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, 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
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
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.