assemble charges, I have to do work,
we discussed that earlier. And we call that electrostatic
potential energy. Today, I will look at this
energy concept in a different way, and I will evaluate the
energy in terms of the electric field.
Suppose I have two parallel plates, and I charge this one
with positive charge, which is the surface charge
density times the area of the plate, and this one,
negative charge, which
is the surface charge density negative times the area of the
plate. And let's assume that the
separation between these two is H, and so we have an electric
field, which is approximately constant, and the electric field
here is sigma divided by epsilon zero.
And now, I'm going to take the upper plate, and I'm going to
move it up. And so as I do that,
I have to apply a force, because these two plates
attract each other, so I have to do work.
And as I move this up, and I will move it up over
distance X, I am creating here, electric field that wasn't
there before. And the electric field that I'm
creating has exactly the same strength as this,
because the charge on the plates is not changing when I am
moving, the surface charge density is not changing,
all I do is, I increase the distance.
And so I am creating electric field in here.
And for that, I have to do work,
that's another way of looking at it.
How much work do I have to do? What is the work that Walter
Lewin has to do in moving this plate over the distance X?
Well, that is the force that I have to apply over the distance
X. The force is constant,
and so I can simply multiply the force times the distance,
that will give me work. And so the question now is,
what is the force that I have to apply to move this plate up?
And your first guess would be that the force would be the
charge on the plate times the electric field strength,
a complete reasonable guess, because, you would argue,
"Well, if we have an electric field E, and we bring a charge Q
in there, then the electric force is Q times E,
I have to overcome that force, so my force is Q times E." Yes,
that holds most of the time. But not in this case.
It's a little bit more subtle. Let me take this plate here,
and enlarge that plate. So here is the plate.
So you see the thickness of the plate, now, this is one plate.
We all agree that the plus charge is at the surface,
well, but, of course, it has to be in the plate.
And so there is here this layer of charge Q, which is at the
bottom of the plate. And the thickness of that layer
may only be one atomic thickness.
But it's not zero. And on this side of the plate,
is there electric field, which is sigma divided by
epsilon zero. But inside the plate,
which is a conductor, the electric field is zero.
And therefore, the electric field is,
in this charge Q, is the average between the two.
And so the force on this charge, in this layer,
is not Q times E, but is one-half Q times E.
So I take the average between these E fields,
and this E field is then this value.
And so now I can calculate the work that I have to do,
the work that I have to do is now my force,
which is one-half Q times E, and I move that over a distance
X. And so what I can do now is
replace Q by sigma A, so I get one-half sigma A times
E times X, and I multiply upstairs and downstairs by
epsilon zero, so that multiply by one.
And the reason why I do that is,
because then I get another sigma divided by epsilon zero
here -- divided by epsilon zero, and that is E,
and therefore, I now have that the total work
that I, Walter Lewin have to do -- has to do is one-half epsilon
zero, E-squared times A times X. And look at this.
A X is the new volume that I have created,
it is the new volume in which I have created electric field.
And this, now, calls for a work done by
Walter Lewin. Per unit volume,
and that, now, equals one-half epsilon zero
times E squared. This is the work that I have
done per unit volume. And since this work created
electric field, we called it "field energy
density". And it is in joules per cubic
meter. And it can be shown that,
in general, the electric field energy density is one-half
epsilon zero E squared, not only for this particular
charge configuration, but for any charge
configuration. And so, now,
we have a new way of looking at the energy that it takes to
assemble charges. Earlier, we calculated the work
that we have to do to put the charges in place,
now, if it is more convenient,
we could calculate that the energy electrostatic potential
energy, is the integral of one-half epsilon zero E-squared,
over all space -- if necessary, you have to go all the way down
to infinity -- and here, I have now, D V,
this is volume. This has nothing to do with
potential, this V, in physics, we often run out of
symbols, V is sometimes potential, in this case,
it is volume. And the only reason why I chose
H there is I already have a D
here, so I didn't want two Ds. Normally, we take D as the
separation between plates. And so this,
now, is another way of looking at electrostatic potential
energy. We look at it now only from the
point of view of all the energy being in the electric field,
and we no longer think of it, perhaps, as the work that you
have done to assemble these charges.
I will demonstrate later today that as I separate the two
plates from these charged planes,
that indeed, I have to do work.
I will convince you that by creating electric fields that,
indeed, I will be doing work. So, from now on,
uh, we have the choice. If you want to calculate what
the electrostatic potential energy is, you either calculate
the work that you have to do to bring all these charges in
place, or, if it is easier, you can take the electric field
everywhere in space, if you know that,
and do an integration over all space.
We could do that, for instance,
for these two parallel plates now, and we can ask what is now
the total energy in these plates -- uh, in the field.
And at home, I would advise you,
to do that the way that it's done in your book,
whereby you actually assemble the charges minus Q at the
bottom and plus Q at the top, and you calculate how much work
you have to do. That's one approach.
I will now choose the other approach, and that is,
by simply saying that the total energy in the field of these
plane-parallel plates, is the integral of one-half
epsilon zero E-squared, over the entire volume of these
two plates. And since the electric field is
outside, zero, everywhere, it's a very easy
integral, because I know the volume.
The volume that I have, if the separation is H -- so we
still have them H apart -- this volume that I have is simply A
times H, and the electric field is constant, and so I get here
that this is one-half epsilon zero.
For E, if I want to, I can write sigma divided by
epsilon zero, I can square that,
and D V, in- doing the integral over all space,
means simply I get A times H, it is the volume of that box.
So I get A times H. And so this is now the total
energy that I have, I lose one epsilon here,
I have an epsilon zero squared and I have an epsilon.
I also remember that the charge Q on the plate is A times sigma,
and that the potential difference V,
this now is not volume, it's the potential difference
between the plates, is the electric field times H.
The electric field is constant, it can go from one plate to the
other, the integral E dot D L in going from one plate to the
other, gives me the potential difference.
And so I can substitute that now in here, I can take for A,
sigma, I can put in the Q, and you can also show that this
is one-half Q V.
V being, now, the potential difference
between the plates. And so this is a rather fast
way that you can calculate what the total energy is in the
field, or, say, the same thing,
the total work you have to do to assemble these charges.
Or, to say it differently, the total work you have to do
to create electric fields. You have crela- created
electric fields that were not there before.
I now will introduce something that
we haven't had before, that is the word "capacitance".
I will define the capacitance of an object to be the charge of
that object divided by the potential of that object.
And so the unit is coulombs per volt, this V is volt,
now, it's potential. Uh, but we never say that it is
coulombs per volt in physics, we write for that a capital F,
which is Farad, we call that,
one farad is the unit of capacitance, undoubtedly called
after the great maestro Faraday, we will learn more about
Faraday later in this course. So let us go to,
um, a sphere which has a radius R, and let us calculate what the
capacitance is of this sphere. Think of it as being a
conductor, and we bring a certain charge Q on
this conductor, it will then get a potential V,
which we know is Q divided by four pi, epsilon zero R.
We've seen this many times, and so, by definition,
the capacitance now is Q divided by the potential,
and therefore, this becomes four pi epsilon
zero R. So that is the capacitance of a
single sphere. And so we can now look at the
values as a function of R.
I have here some numbers, I calculated it for the
VandeGraaff, and I calculated it for the Earth.
If you want one Farad capacitance, that's a real
biggie, you need a radius of 9 times ten to the 9 meters,
that's the four pi epsilon zero that comes in there.
That's huge, that's twenty-five times the
distance from the Earth to the moon, that's a big sphere to
have a capacitance of one Farad. The Earth itself,
with a radius of sixty-four hundred kilometers,
would have seven hundred microfarad, the VandeGraaff
thirty centimeters radius would be 30 picofarad,
the pico is ten to the minus twelve.
And if you take a sphere with a radius of one centimeter,
then you have, uh, roughly,
one picofarad, ten to the minus twelve Farad.
So this gives you a rough idea about the size of objects,
and how they connect to their capacitance.
So if I bring all these spheres,
uh, at the same potential, so I charge them all up to the
same potential, then the one with the largest
capacitance, uh, will have the most charge.
And that, of course, is where the word "capacitance"
comes from, it is the capability of holding charge for a given,
uh, electric potential. Don't confuse that with
electric fields, because if you bring all these
spheres at the same potential, then the one with the strongest
electric field, that's the one which has the
short -- smallest radius,
we discussed that last time. Now, I will look at the
situation a little bit differently.
I have, here, a sphere, B,
positively charged, and I place it close to another
sphere, A, which is negatively charged.
And so, by my definition, I can say that the capacitance
of B is the charge that I have on B
divided by the potential of B. That will be my definition.
But, there is here, this object which charged
negative. And how did we define
potential? Potential was work per unit
charge. I go to infinity,
I put plus Q in my pocket, I approach B,
and the work I have to do per unit charge is the potential of
B, that's the definition of potential.
But B is repelling me. So I have to do positive work.
But A is now attracting me. And so the work I have to do is
less the work per unit charge. And so, because of the presence
of A, the potential of B goes down, and therefore,
the capacitance of B goes up. And so now, you see that that
the presence of this charged sphere here has an influence,
an important impact, on the capacitance of B,
and, therefore, it is really
unintelligible to call this the capacitance of B.
We think of it as the capacitance of B in the presence
of A. So it's no longer just B alone.
And so I'm now going to change the definition of capacitance.
And I'm going to change it in the following way.
I have two conductors. And these two conductors have
the same charge, but different polarities.
And now the capacitance of this combination of two conductors is
the charge on one of them -- which is the same,
of course, on the charge of the other, except different polarity
-- divided by the potential difference.
So that, now, is my new definition of
capacitance. So we always deal with two
objects, not with one in isolation, if you have the
charge on one of the two, and you divide it by the
potential difference between the two.
Uh, you may say, "Well, it's a little artificial
to have two, eh, conductors and one is
positively charged, and the other has exactly the
same amount of negatively charge." Well,
it is not so artificial as you may think.
Uh, remember, then, we have this Windhurst
machine, which I was cranking, and I was charging one plate
positive and the other one negative.
And without my doing anything, if one becomes positive,
the other one becomes negative by exactly the same amount,
because you cannot create charge out of nothing.
So if you charge one thing positive, chances are that
something else is charged negative by the same amount,
but with opposite polarity. So it's not so artificial,
that you have two conductors with the same charge but
opposite polarities. So, now, we have two conductors
there, so if we go to this -- these two parallel plates,
the question, now, is what is not the
capacitance, then, according to our new definition
of these parallel plates? Well, that's capacitance C,
is the charge on one plate divided by the potential
difference between the two plates.
And the charge on one plate is sigma A.
And the potential difference between the plates is the
integral of E dot D L, they are separated there by a
-- a distance H. I will change that,
now, to a D, because that's more commonly
done, that the separation between plates is D.
There was a reason why I didn't want to put a D there,
because I didn't want to get you confused,
but now, there is no confusion. And so the potential difference
is the electric field between the plates times the distance D.
But E itself is sigma divided by
epsilon zero, so we get here,
sigma divided by epsilon zero, divided by D,
I lose my sigma, and so, two parallel plates
have this as the capacitance. It's linearly proportional with
the area of the plates, that's intuitively pleasing.
The larger the plate, the more charge you can put on
there. And it's inversely proportional
with the distance between the plates.
The smaller you make the distance, the larger is the
capacitance. Well, that goes back to this
idea, that the closer A is to B, the larger effect that will
have on the capacitance. And if you bring them very
close together, this potential will go down,
and so the capacitance will go up.
So it's not too surprising that you see D here downstairs.
The closer you bring the plates together, the higher,
uh, the capacitance will be. Let us look at a -- uh,
at some numbers. Suppose I have a a plate,
very large, twenty five meters long, and five centimeters wide
-- twenty five meters long, and five centimeters wide.
I have two of them. Called a plate capacitor.
And let the distance between them, D, let D be -- oh,
let's make it very small, because we want a real big
capacitor, point oh one millimeters.
Very small game between them. So, now I substitute the
numbers in there, I can calculate the area,
I have to calculate the area here for the plates in square
meters, of course, multiply by epsilon zero,
and divide it by D in meters, and when you do that,
you find that the capacitance of this big monster is only one
microfarad. It's not very much.
And when you go to Radio Shack, and you buy yourself a one
microfarad capacitor, you don't by something that is
twenty five meters long, and yea big.
Well, you may actually have -- you may actually buy that
without you realizing that. Because these large plates,
these very long ribbons of conductors, two very close
together, separated by some insulating material,
very thin, they're rolled up often.
And you don't notice that, but they are rolled up,
and they are put in a little canister, and that then gives
you a parallel plate capacitor. Uh, I brought one with me,
unintelligible one that I have used for several years,
but, today I decided to cut it open for you so that you can
look inside, and then you actually will see the,
um, you're going to see, there, this is the canister in
which it was, and so I cut the canister open,
and when you look here, you see, there is this
conductor -- looks like aluminum foil -- and then there is
insulating material, and then you find more
conductor, on the other side. And so you -- and it's rolled
up. Here, if I unroll it here --
I'm breaking it, but that's OK -- so you see the
idea of a parallel plate capacitor, how it can be rolled
up nicely, and you not realizing that you're really talking often
about meters, many meters of material.
Now, through chemical techniques, the distance D can
easily be made a thousand times smaller than this.
And if the distance is thousand times smaller,
then you would get a capacitance of
one thousand microfarads. Compare that with the Earth,
which is only seven hundred microfarads.
So a capacitor like this is one thousand microfarads.
If we bring the potential difference over here,
then we get a tremendous amount of charge on here.
In fact, if I hold this in my hands, and if I assume that the
potential difference between my left hand and my right hand is
ten millivolts, then I would bring on this
capacitor, ten microCoulombs. That is a tremendous amount of
charge. In fact, ten microCoulombs is
the maximum charge we can ever put on the big VandeGraaff,
we calculated it last time. If we put more on the
VandeGraaff, it goes into discharge.
And by simply holding this in my hands, I can put ten
microCoulombs here on this capacitor.
Now, you may say, "Well, yes, but,
uh, potential difference would be your right hand and your left
hand, ten millivolts, isn't that funny?
No, not really. Uh, in the future,
I will give a lecture and then discuss electrocardiograms.
And you will see, then, that there is a potential
difference between the left side of your body and the right side
which is several millivolts. So it is not as artificial as
you may think. Actually, we'll take a
cardiogram in -- in class, so you can see it really
working. How much energy can I store in
a capacitor? Well, we already calculated
that. Uh, we had the energy,
is it, uh this was the plate capacitor, one-half Q V,
and we can now substitute for, um, , we can substitute in
there the capacitance C, and the C is Q divided by V,
and so this is also one-half C V-squared, that's one and the
same thing. So either you take the charge
on the capacitor, multiply it by V,
or you take the capacitance and multiply it by V-squared.
The capacitance is never a function of the charge that is
on the object. V- if you look here,
the capacitance is only a matter of geometry.
And when you look there, the plate capacitor,
it's only a matter of geometry, never does the charge show up
in there. So I mentioned that I can bring
ten microCoulombs on this capacitor, and yet,
on the VandeGraaff, I can also only bring ten
microCoulombs, that's the maximum I can do
before it goes into breakdown. We can think of a capacitor as
a device that can store, uh, electric energy.
I will now return to my promise that I was going to demonstrate
to you that I have to do positive work when I create
electric fields. In other words,
when I take these two charged plates, and I bring them further
away from each other, that I do positive work.
And how am I going to show that to you?
I have two parallel plates. They're on the table there,
you're going to see them shortly, projected there.
And we have, here, a current meter -- I put
an A in there for amperes, symbolic for current meter --
and I'm going to have a power supply and put a potential
difference over here, this is the capacitance C -- we
normally use for capacitor the symbol of two parallel lines --
I'm going to put a potential difference V over the capacitor
of thousand volts. So let me put a delta here to
remind you that it's the difference between the two
plates. As I do that,
as I connect the power supply to these two ends,
charge will flow on here, and so you will see a very
short surge of current. So the amp meter will give you,
only for the short amount of time that I am charging
[wssshhht], will see you -- will show you that there is charge
flowing. And you will see that.
But that's not really the goal of my demonstration.
What I'm now going to do is, I'm now going to increase the
separation, the instance D of these two plates.
And remember that the potential difference over the capac- over
the plates, which I call now a capacitor, is the electric field
times the distance, and the electric field is
constant. If I charge the capacitor up
with a certain charge, there is plus Q here,
there's minus Q there, and then I remove the power
supply, it's no longer there, that charge is trapped,
that charge can never change. And so if the charge doesn't
change, the charge surface density
doesn't change, and so the electric field
inside remains constant. So exactly what we did there.
And now I'm going to move them further apart,
therefore I'm going to make D larger, and that can only happen
if the potential difference between the plates increases.
And I will start off with thousand volts,
whereby D is one millimeter, and then I will open up this
gap up to ten millimeters. And then I have a potential
difference of ten thousand volts.
But since the energy in the capacitor is one-half Q times
the potential difference V -- this V is the same as this delta
V -- and if Q is not changing, but if I go from V from one
thousand volts to ten thousand volts, it's very clear that I
have done work, I have increased the
electrostatic potential energy. And this is what I want to show
you, we're going to have that there -- so I've changed my
television, and I will have to change the lights
a little bit so that you can see that -- well,
turn this one off, this one off,
and all them -- let's wait for the light to settle,
and we want also the the current meter.
So the one on the right there is the, uh -- the amp meter,
the current meter, and you see here these two
plates, they are separated now by about one millimeter.
I have here a very thin sheet, transparency which I can move
in between to make sure that they don't make contact -- and
here is my power supply, and I have there,
this, uh, propeller-type thing which is some kind of a volt
meter. And if it's going to move in
this direction, that means that the voltage
between the plates increases. And so I'm going to charge it
now, with a potential difference of, uh, thousand volts,
and as I do that, you will see a very short surge
here on this amp meter. That's not very spectacular,
but at least you can see, for the first time in your
life, that charge is actually flowing from my power supply
onto the plates. Then you will see,
[pssshhht], and that's it. There will only be a current as
long as the charge is flowing. So let my first do that,
look at the amp meter there, three, two, one,
zero. That's all it took to charge
these plates. It's now fully charged,
thousand-volt difference, and now, as I'm going to
increase the gap, there's no reason for any
charge to go away from the plates, so the amp meter will
not do much, probably nothing, but you're going to see this
propeller which indicates the potential difference between the
plates, you're going to see it move, because I'm doing all this
work, I'm going from one millimeter to ten millimeters,
I'm creating all this electric field, and this hard work pays
off in terms of increasing the potential from thousand volts to
ten thousand volts. So there I go,
I'm two millimeters now, look at the volt meter,
there's going -- aargh, three millimeters,
I'm doing all this hard work while you're doing nothing --
four millimeters, I'm creating electric fields --
you should be proud of me, I'm creating electric field,
look at that. The electric field remains
constant between the plates, because the charge is trapped,
the charge can't go anywhere. I'm not at seven millimeters,
seven thousand volts, eight thousand volts,
I'm at nine millimeters, nine thousand volts -- notice
that the amp meter does nothing,
no charge is flowing to the plates, no charge is flowing
from the plates, I'm not at ten millimeters,
and now I have created a huge volume electric field,
and the potential difference is ten times larger than it was
before, and so, you see that I,
indeed, have done work. You see it here in front of
your own eyes. All right, let's get this down,
and I'll take the -- bring the lights back up, and we go back to normal.
I have here a hundred microfarad capacitor -- it's a
dangerous baby -- and we can charge that up to three thousand
volts, and when we do that, we get three-tenths of a
Coulomb of charge on that capacitor.
So the, um, I'll give you some numbers -- so it is one hundred
microfarads, I'm going to put a potential difference over it of
three thousand volts, that gives it a charge Q of oh
point three Coulombs, and that means that one-half C
V squared, which is the energy that is stored,
then, in the capacitor, is four hundred and fifty
joules. And this will take fifteen
minutes. And so th- I'm going to charge
it now, because at the end of the lecture, I need a charge
capacitor for a demonstration. And so I can show you there the
potential difference over the capacitor, which will slowly
change, and we'll keep an eye on it during the lecture,
and then, by the time it's fully charged,
we will have reached the end of the lecture and then we can
continue. So here is, then,
this monster, the hundred microfarad -- I
call it a monster because the amount of energy that you can
pump in there is frightening, it's four hundred and fifty
joules. And my power supply is here,
that will deliver, comfortably,
the three thousand volts. In fact, this is the voltage of
the power supply, this is about thirty eight
hundred volts. And so, now,
the idea is that I'm going to charge this capacitor -- always
have to be very slow and careful that I don't make mistakes,
because this is really a device that could be lethal if you are
not careful. So I think we're OK.
Uh, the moment that I'm going to charge this capacitor,
the reading there will show you the potential difference over
these plates, and it will take a long time
for that to go up to three thousand volts.
And so I think I'm ready to go, and I'm going to charge it now.
So you see now that the potential difference over the
plates is very low, it's near zero,
but if you wait just a -- a few seconds, you will see,
very slowly, that, um, it is charging up,
and fifteen minutes from now, we will be very close to the
three thousand volt mark, and then we will return to
this. So we'll leave it on just for
now, while it is charging. The idea of a photo flash is
that you charge up a capacitor, and that you discharge it over
a light source. So the idea being that you have
a capacitor -- let me erase some of this -- and that we charge
the capacitor up, put a certain amount of energy
in there, and then we dump all that energy in a bulb.
So here is the capacitor, we're going to charge it up,
we have a switch here, and here is a
light bulb, and when we throw the switch, then all the energy
will be going to the light bulb, if this is positively charged
and this is negatively charged, a current will start to flow,
and you will see a flash of light.
I have, here, a capacitance of thousand
microfarad. So C equals thousand
microfarad, I'm going to put a potential difference over that
capacitor of one hundred volts, which then gives me a energy of
one-half C V squared, which is five joules.
In fact, this is not just one capacitor, but these are twelve
capacitors which I hooked up in such a way that the twelve
capacitors of eighty microfarad each are a combined capacitor of
one thousand microfarads. And so I'm going to charge it
up, and then I'm going to discharge the capacitor through
the light, and then you will be able to
see some lights, perhaps, depending on how much
energy we dump through there. So concentrate now on this
light bulb. The hundred volts -- you should
see here, do you see it? -- so it's set at hundred volts
now, and I'm now going to charge it, and the moment that I
charge, you will see the voltage over the capacitor,
and so it takes a while for it to charge up,
so it goes unintelligible down to zero and then slowly comes
back to a hundred, it may take five
or ten seconds. So if you're ready,
then there we go. Took only five or six seconds.
And so now we have a hundred volts, so we have five joules
stored in there, and I'm going to discharge that
now over this light bulb, if you're ready,
three, two, one, zero.
A little bit of light. I can tell that you're
disappointed. It's not very exciting.
It's not really my style, is it?
Well, what we can do, we can increase the voltage a
little bit.
Uh, we could go to two hundred and fifty volts,
in which case, since it goes with V-squared,
we would have six times more energy, so then we have thirty
joules, so let's see whether that's a little bit more
exciting. So now I have to jack up the
voltage to two hundred fifty volts -- now you see the power
supply again -- two hundred fifty volts -- we've getting
there, we don't have -- oh, boy, huh, am I lucky,
on the button. So two hundred fifty volts,
and noW I can charge up again, and it will take a little
longer, so you'll see the voltage over the capacitor,
hundred forty, hundred seventy,
two hundred, two fifty, there we are.
And now we can see whether we get a little bit more light.
So you go from five joules now, to thirty joules.
Three, two, one, zero.
Waahaa, now we're getting somewhere.
Now you really see how a photo flash works.
Now, we all, of course, have destructi-
destructive instincts. And so you wonder right?
You- you're thinking the same thing that I do.
Shall we try three hundred forty volts and see whether the
bulb [ptchee], maybe explodes?
I don't know how high this voltage supply can go,
let's see. Let's - let's go all the way.
Three hundred thirty seven volts.
OK. So that would mean that we
have fifty joules, roughly.
It goes as the voltage squared. Well, let's charge again,
so we're charging now. Two hundred,
two eighty, three hundred, there we go,
three hundred and thirty seven volts.
Now let's see -- AAAAH, we did it! It broke!
I have a photo flash, and I have the photo flash
here, and this photo flash has a capacitor of about five thousand
microfarads, a real biggie, and we can charge that up to a
potential difference of one hundred volts,
even though the batteries in there are only six volts,
there is a circuit in there -- we'll learn about that later --
which converts the six volts to a hundred volts,
and so we can charge up this capacitor to a hundred volts.
And that means that the one-half C V squared,
the energy stored, then, in that capacitor,
will be twenty five joules. And I can dump that energy over
the light bulb, and then we see a bright flash
of light, because this discharge can occur in something,
like, only a millisecond. So you get a tremendous amount
of light, only for that millisecond.
And I want to demonstrate that to you.
And the only way I can demonstrate that to you is by
aiming this flashlight you -- I don't want to damage your
eyes, so I warn you in advance -- so I am charging up,
now, my capacitor, it will take a while,
and I'm going to take your picture.
I might as well. But, um, it's going to be very
dark in the back, there, and so I've asked Marcos
and Bill to also have some flashlights, which go off at the
same time that my flashlight goes off.
Now, you may say, "Well, how can you do that,
because if this flash only lasts a
millisecond, how can you synchronize that?"
Well, the way that's done is that those flashlights are
waiting for my light signal to reach them, and that goes with
the speed of light. Takes way less than a
millisecond to get there, and they go at the same time
that they receive my light flash.
And so we call them flash-assists.
And so let's, uh, let's see whether we can do
this. I, uh, I have a green light
here, that means I can take my picture, and,
uh, yes, you can -- oh, you don't have to comb your
hair, but -- you're looking good.
OK, let me -- let me, let me focus,
because that's important -- so make sure you see the flash.
You ready for this? Did you see the flash?
Did it flash? Oh, it did.
Oh, you can say yes. So, um, did the -- did the
light-assists also flash? OK, but you haven't seen that,
yet, right? Because you were looking at
them. You should have looked -- you
really should have looked at me. So why don't we take a picture,
Marcos, Bill, aim the fli- li- the
flash-assists at the students here,
and then we'll try it again. You ready?
OK. Oh, boy.
Why don't you say cheese for a change?
OK, look at me -- oh, boy, you're looking great,
you really -- unintelligible out of focus.
Uh, one person's sleeping there, oh, we'll let him sleep,
that's OK. Did that work?
Did you see the flash? You did, eh?
Twenty five -- twenty five joules.
But those haven't seen it yet. So Marcos, Bill,
make sure that we go this way, and give them a chance to see
this light flash. So we get a little bit of
assistance there, the lights, and let's see how
this works, make sure that you see the flash,
very good, you can -- going to see another twenty five joules
going through this light bulb -- very good -- oh,
oh, oh, yes, yes, uh, yes,
your hand is in front of your mouth,
sir, yes, that's OK, thank you.
Very good. Did you see the flash?
Did the f- did the -- did the assist go?
So that's the idea of, um, of photo flashes.
So you dump a lot of energy in a very short amount of time,
and you get a very bright flash.
Professor Edgerton at MIT became very famous for his
flashlights. He invented flashed that can
handle way more energy than this
flash, and they can dump that energy in less that one
microsecond. And so this opened up the road
to high-speed photography, and that made it possible to
study the motion of objects on time scales of microseconds,
and even shorter than that. And I'd like to show you some
of the pictures that were taken with Doc Edgerton's flashes.
The first slide -- you see a bullet coming from the
right going for a light bulb. The exposure of this,
uh, picture, is only one-third of a
microsecond, during which the bullet probably moved only a
third of a millimeter, so it looks like it's
completely standing still. And the bulb is heading for
disaster, but it doesn't know that yet.
Uh, the bullet, uh, moves, uh,
in hundred microseconds about eight centimeters,
and then next picture is taken a hundred microseconds later,
again one-third of a microseconds
exposure. So if we can look at that --
there, you see, so the bullet now just
penetrates the light bulb, and then the next picture is
another hundred microseconds later, and there you see the
bullet emerging from the light bulb.
And, uh, this, uh, light bulb has hardly
realized that it is broken. But it's beginning to dawn on
it, and and then the next slide is one unintelligible wonderful
picture of a boy who is popping a balloon,
and you see half the balloon doesn't even know yet,
that it is broken. Doc Edgerton also -- that's
enough for these slides -- he also developed a lot of,
um, strobes. A strobe -- I have one here --
is an instrument that repeatedly discharges, um,
energy over a -- over the light bulb, and so you get repeated
flashes, and that, then,
gives you instrument like this.
Uh, you've seen them in use -- uh, they are being used at
airplanes, just for warning signals, and you've also seen
them on tall towers in the airports, also warning signals,
but there are lot of more things you can do with strobes.
And later, in eight oh two, uh, I will show you,
for instance, that you can measure the
rotation rate of motors with flash lights,
with these, uh, stroboscopes,
and the motors are going to play a more important
role in eight oh two than, uh, than you may have guessed
before you took this course. You can also measure with
strobes the rotation, the speed of your record
player, if you still have one, and then you can adjust it so
that it just has the right speed that is required.
So [inaudible] lot of things you can do with strobes,
and some of which we will see also in eight oh two.
So, now, I return to my capacitor there.
And let's see how it is doing.
Oh, boy, we are close to the three thousand,
which was my goal. It takes a -- you see,
a good fifteen minutes, to actually reach the three
thousand volts on this huge capacitor, and to get in there,
the energy, the four hundred fifty joules that I wanted.
And why is it that I want to show you this?
Well, I want you to appreciate the idea of a fuse.
You have lots of fuses at home.
A fuse is a safety device. A fuse is something that melts,
something that breaks if the current that you are using is
too high. Suppose you have a short,
electric short without realizing it,
in your desk lamp, and a very high current could
start to flow, then the fuse will say,
"Sorry, you can't do that, the fuse will melt,
and then that's -- prevents you from a
disaster, which, actually, might,
give you a fire. And we already showed,
in a way, the idea of a fuse, because when we broke this
light bulb, that was, in a way, a fuse.
We dumped too much energy through that light bulb,
and so, the light bulb itself [klk] was already like a fuse.
This is really more like a fuse that we are used to,
it is a -- we have a wire there, which is an iron wire,
which is twelve inches long, and it has a thickness of
thirty thousandths of an inch.
And we're going to dump the four hundred fifty joules
through that wire. So the idea is very much like
we had the -- the photo flash, we, um, have all this energy in
the capacitor, and instead of dumping it
through the light bulb, which was this system,
we now have here, a wire, and when I throw this
switch, the energy will go through the wire.
And chances are that you may see the
wire glowing a little bit, and then it would melt,
and that would then give you the idea of a fuse.
And it's also possible that, after we have done that,
that there may still be energy left on this capacitor,
and I can show that to you too, then, because I can short out
the two ends of the capacitor and see whether we still see
some -- some sparks, which would indicate that
there's still some energy left. So if you are ready -- I'm
always a little bit scared with this demonstration --
not so much about what's going happen, that thing will probably
just melt, and maybe we'll see a little bit of light,
that's not the issue -- but I'm afraid of this baby,
because that has, now, a tremendous amount of
energy. So I stop the charging -- so
let's do that -- and if you're ready, then I will try to dump
all that energy through this wire.
Three, two, one, zero.
[bang] [hum] [bang]. This is the way a fuse works.
This is very effective, as you see.
And if you hear this happening in your basement,
then, well, maybe that's a fuse.
We can now check whether there is energy left on that
capacitor. Maybe not very much,
but it's unlikely that everything was dumped in the
iron, so let's see whether there is some left,
if I'm going to be able to short it out with this
conducting bar, and see whether we can get a
spark. And we can.
So there's still some energy left.
OK, see you Friday.