When I 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 a 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 that 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 dV,
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,
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 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 dV 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 dl
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 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.
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 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, 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,
at the same potential,
so I charge them all up
to the same potential,
then the one
with the largest capacitance,
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 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 the presence
of this charged sphere here
has an influence, an important impact,
on the capacitance of B and therefore,
it is really unfair 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.
You may say, "Well,
it's a little artificial
to have two 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.
Remember, then, we have this Windhurst
machine, which I was cranking
and I was charging one plate positive
and the other one negative.
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 now the capacitance then,
according to our new definition
of these parallel plates?
Well, that 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 dl,
they are separated there by 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 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-- ooh, let's make it very small,
because we want a real big capacitor,
point oh one millimeters.
Very small gap between them.
So, now I substitute the numbers in there,
I can calculate the area,
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 buy 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.
I brought one with me, that is 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 eh--
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
between 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.
We had the energy, is it uh--
this was the plate capacitor,
one-half Q V
and we can now substitute for, uh--
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.
Here, 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 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 dim [?]--
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 do 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 it's going...
Aargh, three millimeters,
I'm doing all this hard work
while you're doing nothing--
four millimeters...
I'm creating electric field--
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 now 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 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 upon 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 very [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.
[laughter]
It's not very exciting.
It's not really my style, is it?
[laughter]
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're 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
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...
[laughter]
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?
[laughter]
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--
Aaah! We did it! It broke!
[laughter]
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-- let's see
whether we can do this.
I-- I have a green light here,
that means I can take my picture,
and-- yeah, 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?
[click]
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 -- oh, you're, you're out of focus.
[laughter]
Uh, one person's sleeping there,
oh, we'll let him sleep.
[click]
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.
[click]
Very good, did you see the flash?
Did the f- did the-- did the assist go?
So that's the idea of--
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 flashes 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.
[laughter]
Uh, the bullet, uh, moves, uh, in hundred
microseconds about eight centimeters,
and the 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--
[laughter]
and then the next slide--
is one wonderful picture of a boy
who is popping a balloon,
and you see half the balloon
doesn't even know yet--
[laughter]
that it is broken.
Doc Edgerton 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 an instrument like this.
[laughter]
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 near airports, also warning signals,
but there are lot of more things
you can do with strobes.
And later in 802, 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 802 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 you have a lot of things
you can do with strobes
and some of which
we will see also in 802.
So, now,
I return to my capacitor there.
And let's see how it is doing.
Ah, 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 [crack]
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
thirtythousandths 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.
[loud bang]
[low rumbling sound due to slowmotion]
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 short it out with this--
conducting bar and see
whether we can get a spark.
[spark]
And we can, so there's still
some energy left.
OK, see you Friday.
[applause]
