Last time I mentioned to you that charge resides at the
surface of solid conductors but that it's not uniformly
distributed. Perhaps you remember that,
unless it happens to be a sphere.
And I want to pursue that today.
If I had a solid conductor which say had this shape and I'm
going to convince you today that right here the surface charge
density will be higher than there.
Because the curvature is stronger than it is here.
And the way I want to approach that is as follows.
Suppose I have here a solid conductor A which has radius R
of A and very very far away, maybe tens of meters away,
I have a solid conductor B with radius R of B and they are
connected through a conducting wire.
That's essential. If they are
connected through a conducting wire, then it's equipotential.
They all have the same potential.
I'm going to charge them up until I get a charge
distribution QA here and I get QB there.
The potential of A is about the same that it would be if B were
not there. Because B is so far away that
if I come with some charge from
infinity in my pocket that the work that I have to do to reach
A per unit charge is independent of whether B is there or not,
because B is far away, tens of meters,
if you can make it a mile if you want to.
And so the potential of A is then the charge on A divided by
four pi epsilon zero the radius of A.
But since it is an equipotential because it's all
conducting, this must be also the potential of
the sphere B, and that is the charge on B
divided by four pi epsilon zero R of B.
And so you see immediately that the Q, the charge on B,
divided by the radius of B, is the charge on A divided by
the radius on A. And if the radius of B were for
instance five times larger than the radius of A,
there would be five times more charge on B than there would be
on A. But if B has a five times
larger radius then its surface area is twenty-five times larger
and since surface charge density sigma is the charge on a sphere
divided by the surface area of the sphere, it is now clear that
if the radius of B is five times larger than A,
it's true that the charge on B is five
times the charge on A, but the surface charge density
on B is now only one-fifth of the surface charge density of A
because its area is twenty-five times larger and so you have
this -- the highest surface charge density at A than you
have at B. Five times higher surface
charge density here than there. And I hope that convinces you
that if we have a solid conductor like this,
even though it's not ideal as we have here with these two
spheres far apart, that the surface
charge density here will be larger than there because it has
a smaller radius. It's basically the same idea.
And so you expect the highest surface charge density where the
curvature is the highest, smallest radius,
and that means that also the electric field will be stronger
there. That follows immediately from
Gauss's law. If this is the surface of a
conductor, any conductor, a solid conductor,
where the E field is zero inside of the conductor,
and there is surface charge here, what I'm going to do is
I'm going to make a Gaussian pillbox, this surface is
parallel to the conductor, I go in the conductor,
and this now is my Gaussian surface, let this area be
capital A, and let's assume that it is positive charge so that
the electric field lines come out of the
surface like so, perpendicular to the surface.
Always perpendicular to equipotential,
so now if I apply Gauss's law which tells me that the surface
integral of the electric flux throughout this whole surface,
well, there's only flux coming out of this surface here,
I can bring that surface as close to the surface as I want
to. I can almost make it touch the
conductor. So everything comes out only
through this surface, and so what comes out is the
surface area A times the electric field E.
The A and E are in the same direction because remember E is
perpendicular to the surface of the equipotentials.
And so this is all there is for the surface integral,
and that is all the charge inside, well the charge inside
is of course the surface charge density times the area A,
divided by epsilon zero, this is Gauss's law.
And so you find immediately that the electric field is sigma
divided by epsilon zero. So whenever you have a
conductor if you know the local surface charge density you
always know the local electric field.
And since the surface charge density is going to be the
highest here, even though the whole thing is
an equipotential, the electric field will also be
higher here than it will be there.
I can demonstrate this to you in a
uh very simple way. I have here a cooking pan and
the cooking pan I used to boil lobsters in there,
it's a large pan. The cooking pan I'm going to
charge up and the cooking pan here has a radius whatever it
is, maybe twenty centimeters, but look here at the handle,
how very small this radius is, so you could put charge on
there and I'm going to convince you that I can scoop off more
charge here where the radius is small than I can scoop off here.
I have here a small flat spoon and I'm going to put the spoon
here on the surface here and on the surface there and we're
going to see from where we can scoop off the most charge.
Still charged from the previous lecture.
So here, we see the electroscope that we have seen
before. I'm going to charge this
cooking pan with my favorite technique which is the
electrophorus. So we have the cat fur and we
have the glass plate.
I'm going to rub this first with the cat fur,
put it on, put my finger on, get a little shock,
charge up the pan, put my finger on,
get another shock, charge up the pan,
and another one, charge up the pan,
make sure that I get enough charge on there,
rub the glass again, put it on top,
put my finger on, charge, once more,
and once more. Let's assume we have enough
charge on there now.
Here is my little spoon. I touch here the outside here
of the can -- of the pan. And go to the electroscope and
you see a little charge. It's very clear.
What I want to show you now it's very qualitative is that
when I touch here the handle, it's a very small radius,
that I can take off more charge.
There we go. Substantially more.
That's all I wanted to show you.
So you've seen now in front of your own eyes for the first time
that even though this is a conductor that means that it is
an equipotential, that the surface charge density
right -- right here is higher than the surface charge density
here. Only if it is a sphere of
course for s- circle symmetry reasons will the charge be
uniformly distributed. If the electric field becomes
too high we get what we call electric breakdown.
We get a discharge into the air.
And the reason for that is actually quite simple.
If I have an electron here and this is an electric field,
the electron will start to accelerate in this direction.
The electron will collide with nitrogen and oxygen molecules in
the air and if the electron has enough kinetic energy to ionize
that molecule then one electron will become two electrons.
The original electron plus the electron from the ion.
And if these now start to accelerate in this electric
field, and if they collide with the molecules,
and if they make an ion, then each one will become two
electrons, and so you get an avalanche.
And this avalanche is an electric breakdown and you get a
spark. When the ions that are formed
become neutral again they produce light and that's what
you see. That's the light that you see
in the spark.
And so sparks will occur typically at the -- at sharp
points -- at areas where the curvature is strong,
whereby the radius is very small, that's where the electric
fields are the highest. How strong should the electric
field be? Well, we can make a back of the
envelope calculation. If you take air of one
atmosphere, dry air, at room temperature,
then the -- the electron on average, on average,
will have to travel about one micron, which is ten to the
minus six meters, between the collisions with the
molecules, it's just a given. On average.
Sometimes a little more, sometimes a little less.
Because it's a random process of course.
To ionize nitrogen, to ionize oxygen,
takes energy. To ionize an oxygen molecule
takes twelve-and-a-half electron volts.
And to ionize nitrogen takes about fifteen electron volts.
What is an electron volt? Well, an electron volt is a
teeny weeny little amount of energy.
It's one point six times ten to the minus nineteen joules.
Electron volt is actually a very nice unit of energy.
Because once you have an electron and it moves over a
potential difference of one volt,
it gains in kinetic energy, that's the definition of an
electron volt, it gains one electron volt.
It's the charge of the electron, which is one point six
times ten to the minus nineteen coulombs, multiplied by one
volt. And that gives you then the
energy, one electron volt. And so what it means then --
let's assume that this number is ten electron volts.
Do we -- we only want a back of the envelope calculation.
So we want the electron to move over a potential difference
delta V which is roughly ten volts and we want it to do that
over a distance delta X which is ten to the minus six meters,
that's your one micron. And if that happens you'll get
this enough kinetic energy in the electron to cause an ion.
So what electric field is required for that,
that is delta V, the potential difference,
divided by the delta X, so that is ten divided by ten
to the minus six, so that's about ten to the
seven volts per meter. That's a very strong electric
field. In reality when we measure the
electric fields near breakdown, it is more like three million
volts per meter. But it's still very close.
This was only a back of the envelope calculation.
So very roughly at one atmosphere air room temperature
when the air is dry we get electric breakdown at about
three million volts per meter. When the ions neutralize you
see light, that's why sparks can be
seen. They heat the air,
they produce a little pressure wave, so you can also hear
noise. If you had two parallel plates
and you would bring those plates closely together and suppose
they had a potential difference of three hundred volts,
then you would reach an electric field of three million
volts per meter when the distance D is about one tenth of
a millimeter. So that's when you expect
spontaneous discharge between these two plates.
In practice however it probably will happen when the plates are
further apart than one tenth of a millimeter.
And the reason for that is that there is no such thing as
perfect plates. The plates have imperfections.
That means there are always areas on the plate which are not
flat, which are a little bit like what you see there,
small radius, and that's of course where the
electric field then will be larger and that's where the
discharge will occur first.
However, if you touch the doorknob and you get a spark,
you feel a spark, and you look at the spark and
you see that when you're three millimeters away from the
doorknob that the spark develops, you can s- pretty sure
that the potential difference between you and the door was of
the order of ten thousand volts, several thousand volts,
at least. Because over three millimeters
it requires ten thousand volts to get the three million volts
per meter. When you comb your hair or when
you take your shirt off you get
little sparks, you can hear them and if it's
dark you can see them, and you can be sure that at the
sharp ends of this hair, of the fabric,
that you have developed electric fields of the order of
three million volts per meter. And then you get the automatic
breakdown. Now of course high voltage
alone doesn't necessarily kill you.
What -- what -- what matters is not so much the voltage to get
killed but it's the current that goes through you.
And current is charge per unit time.
And so in SI units it would be coulombs per second.
For which we write a capital A which stands for Ampere,
the man who did a tremendous amount of research in this area,
Frenchman. And so if you touch the
doorknob the instantaneous current may actually be quite
high. It may be an ampere even,
but it may only last for one millisecond.
And so that's not going to kill you.
We all know that when you comb your hair that you don't die and
you also know that when you take your shirt off even though you
may hear the sparks that that's not lethal.
So maybe in a future lecture we can discuss in some more details
what it does take to actually execute someone electrically
which is very unpleasant but nevertheless we would have to
evaluate how long the current should last,
how strong the current should be and then also during which
parts of the body the current would cause lethal reactions.
So I want to be a little bit more quantitative now uh and
deepen our knowledge of the VandeGraaff.
Slowly we're going to understand how the VandeGraaff
works. And today I want to calculate
with you how much charge we can put on the VandeGraaff and what
the maximum potential is at the surface.
If we charge up the VandeGraaff,
with charge Q, then the potential of the
surface is an equipotential, is Q divided by four pi epsilon
zero R. And the electric field right
here at the surface would be Q divided by four pi epsilon zero
R squared. So in this case of spherical
symmetry we have that the potential V equals E times R.
But we know that E cannot exceed
three million volts per meter. And so that gives you now a
limit on the potential that we can give the VandeGraaff.
So if you substitute in here three million volts per meter
you can calculate what potential you can maximally reach for a
given sphere with a given radius.
And if we here have the radius and we here have the voltage,
then if the radius of the sphere were three millimeters
then you could not exceed a voltage
of ten kilovolts. If you did you would get this
automatic electric breakdown. You would get a spark.
If you have a sphere of three centimeters that would be a
hundred kilovolts and our VandeGraaff, which has a radius
of thirty centimeters, would therefore be one million
volts. And you could not exceed that.
And in practice in fact this one doesn't even make it to one
million volts. The sphere is not perfect.
There are imperfections of the sphere.
There are areas which have so-to-speak sharp points and so
we won't make it to one million volts.
We get a breakdown maybe at a few hundred thousand,
maybe three hundred thousand volts.
You can now also calculate what the maximum charge is on the
VandeGraaff. Because if the maximum
potential is three hundred thousand volts,
you know the radius is point three meters,
so you can calculate now what the maximum charge is that you
can put on the VandeGraaff using that equation,
will give you ten microcoulombs.
And so the maximum potential for our
VandeGraaff is of the order of three hundred thousand volts.
So this gives you now a feeling, a quantitative feeling,
for numbers, for what the -- can I put this
down, haha, so that gives you an idea of what our VandeGraaff can
do, and later we will understand how the charge gets there.
But at least you have some feeling now for potentials,
and for the charges that are involved.
If here's my VandeGraaff and I approach the VandeGraaff with a
sphere which is connected to the earth and if this
VandeGraaff had positive charge on it then the sphere will
become negatively charged through induction and so you get
field lines which go from the VandeGraaff to this object,
always perpendicular to the equipotentials,
so they go like this, and so the electric field here
will probably be the strongest, and so the spark will then
develop between this sphere and the VandeGraaff provided that
you were close enough. So that you do achieve a
electric field close to this sphere of about three million
volts per meter. And I will show you that later,
you will see more sparks today than you've ever seen before in
your life, but I want you to appreciate a little bit more
about the sparks about lightning before uh I demonstrate that.
So you get a little bit more out of it.
If I approach the VandeGraaff not with the sphere but I would
walk to the VandeGraaff being very courageous like this,
I'm also a pretty good conductor,
I'm also connected with the earth, then the chances are that
the spark would develop first between my nose and the
VandeGraaff, because that is the smallest curve -- the sha- the
sharpest curvature, the smallest radius,
or certainly my head, would be a good candidate for
being hit first. If I approach the VandeGraaff
like this with my hand stretched, then chances are of
course that the sparks will first develop between my
fingertips. Because it's a very small
radius and they're very close to the VandeGraaff,
and so that's where the discharge
will occur. So before we will enjoy some of
this, you will enjoy it, I will enjoy it less,
um I want to talk a little bit about lightning with you first.
Because what you're going to see in a way is a form of
lightning. There are four hundred thousand
thunderstorms every day on average on earth.
Four hundred thousand thunderstorms.
There are about a hundred lightning
flashes every second. The top of a thundercloud
becomes positive and the bottom becomes negative.
The physics of that is not so easy, and probably incomplete,
and I will not go into the details of the physics,
but it does have to do with the flow of water drops.
They become elongated, they can become charged because
of friction, and they can break off, and they can transport
charge. I will simply give you some
facts. And so I will accept the fact
that the cloud is going to be
charged. This is the cloud.
Positive at the top, negative at the bottom.
And here is the earth. Because of induction,
the earth of course will therefore become positively
charged here, and so we're going to see field
lines, electric field lines, which go from the earth to the
cloud, always perpendicular to the equipotentials,
something like this. I'll give you some dimensions,
uh this may be something like five kilometers,
this vertical distance D is about one kilometer.
These are typical numbers, of course, it can vary
enormously from thunderstorm to thunderstorm.
And this height is something typically like ten kilometers.
And this allows us now to make some
very interesting calculations to get some feeling for the
potential difference between the cloud and the earth.
That's the first thing we can do.
If we make the simplifying assumption that the electric
field is more or less constant here, it's like having two
parallel plates, where the electric field is
constant between them, then the potential difference
delta V between the bottom of the cloud and the earth,
is simply the electric field times the distance D.
So this becomes E times D. But if the breakdown occurs at
three million volts per meter -- by the way that's dry air,
when it -- when there is a thunderstorm it's probably not
so dry, but let's take the three million volts per meter,
so we get three times ten to the six, that is for E,
and the distance between the cloud and the earth let's take
one kilometers. So that's ten to the third
meters, so we get of the order of three billion volts between
the earth and the clouds. And the values that are
typically measured are several hundred million
to one billion volts, so it is not all that
different. You expect that the potential
is probably less than what we have calculated because clearly
uh these are not flat surfaces, there are trees,
here on the ground, there are buildings on the
ground, which are like sharp points, where the electric field
will be locally higher, and so you will get a discharge
at these sharp points first. And that means the potential
difference between the cloud and the earth could then be less
than the three billion that we have calculated here.
It's only a back of the envelope calculation.
The details of the physics of the discharge very complicated.
But I want to share with you some facts without giving
detailed explanations. The start of the lightning
begins when electrons begin to flow from the cloud to the
earth. They form a funnel,
which is about one to ten meters in diameter and we call
that the step leader. The step leader moves about
a hundred miles per second and so it comes down in about five
milliseconds. Five milliseconds from here to
here and it takes about half a coulomb to the earth.
Half a coulomb, for about five milliseconds,
that means the current is about one hundred amperes.
The step leader creates a channel of ionized air,
full of ions and full of electrons, which is an extremely
good conductor. And with -- when this step
leader reaches the ground there is this
highly conductive channel and the electrons can now very
quickly flow from this channel to the ground.
And that starts first right here at the surface of the
earth. That's where the electrons will
first go to the earth. And then successively electrons
which are higher up in the channel will make it down to the
earth. And so you're going to see
electrons going through the channel to the earth but first
the electrons are closer to the earth than the
electrons farther away and then even farther away.
And this is actually where most of the action occurs.
The current is now enormously high, ten thousand to some
hundred thousand amperes, and you heat the air,
get a tremendous amount of light, the ions recombine and
you get pressure, heat can produces pressure,
and there comes your thunder. And so most of the action is
not in the step leader but is in the second
phenomenon, which we call the return stroke.
Which is from the earth to the cloud.
And the speed of that return stroke is about ten to twenty
percent of the speed of light. During the return stroke there
is about five coulombs exchange between the cloud and the earth,
and five coulombs is a sizable fraction of the total charge
that was on the cloud -- on the cloud the first place -- t- to
start with. After a return
stroke, maybe twenty milliseconds later,
this whole process can start again.
You can get a step leader. And you can get the return
stroke. However, the step leader will
now follow exactly the same path that was made before because
that's where the air is ionized so that's where the conductivity
is very high, so that's the easiest way to
go. And this process can recur
five, ten, maybe fifteen times. So what a- appears to you as
one lightning bolt in fact could be ten flashes back and forth
between the cloud and the earth.
And the -- the real light is not in the step leader,
that's very little light, but the real light is in the
return strokes. So t- ten return strokes,
which may be twenty, thirty, forty milliseconds
apart, appear to you and to me only as one flash,
which would take place maybe in as little as a tenth of a
second. And during these five or ten
return strokes you exchange between the cloud and the earth
maybe a total of twenty-five to fifty coulombs,
and that of course will lower the potential difference.
And if the potential difference becomes too low then the process
stops. You have to wait now for the
clouds to charge up again. And then lightning will strike
again. And that can take anywhere from
maybe four, five, ten, twenty seconds.
And then you get another lightning bolt.
The study of these -- of this process, of the step leader and
of the return stroke, can be done with a camera,
which is called the Bors camera.
Let me first explain to you in detail -- in principle how it
works. If this is the area on the film
that is exposed by your lens suppose that I move the film at
a very high speed to the left and suppose the step leader
comes down and it sees some light from the step leader,
then I may see on the film this.
Some light. And from here to here would
then be the five milliseconds which it
takes the step leader to go from the cloud to the earth.
Now the return stroke takes place with way higher speed and
so I see a tremendous amount of light because there's a lot of
light in the return stroke. And of course this is very
steep. Because it goes a hundred times
faster up than the step leader came down.
And so you can measure these times and so you can get the
speed of the return stroke. And then later in time,
maybe thirty, forty seconds later,
on the film, you may see another return
stroke. And you may see another one.
And so you can see then how long the time was between the
return strokes and you can also calculate their speeds.
With a real camera it's not really the film that is moving
but it is the -- the lens that is moving, and the way these
pictures are taken, and I will show you one,
is if this is photographic plate, then it is the camera
that moves over the plate with a um very high speed,
about three thousand revolutions per minute,
and so you would get these -- this information then not
horizontally but you get it spread out over the film.
But you get the same information, you can calculate
speeds and times. During the past decade,
new forms of lightning have been discovered which occur way
above the clouds. Way higher up.
Red colors have been seen. Red sprites they are called.
And also blue jets. The light is
very faint and it occurs only for a very short amount of time.
It's very difficult to photograph.
I have not been able to get good slides for today.
However, I did see some pictures on the Web.
And when you log into the Web, when you visit the Web eight oh
two which you should, then I give you directions how
to access slides pictures of the red sprites and of the blue
jets. The physics of that is not very
well understood. It's being researched very
heavily. But it's way above the clouds.
There are also other forms of electric breakdown,
of discharge. They are different in the sense
that it's not an individual spark.
But there is a continuous flow of -- of -- of charge.
It occurs always from very sharp points.
So there is a continuous current actually going on.
And some of that you may have seen but you may not remember
when we used a carbon arc here. We had two carbon arcs,
two carbon rods, and we had a potential
difference between them and we got a discharge between them
which caused a tremendous amount of light, which we used for
projection purposes. So a carbon arc discharge is
such a form of discharge whereby you have a continuous current.
It's not just sparks. If you take grass or trees or
brushes for that matter, with thunderstorm activity,
they can go into this discharge at their sharp tips.
And we call this brush discharge,
we call it St. Elmo's fire,
it's all the same thing, it's also called corona
discharge. I normally call it corona
discharge. It produces light because the
ions when they neutralize produce light.
Heat makes sound, pressure, and so you can hear
this cracking noise of the corona discharges.
An airplane that flies or a car that drives, there is friction
with the air, and any form of friction can
charge things up. And so it's not uncommon at
night that you can see this corona discharge from the tip of
the wings of an airplane. I've also seen it from cars.
Corona discharge from cars. Which charge themselves up
simply by driving through the air.
The air flow would charge them up.
You can hear it, cracking, and you can see it
sometimes if it's dark enough, you see some light.
In general it's bluish light. Something completely on the
side, going back to the lightning bolts,
the discharge,
the moving electrons, can cause radio waves.
And these radio waves you can receive on your car radio.
And all of you have experienced this.
Driving around, lightning very far away,
you can hear it on the radio. So that's telling you that
there is lightning going on somewhere.
After a thunderstorm, something that many of you may
not have experienced because in the cities there is always --
always exhaust from cars, that spoils everything,
but when you're out in the country after a thunderstorm
there's a very special smell in the air.
I love it. And that's ozone.
Oxygen two, oxygen two in lightning becomes oxygen three.
And oxygen three has a wonderful smell,
and you can really smell that. It's very typical.
I hope that most of you sooner or later in life will have that
experience. Go to the country after a
thunderstorm and you can really smell this ozone.
Let's now look at some slides. The first slide that you will
see is one very classic slide made by Gary Ladd,
a Kitt Peak Observatory in Arizona, uh what I like about
this is that uh these are the observatories,
the telescopes, in the domes,
and of course when you're an astronomer, this is the kind of
weather that you can do without. But nevertheless it happens.
Uh you see here return strokes, the light is definitely due to
the return strokes, it's very bright.
These are step l- leaders that never made it to the earth,
and if a step leader doesn't make it to the earth you don't
get a return stroke and so the light as you can see here is
much less. And what you think here is only
one bolt is probably at least ten, five to ten,
maybe fifteen, flashes.
Return strokes. All right next slide please.
Here you see the result of a Bors camera exposure.
For those of you who are sitting in front you can
recognize maybe the Empire State Building here.
And the Empire State Building is hit here by lightning at the
very tip, that's the sharp edge, that's where you expect it to
be hit. This is not taken when the
camera was rotating. This is just the exposure the
way you and I would see it. Not moving camera but here you
see the result of the rotating Bors camera.
And this is the same flash. So here you see the return
stroke, the -- the light from the step
leader is too faint. You can't see that.
So here is the return stroke and then this time separation
may be thirty or forty milliseconds,
see another stroke, you see another one,
and another one, so there's six here,
looks like you see a double one here.
And so you have six or seven of these return strokes.
And this is the way that you can study speeds and how much
charge actually is exchanged between these uh between the
cloud and in this case the Empire State Building.
Uh the next slide shows you a corona discharge in the
laboratory this is a high voltage supply with a very sharp
tip -- tip here at the end, the sharp point,
and here you see not individual sparks, you don't call this
lightning but this is what you would call the St.
Elmo's fire, the corona discharge is bluish
light. And in fact when you are close
to this power supply you can also smell the ozone.
It also produces locally ozone. And you can see it.
If you make it dark in the laboratory you can see some
bluish light. Uh when I was a graduate
student I had to build power supplies, high voltage power
supplies, and I remember when my soldering job was not a very
good job that means when I take the solder ironing off then I
could draw a little sharp point, the solder, and that would then
later cause me problems with corona discharge,
that means I would have to redo the soldering so that the radius
of the solder joint would become larger, so no sharp points.
That's enough for the slides right now.
Benjamin Franklin invented the lightning rod.
His idea was that through the lightning rod you would get a
continuous discharge, corona discharge,
between the cloud and the building.
And therefore you would keep the potential difference low.
And so there would be no danger of lightning.
And so he advised King George the third to put these sharp
points on the royal palace and on uh powder
houses, ammunition storage places for ammunition.
There was a lot of opposition against Franklin.
Uh they argued that uh a lightning rod will only attract
lightning. And that the effect of the
discharge, lowering the potential difference,
would be insignificant. But nevertheless the King
followed Franklin's advice and after the sharp rods,
the lightning rods, were placed,
there was a lightning bolt that hit one of the ammunition places
at Pearl Fleet,
but there was very little damage.
And so we now know that on the one hand the discharge is indeed
insignificant. And so the opposition was
correct. And in fact you do attract
lightning, unlike what Franklin had hoped for.
However, if your lightning rod is thick enough that it can
handle the high current, which is ten thousand or a
hundred thousand amperes, then the current will go
through the lightning rod and therefore
there will not be an explosion. So it will not hit the
building. So it will be confined to the
lightning rod. And so it worked but for
different reasons than Franklin had in mind, but he had the
right intuition. Was a very great scientist,
and great statesman. And so his lightning rod
survived up to today. So now I want to return to the
VandeGraaff and show you some of the things that we have
discussed. And the first thing that I
would want to do is create some sparks.
Lightning. I run the VandeGraaff and I
will approach it with this small sphere, small radius,
and as I come closer and closer, the electric field will
build up here and then I would predict that as sparks fly over,
that they would go between the VandeGraaff and this uh this
sphere. This sphere is grounded.
And so any current that will flow will flow not through
Walter Lewin but will go through the ground, so there's no danger
that anything will happen to me. At least not yet.
You already hear some cracking noise.
That means there are already sparks flying around inside
there. It's very hard to avoid,
there are always some sharp edges in there that we cannot
remove. This is not an ideal
instrument. But I still think I will be
able to show you some lightning. By coming closer.
There we go. So what you think is only one
spark may well be several like these return strokes,
the way I described with lightning.
So what you're seeing here now is that the electric field
locally has become larger than three million volts per meter
and then you're going to this discharge phenomenon that we
described, and that gives you then -- that
gives you the lightning. What I will do now is I would
like you to experience -- although it may not be so
fascinating for you -- to experience a corona discharge
between a very sharp point that I have here, extremely sharp,
and the VandeGraaff. And the only way that I can
convince you that there is indeed going to be a discharge
between this point and the VandeGraaff is by
approaching the VandeGraaff and this cracking noise that you
hear now will disappear. And the reason why it will
disappear is that if I get a corona discharge between the tip
and the VandeGraaff it will drain current,
it will lower the potential and so that cracking noise will
disappear. So the sparks which are now
flying over will not fly over anymore.
You will not be able to see the light.
It's -- it's too much light here.
Although I can probably see at the tip here this blue light.
So I'm going to approach the VandeGraaff now.
It's almost as if I had a lightning rod and I'm not
worried at all because if any current starts flowing it goes
through this rod, which is like a lightning rod
to the earth. So I'm not worried at all.
I just am very brave, very courageous,
approaching the V- the VandeGraaff, and I want you to
listen to that cracking noise. That cracking noise will
disappear when I'm going to be -- draw a current through this
sharp point. Oh, boy, there I go.
And the cracking stops. And I can actually see here
some glowing discharge, bluish.
Will be impossible for you to see.
I can come closer, I'm not worried.
And so I'm draining charge now off the VandeGraaff thereby
lowering the potential of the VandeGraaff and so these crazy
sparks that occur here can no longer occur.
But now they will. Can you hear them?
And now you can't. If I were crazy then I would
develop a corona discharge between the VandeGraaff and
myself. One way I could do that is by
approach it with my fingertips as I mentioned earlier,
but that may be a little bit too dangerous because I may draw
a spark, I may be hit by lightning, which is the last
thing that I would want today. However, a corona discharge
using these tinsels may be less
dangerous. So I get a continuous flow of
current which now unfortunately doesn't go through the lightning
rod but now it goes straight through my body.
And I can assure you that I can feel that.
It's probably a very low current.
It may be only a few microamperes.
But it's not funny. It's not pleasant.
But anything for my students, what the hell.
There we go. Ya ya ya ya ya.
You see tinsels, I'm now in a corona discharge
and I feel the current through my fingers, it's a continuous
discharge now. This is St.
Elmo's fire. You can't h- ah,
there was lightning. Boy, you got something for your
twenty-seven thousand dollars. Oh, man.
OK. So you saw both corona
discharge and you saw lightning. Boy, you were luckier than the
-- than the first class by the way.
Clearly lightning can be dangerous, lightning can cause a
fire, it can excite, it can explode fumes,
if you gas your car just the flow of gasoline can charge up
the nozzle, friction can charge things up, that's why the nozzle
is always grounded, because a spark could
cause a major explosion. If you fill a balloon with
hydrogen then the flow of hydrogen is friction can charge
up the balloon and a spark can then ignite the hydrogen.
And this has led to a classic tragic accident,
it's a long time ago. But it's so classic that I
really have to show this to you. Hitler was very proud of his
large airships. They're named after Gar
Zeppelin the Germans called them the
Zeppelins, we call them dirigibles or bl- blimps.
And one of the largest ones that Hitler's Germany ever built
was the Hindenburg, eight hundred three feet long
and seven million cubic feet of hydrogen.
And the Germans couldn't fill their Zeppelins with helium
because they didn't have helium. And the Americans were not
going to sell them helium, for very good reason.
And so they had to fill them with
hydrogen. And so the Hindenburg which was
the name of this Zeppelin came over in May nineteen
thirty-seven and when it arrived at Lakehurst in New Jersey it
started a gigantic fire. It came over in thirty-five
hours trans-Atlantic and you see here the explosion.
May six at seven twenty-five in the afternoon.
There were forty-five passengers on
board and thirty-five died in this fire.
The speculation was that this may have been sabotage.
It's still quite possible. Although the official inquiry
board concluded that it was St. Elmo's fire,
that as the uh ship moored on this mast here,
that a spark flew over and that that caused the uh the
explosion, the fire. And it was the end of the
dirigibles for Germany. Napoleon, also not the nicest
man on earth, uh had the suspicion
when many of his soldiers got sick in Egypt that this was the
result of marsh gas. And they suspected that this
bad air that they could smell when they were near marshes that
that was the cause of the disease, bad air in French is
mal air, and so they called the disease malaria.
And so the way that they tested the
air to make sure that the soldiers wouldn't get malaria
was to build a small gun which was like so, this was a
conducting barrel. And they would let some of this
marsh gas in the gun and put a cork on here,
close it off, and here was a sharp pin,
this pin was completely insulated from the barrel,
the conducting barrel, and then they would put some
charge on here, so that the spark would fly
over there. This is really the precursor of
the spark plug that we have in our cars.
It's no different. And so if indeed there was then
this marsh gas in there, there might be an explosion and
that was a warning then that um there may be danger for the
soldiers. Well, this morning I was
walking through the building and I was in Lobby seven and I
smelled some funny, it was a funny smell,
and I was just wondering whether perhaps,
who knows, at MIT anything can happen, whether uh there was
some uh some uh gas there that shouldn't be there.
And so I brought my uh my special gun which is here,
which is uh built after Napoleon and uh you see here
this uh little sphere and I opened up the cork
here and I let some of that air in, Building seven,
and then I decided that we, you and I would do the test and
see whether perhaps there was some uh some gas there that uh
may cause some danger. So I would have to cause a
discharge then inside the -- the barrel here.
I can try to do that by combing my hair uh but that may not be
sufficient amount of charge so I can
always make sure that there will be a spark inside that gun
and use this -- this disk. Which has a little bit more
charge on it. So here is then this uh Lobby
seven gas inside. Now of course there's one
possibility that there was nothing wrong with the air,
in which case you will see nothing.
And there is another possibility that the air wasn't
kosher enough and that you may see here small bloop and since
it's going to be very small at best you
have to be very quiet otherwise you won't hear anything.
And so let's first try now with my comb.
I have my comb here. To see whether I can generate a
spark inside this barrel and that may not work because I'm
not sure that I get enough charge on this comb.
No, that doesn't work at all. Well, let's see whether we can
use this instrument.
I sure hope that we won't get malaria.
See you tomorrow.