly in time the water will spread.
And so now I will do a series of demonstrations which will
support what we know and what we perhaps don't know.
Let's first give a little bit of light here,
because we will need that, and then I'm going to make it
completely dark, so that you get maximum
pleasure for your money. And I will first show you here
the- the gap those two bowls and this time we have a real treat,
which we owe to Marcos, who is standing behind the
instrument very modestly. This time we have a gauge,
a meter, which measures the electric fields very close to
can A, and the reason why that is nice
is that as this system charges up, we just don't have to wait
now just until we see the spark, but we can look at the
galvanometer there and slowly see it being charged up and then
we get a spark and then it discharges, so you get a lot
more for your money. So I propose that the first
thing we do is what we did last time, that we simply let it run
and see whether we get a spark. Uh, there's always air bubbles
in the system which I have to get out.
OK, I think I get that. OK, let's just be patient.
Ah, it starts already. Look at the- look at the
e-field. Bang!
First spark. Can you see the spark on the
screen? Look at it again.
There's a spark. And at the same time you see
how the electric field goes away,
charges up, bang. Charges up, bang.
So it cha- it starts the whole system charged because of a
random positive or negative charge that would be present on
one of the cans. What I want to do now is I want
to increase the gap between the two bowls, and I make it so
large that you will never achieve a magnetic-
an electric field there of three million volts per meter.
But somewhere else on the unit, it has lots of sharp edges and
sharp points, somewhere else the electric
field will reach the breakdown voltage and so the system will
go into dis- into discharge, into corona discharge.
You will never see sparks but it goes into discharge.
And you can see that because now, I will open the gap now.
If you now look at the electric field it will reach a maximum
value and now it goes into discharge, you see.
It begins to sort of sputter a little bit back and forth,
so now there is no longer the spark on the bowl,
so you don't see anything between the bowls,
but it is somewhere else. I don't know where,
where there is a continuous stream now of charging,
leaving the system, and so it's discharging to
corona discharge. And so in this mode,
you expect the water to be spread all the time.
And I will show that to you by switching now to the water.
Maybe Marcos, you can improve on the- on the,
on the lights. I could turn this off,
maybe then you'll see it better.
But you see that the water is spread and I will now bring the
two bowls closer together -- ah, you also want to see of course
the electric fields, to see the discharge.
I bring them closer together, stopping the corona discharge.
There's a spark. And now watch the water.
See, the water is now just not interesting, and there it
spreads. I'll turn the light off.
You look at the water. And slowly the system is
charging up. You see the water?
Bingo. You can even tell by the water
when it sparks. There it goes.
Now I want to do something real mean.
What I want to do now is to raise
the spout so high that A can not reach out all the way to the
spout. It's too far away,
and can not polarize the water. So the poor battery can not
start. That's a pretty mean thing to
do to a battery. But on the other hand,
I'm not all bad. What I can do is I can start
the system, I can help the system.
I use my extrophorus disk and I'm going to hold my extrophorus
disk very close to one spout, temporarily allowing it to
polarize the water and once it starts, chances are that it will
feed on itself and go into the runaway.
It's not very predictable, but I will make an attempt.
So the first thing that I will have to do is maybe you can zero
the E field. Yeah, thank you.
So the first thing I want to do is
to make sure that if we start running water now,
that the system doesn't start by itself, because then I can't
make -- then I can't be nice to the system anymore.
So let's just run some water. I hope that Marcos brought it
high enough, and let's see -- and you can really tell by
looking at the Oh, there's the air bubbles in the
system. I have to get rid of the air
bubbles. There we go.
OK. So look at the electric field
doing nothing. The system can't start.
A is desperately reaching out through this water,
but it's too far away. It can't polarize it and the
battery can't get going. Ah, ay, ay, it does get going.
Oh, Marcos, we didn't bring it far enough!
You have to bring it higher! Oh, by the way,
this is interesting. Let's see where it actually --
oh, boy, this is incredible. This is a distance of about
fifty centimeters, and look at it!
That is amazing! The little sucker,
I had never expected that. Let's give it a fair chance.
Let's give it a chance. It's only reasonable.
Goes very slowly now. You can see why it goes so
slowly, because A very far away from the spout.
But boy, and- and you can see the water.
The water is still pretty normal.
Oh, man, it's almost cheating on me!
Uh-oh, uh-oh, we'll have to raise it a little
further, er, aft- but I- I want to give it a chance to,
uh, to spark. Yeah, the two balls are close
enough, so I will probably get there.
Boy, this is almost torture for me.
Aw, look at that, look at that.
I begin to see the water already.
Look at the water, it's already spreading it --
ah, there it is. Marcos, can you run it even
higher and then we'll see whether we
can actually stop it altogether, bring it a lot higher and then
we will make an attempt to start it with some help from a friend.
You ready? Oh, man, I can hardly -- OK.
Don't tell me that it going to- it
can go to the other direction, of course, because it's a
random choice that it has at the start.
Ah, ah, it's letting me down! Let me see whether I can help
it a little. My electr- electrophorus disk.
I'm going to hold it here. You know why I held it there?
Because I was hoping it would reverse the direction.
It doesn't even want to do that.
It's really recalcitrant today, isn't it?
Hold it here, negative charge.
The reason why you see the sudden change in the electric
field is because of the e-field probe, which senses the
electrophorus disk when I held it near the spout above B.
It has decided, no matter what -- well,
has it really? Ah, ah, ah, ah.
Has it really made any decision?
Ah! It's thinking now what it's
going to do. Oh, man.
Yeah, it's going in the direction that I wanted it to go
because I held negative charge close to B and I know that would
force it into the direction that it's going now.
Oh, man. Yeah.
Well, look, the distance is -- now, what is it,
now, something like eighty, eighty-five centimeters?
The system is desperate, but it's, it's,
it's doing what it's supposed to do.
Physics works again. And we will get a spark because
-- is this close enough? Ah, boy you got a lot for your
money this time. You really did,
didn't you? You saw for one thing that the
system first started up going in one
direction and later in the other because there was a random
charge which changed polarity, which is something that we can
not always control, but by holding this negatively
charged disk close to the spout above B, I forced the
polarization in the way that I wanted it, and that's what
you're seeing now. We've got to give it a fair
chance, and then I'll give you light and then you have four
more minutes left to fill out the evaluation.
But let's at least give this battery a charge now,
to lay its egg. The water, it still doesn't
show much of a sign of spreading, but I expect that
that will happen very shortly because we've seen this now
before. It's slowly increasing the
charge on the cans, A and B.
It's creeping so slowly that if we wait you may never able to
fill out your -- I'll give you a little light so that you can s-
fill out the evaluation and then we can still [inaudible]
and see what happens. So please leave the evaluations
here as you leave, and I will keep that going for
some of you who have the patience to see what will
happen.