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
then 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 and so I get a
charge on 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.
Or 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 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 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 at rest
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
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--
I put this down [chuckles] 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
before 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,
I want to talk a little bit about lightning
with you first.
There are 400,000 thunderstorms
every day on average on earth,
400,000 thunderstorms.
There are about a hundred lightning
flashes every second.
In general, 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,
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.
If we oversimplify the situation,
by assuming that the cloud and the ground
behave like plane parallel conductors,
then we can roughly calculate
the potential difference
between the cloud and the ground.
I will do that first.
But I warn you in advance
that this is not kosher.
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
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.
But now comes the catch.
As I was told by Amir Rizk of Lightning Electrotechnologies
that you can not
extrapolate the values
from a small uniform field gap
between two plates to a lightning strike.
This is because the conditions for the continued progapation of an electric discharge
are not the same
as the conditions for its initiation.
If an electric discharge is spanning a gap
that is longer than a few meters
a discharge can move in electric fields
that are orders of magnitude smaller
than the electric fields that initiated
the original electron avalanche.
At a height of one kilometers that is somewhat
lower than three million volts per meter.
Consequently, the potential difference
between the cloud and the earth
can vary between fifty million
and hundred million volts.
It can even be either
positive or negative.
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,
then 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--
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 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 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 802
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 cloud.
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,
[unintelligable]
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,
lighting 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,
at Kitt Peak Observatory in Arizona,
what I like about this is that
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.
You see here return strokes.
The light is definitely
due to the return strokes,
it's very bright.
These are step 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 lightning rods
sharp point,
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
between the cloud
and in this case the
Empire State Building.
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.
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 powder houses, ammunition storage
places for ammunition.
There was a lot of opposition
against Franklin.
They argued that 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.
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 if sparks fly over,
that they would go between the VandeGraaff
and 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 sparks.
By coming closer.
[spark]
There we go.
[multiple sparks]
So what you think is only one spark may well
be several like these return strokes,
the way I described with lightning.
[multiple sparks]
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.
[multiple sparks]
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 VandeGraaf
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 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,
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.
[laughter]
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 [spark! ah!]
there was a spark.
[laughter]
Boy, you got something for your
twenty-seven thousand dollars.
[laughter]
Oh, man.
OK.
So you saw both corona discharge
and you saw sparks.
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 Graf [Count] Zeppelin
the Germans called them the Zeppelins,
we call them dirigibles or 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 1937
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 6th at 7:25
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 ship moored on
this mast here, that a spark flew over
and that that caused the--
the explosion, the fire.
And it was the end of the
dirigibles for Germany.
Napoleon, also not the nicest man on earth,
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 there may be danger
for the soldiers.
Well, this morning I was walking
through the building
and I was in Lobby seven [sniffs]
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 there was some [snifs]
some gas there that shouldn't be there.
And so I brought my--
my special gun which is here,
which is built after Napoleon
and you see here
this 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 gas there
that 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
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 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
a 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.
[loud bang, audience reacts surprised]
[laughter]
I sure hope that we won't get malaria.
See you tomorrow.
[applause]
