I’m Walter Lewin.
My lectures will in general not be a repeat of your book but
they will be complementary to the book.
The book will support my lectures.
My lectures will support the book.
You will not see any tedious derivations in my lectures.
For that we have the book. But I will stress the concepts
and I will make you see beyond the equations,
beyond the concepts. I will show you whether you
like it or not that physics is
beautiful. And you may even start to like
it. I suggest you do not slip up,
not even one day, eight oh two is not easy.
We have new concepts every week and before you know you may be
too far behind. Electricity and magnetism is
all around us. We have electric lights.
Electric clocks. We have microphones,
VCRs, radio, computers.
Light itself is an electromagnetic
phenomenon as radio waves are. The colors of the rainbow in
the blue sky are there because of electricity.
And I will teach you about that in this course.
Cars, planes, trains can only run because of
electricity. Horses need electricity because
muscle contractions require electricity.
Your nerve system is driven by electricity.
Atoms, molecule, all chemical reactions exist
because of electricity. You could not see without
electricity. Your heart would not beat
without electricity. And you could not even think
without electricity, though I realize that even with
electricity some of you may have a problem with that.
The modern picture of an atom is a nucleus which is very small
compared to the size of the atom.
The nucleus has protons which are positively charged and it
has neutrons which have no charge.
The mass of the proton is approximately the same as the
mass of the neutron. It’s about six point seven
times ten to the minus twenty-seventh kilograms.
One point seven. The positive charges here with
the nucleons, with the neutrons,
and then we have electrons in a cloud around it.
And if the atom is neutral the number of electrons and the
number of protons is the same. If you take one electron off
you get a positive ion. If you add an electron then you
get a negative ion. The charge of the electron is
the same as the charge of the
proton. That’s why the number is the
same for neutral atoms. The mass of the electron is
about eighteen hundred thirty times smaller than the mass of
the proton. It’s therefore negligibly small
in most cases. All the mass of an atom is in
the nucleus. If I take six billion atoms
lined up touching other, I take six billion because
that’s about about the number of people on earth.
Then you would only have a length of sixty centimeters.
Gives you an idea of how small the atoms are.
The nucleus has a size of about ten to the minus twelfth
centimeters. And the atom itself is about
ten thousand times larger. The cloud of electrons.
Which is about ten to the minus eight centimeters.
And if you line six billion of those up you only get this much.
Already in six hundred BC, it was known that if you rub
amber that it can attract pieces of dry leaves.
And the Greek word for amber is electron.
So that’s where electricity got its name from.
In the sev- sixteenth century there were more substances known
to do this. For instance glass and sulfur.
And it was also known and written that when people were
bored at parties that the women would rub
their amber jewelry and would touch frogs which then would
start jumping of desperation which people considered to be
fun, not understanding what actually was happening to the
amber nor what was happening to the frogs.
In the eighteenth century it was discovered that there are
two types of electricity. One if you rub glass and
another if you rub rubber or amber for that matter.
Let’s call one A and the other B.
It was known that A repels A and B repels B but A attracts B.
And it was Benjamin Franklin without any knowledge of
electrons and protons who introduced the idea that all
substances are penetrated with what he called electric fluid,
electric fire. And he stated if you get too
much of the fire then you’re positively charged and if you
have a deficiency of that fire then you’re
negatively charged. He introduced the sign
convention and he decided that if you rub glass that that is an
excess of fire and he called that therefore positive.
You will see later in this course why this choice he had
fifty percent chance is extremely unfortunate but we
have to live with it. So if you take this fluid
according to Benjamin Franklin and bring it from one substance
to the other then the one that gets an excess becomes
positively charged but automatically
as a consequence of that the one from which you take the
fluid becomes negatively charged.
And so that’s the whole idea behind the conservation of
charge. You cannot create charge.
If you create plus then you automatically create minus.
Plus and plus repel each other. Minus and minus repel each
other. And plus and minus attract.
And Benjamin Franklin who did experiments also noticed that
the more fire you have the stronger the
forces. The closer these objects are to
each other the stronger the forces.
And there are some substances that he noticed which conduct
this fluid, which conduct this fire, and they are called
conductors. If I have a glass rod as I have
here and I rub it then it gets this positive charge that we
just discussed. So here is this rod and I rub
it with some silk and it will get
positively charged. What happens now to an object
that I bring close to this rod and I will start off with taking
a conductor. And the reason why I choose a
conductor is that conductors have a small fraction of their
electrons which are not bound to atoms but which can freely move
around in the conductor. That’s characteristic for a
conductor, for metals. That’s not the case with
nonconductors. There the all electrons are
fixed to individual atoms. So here we have a certain
fraction of electrons that can wander around.
What’s going to happen that electrons want to be attracted
by these positive charges. Plus and minus attract each
other. And so some of these electrons
which can freely move will move in this direction and so the
plus stay behind. This process we call induction.
You get sort of a polarization. You get a charge division.
It’s a very small effect, perhaps only one in ten to the
thirteen electrons that was originally here will end up here
but that’s all it takes. So we get a polarization and we
get a little bit more negative charge on the right side than we
have on the left side. And so what’s going to happen
is since the attraction between these two will be stronger than
the repelling force between these two because the distance
is smaller and Franklin had already noticed the
shorter the distance the stronger the force.
What will happen is that if this object is free to move it
will move towards this rod. And this is the first thing
that I would like you to see. I have here a conductor that is
a balloon, helium-filled balloon.
And I will rub this rod with silk.
And as I approach that balloon you will see that the balloon
comes to the rod. I will then try to rub with
that rod several times on that balloon.
It will take a while perhaps because the rod itself is a very
good nonconductor. It’s not so easy to get charge
exchange between the two. But if I do it long enough I
can certainly make that balloon positive.
Then they’re both positive. And then they will repel each
other. But first the induction part
whereby you will see the balloon come to the glass rod.
These experiments work best when it is dry.
In the winter. They don’t work so well when it
is humid so it’s a good time to teach eight oh two in the
winter. OK there we go this should be
positively charged now. And the balloon wants to come
to the glass. You see that?
Very clearly. Come on baby.
OK. So now I will try to get this
balloon charged a little so there is a change of electrons
that go from the balloon to the glass.
And the glass doesn’t it’s not a conductor itself so it is not
always so easy to get charge exchanges.
OK let’s see whether I have succeeded now in making the
balloon positively charged as well as the glass rod.
If that’s the case then the balloon is not going to like me.
The balloon will now be repelled.
And you see that very clearly. To show you now that there are
indeed two different kinds of electricity if I now rub with
cat fur by tradition we do that with cat fur I don’t know why by
tradition we use silk for the glass.
So if we do this with cat fur now then this becomes negatively
charged. Remember there were two types
of electricity. And since that balloon is
positively charged now the balloon will come to me.
And there it is. Now it comes to me.
So you’ve seen for the first time now clearly
that there are two different kinds of electricity.
The positive charge is chosen by Franklin on the glass rod and
the negative charge on the rubber.
So now you may think that if I approach a nonconducting balloon
with a glass rod and I have a nonconducting balloon here you
may think now that this balloon will not come to the glass rod
because there are no free electrons.
So these electrons cannot freely move and so you don’t get
this polarization. You don’t get this induction.
But that is not the case. And this is actually quite
subtle. You have to look now at the
atomic scale. If I take an atom like you have
here. You have positive charge and
you have the electrons here in a cloud
around the positive nucleus. If I bring a glass rod
positively charged nearby then these electrons which are stuck
to the atoms, they cannot freely move like in
conductors, however will spend a little bit more time on the side
where the glass rod is because they feel attracted by the glass
rod, whereas the nuclei if anything want to go away from
the glass rod, so what you’re going to see is
that in a way if I started off with
a spherical atom let’s suppose this were a spherical atom or a
spherical molecule then what will happen is that you get sort
of a shape like this and the electrons spend a little bit
more time here than they spend here and that means that I have
actually polarized that atom. If the electrons spend more
time on this side of the atom than on this side I have also
created the phenomenon of induction and I therefore expect
that this side becomes more negative than that
side. And I can show you that in a
nice way with a transparency whereby I have plus and minus
signs and I have equal number of plus and minus signs.
So they represent neutral atoms.
There you see them. Boy.
It’s a little dirty but maybe see I can
clean it a little. OK.
OK. So here we go.
So notice there are equal amount of pluses and minuses,
so think of the plus and the minuses as one neutral atom.
Just a representation. Now I’m holding a glass rod on
this side which is positively charged.
And so each atom the electrons want to go a little bit to this
side and so the nucleus stays behind.
And if each atom does that this is what’s going to happen.
And now notice what you end up with.
In the middle of the substance plus and minuses cancel each
other out again. But on the right side you have
created a negatively charged layer and on the left side you
have created a positively charged layer.
And so in a way you have again induction.
So even in the nonconducting objects this side will turn
negative and this side will turn positive and therefore if I
approach a nonconducting balloon with a glass
rod I will also see the balloon come to me.
And so I can easily show you that.
It doesn’t make any difference whether I choose glass or
whether I choose rubber. I can do it with both.
Nonconducting balloons always have a potential problem.
The potential problem is that they can be charged by
themselves just like the metal balloons can be charged by
themselves. However, if I touch the metal
balloon then any charges there will immediately flow through me
to the earth we will understand that later.
Because this is a conductor. That remember the electric
fluid is conducted by a metal but not by a nonconductor.
So with this it’s more difficult.
Even if I kiss it and touch it it’s not clear that I can take
all the charge off. In fact by doing that I may
even make it worse. Let’s hope that it is not
charged too much and let’s approach it
with this glass rod and see whether I can convince you that
indeed it’s coming to the rod not because of the free
electrons but because of that process.
Oh boy. Ho.
And it should also do the same with rubber I hope.
If it were negatively it’d go away.
Ha it does go away so it is negatively charged you see that.
By touching it I actually probably charged it and there’s
not much I can do about it. Very difficult to get charge
off. I already had a suspicion when
I approached it with the glass it was too eager to come to the
glass. Still negatively charged.
That’s the way it goes. It’s not because the
demonstration failed but it’s because the
balloon is charged and doesn’t want to give it up because it’s
a it is a nonconductor. Friction can cause electric
charge and that’s exactly what happened when I touched this
balloon and tried to discharge it.
Through friction I may actually have charged it.
If I take these party balloons that all of you may have seen
and you just rub them on your shirt on your trousers they
stick to my hand. They have charge on them.
Whether it’s positive or negative I don’t know,
I don’t even remember. It’s not important.
And so when I bring them to my hand, my hand is not a good
conductor but you get induction, this phenomenon that we just
discussed and so the two attract each other.
The positive and the negative side attract each other.
And you can stick them on the ceiling.
Or you can stick them on the board.
You can decorate your room that way.
Very pretty isn’t it. All that you can do now because
of eight oh two. Now these heavy balloons may be
a little bit more difficult. Also I’m wearing cotton.
If you wear nylon or polyester it’s much better.
It’s much easier to get oh that’s good, that’s a nice one,
I think we need a blue one. There we go.
So you see friction causes electricity.
That’s of course why the silk when we rubbed the glass and the
cat fur we rub the rubber then we create charge on one.
Of course if you make the glass positively charged your silk
will be automatically negatively charged.
When you comb your hair you may have noticed with dry weather
that you hear some cracking noise.
Cracking noise means sparks. And you will learn all about
sparks in this course though not
today. But you can hear it if you’re
very quiet. And as you do that you charge
the comb. I can hear the cracking.
Interesting. So the comb is now charged.
Probably so am I and there it comes.
See. It’s not as good as the glass
but same idea. If you take your shirt off and
you make it and you make it dark in your dormitory and you stand
in front of a mirror an amazing experience.
And I’d be happy to do it for you because but I told you I
really wear cotton and it doesn’t work with cotton so
well. You really have to do it with a
nylon shirt. And when you take that nylon
shirt off not only do you hear the
cracking but you actually see the glow of these teeny weeny
little sparks. You actually are like a light
bulb. It is an experiment that you
cannot miss. And I would suggest you try
that this weekend. Do it with a friend.
That’s even more fun. We’ll all perhaps remember when
you just walk around. Do your normal things during
the day. There are rugs in rooms and
you want to leave the room and you touch the doorknob and you
get a shock. It’s a spark that flies over.
It’s electricity. Even when you touch a person
you sometimes feel this shock. When you cook and you take
saran wrap off these rolls the damn stuff just doesn’t want to
come off because as you roll it off there is friction and it
gets charged and it often gets crumpled up and it’s very bad,
very difficult to handle it. You’ve all experienced that.
Also cellophane around boxes with chocolate the same thing
happens. As you take it off you charge
it, whether you like it or not. I now want to do an experiment
and I need a volunteer. I need a student who actually
is wearing preferably not all cotton but I think Simon you
have a beautiful wonderful nylon parka.
So if you are willing to sacrifice a
little bit for the sake of science and come over here and
sit down here. Just relax.
Make sure that your feet are off the ground.
OK. So what I’m going to do now
Simon I’m going to beat you with cat fur.
And as I beat you with cat fur you
will get charged and since I don’t want you to be the only
person who suffers under this experiment I will also stand on
an insulated stool so if you become for instance positively
charged I don’t know whether it’s positive or negative I
would get the other amount of charge.
So we share in the charge. And as I beat you you will
charge up more and more and I will charge
up more and more and then we will have to convince the class
that that we are both charged. And we will do that in a way
that will be hopefully rather convincing.
I let me just start beating you a little bit.
To make you feel at home. We know each other right.
OK. Now of course as I mentioned to
you these experiments work well when it is dry and so if you are
too wet it won’t work. But let’s see if you sweat a
little bit too much then it doesn’t work too well.
So we ready? I have here in my hand a neon
flash tube. And although we don’t know
yet what voltage is because we will learn about that in this
course, to get a good flash out of these you need about a few
thousand volts. And so we will see and we’ll
make it dark shortly and I will hold the flashlight,
the flashlight in one hand, the neon discharge tube,
and then Simon will touch it on the other side.
And if we’ve succeeded then you may see some light.
So Simon look at me first, don’t touch it yet,
because we’re going to make it all the way dark.
You know where it is, it’s there, OK,
make it darker Marcos. Touch it.
Touch it. OK, try it again,
touch it again. OK.
Thank you. Can we have some light.
[applause] Thank you very much. Equal charges repel each other.
I’ve shown that, the demonstration with the
balloons. Here we have an instrument
which is called the Vandegraaff. It’s named after Professor
Vandegraaff, who invented it. It was an MIT professor.
And this instrument, which I will not discuss in any
detail though but you will understand it later on in the
course, I’ll tell you all about it later.
Just think of this instrument as a super amber rod.
And although we don’t know yet what voltage is,
I mentioned already the twenty thousand volts between Simon and
me, in this instrument you have to think in terms of several
hundred thousand volts. So this instrument is not
without danger. But that of course makes it
more exciting to work with it. So it’s a super amber rod and
what I will do first now is to put some confetti on top and
when we turn on the Vandegraaff the confetti may at first go to
the charged dome, it is already on top of it,
and when it picks up some of the charge it will then spread
out because it it will repel. So let’s get some some light on
there which will make it a little bit better to see.
Let me put some of this on top.
It’s just regular confetti, pieces of paper.
All right now all I have to remember is how to start the
most of the action has already occurred.
I will put a little bit more on.
[laughter] If you see sparks don’t worry yet.
[laughter] Put some more on. More and nothing left for the
[laughter] Make it perhaps a little darker.
Ah that’s too dark. [laughter] OK.
We’ll try it once more give it a zap so look at the confetti on
top. And I think it’s quite
convincing. Some of the confetti will stay
there. Well that’s the reason that
it’s not a good conductor and so it get it first sucked in and
if it doesn’t get charge of the Vandegraaff then it will not
spread out. All right.
So now let’s try for the first time to be a little bit more
quantitative. If I take two charges and we
use in general we use for charge the
symbol Q. So here we have Q one.
And here we have Q two. And let’s say they’re separated
by a distance R. And the unit vector in the
direction from one to two I call that R roof one-two.
The roof stands for unit vector.
These charges are equal, both minus or both plus,
then they will repel each other and so here there is a force F
which I call one-two. It is the force on two due to
number one and since action equals minus reaction force here
is to one equal in magnitude but a hundred eighty degrees in
opposite direction. Coulomb, the French physicist,
who did a lot of research on this in the nineteenth
eighteenth century actually. Coulomb found the following
relationship. That the force is proportional
to the product of the two charges.
So it’s Q one times Q two. Times a constant which nowadays
we call Coulomb’s constant, K.
Divided by the distance between these charges squared.
And it is in direction of the unit vector that goes from one
to two. This is the force on number two
due to one. And notice that this equation
is sign sensitive. Because if Q one and Q two are
both negative the source is in the the force is in this
direction and if they are both positive it’s also in this
direction as I have it. However if the if one is
positive and one is negative you get minus
this direction so this force flips over and that one then
obviously also flips over. In the SI units in this course
we will use for the unit of charge the coulomb named after
this great man. One coulomb charge is a
horrendous amount of charge. More than you will ever see in
your lifetime. We normally work with
microcoulombs, sometimes even less than that.
The charge of one proton, which is exactly the same as
the charge of one electron, is approximately one point six
times ten to the minus nineteen coulomb.
So one coulomb is something like six times ten to the
eighteen protons or electrons if the charge is negative.
This constant K in SI units is nine times ten to the
ninth. And the unit you can find out
because you know that this is newtons, this is coulomb squared
and this is square meters. So the unit is newton square
meters newtons square meters divided by square coulombs.
But that’s not so important. No one ever thinks of it that
way. For historical reasons which
may at times be a pain in the neck for
you we write for K one divided by four pi epsilon zero.
There is nothing magic about that.
It’s just a historical reason. And so one divided by four pi
epsilon zero is nine times ten to the ninth.
That’s all that matters. This epsilon zero has a name
it’s called the permittivity of free space.
But you can forget about that. It’s not important the name.
Notice that there is a clear parallel with gravity.
Newton’s law of gravity that the force, which in that case is
always attracting, gravity never repels,
is the product of two masses and then you have here the
gravitational constant and again you have the distance squared.
So there is an enormous parallel between the two.
There’s a great beauty that electricity acts in a way that
is very parallel to the way that
gravity works. If I added a third charge,
for instance here, Q three, and if now I want to
know what the force is on Q two, then I use the superposition
principle which we’ve used many times in eight oh one,
and we say OK the net force on number two is the force due to
number one plus the force from number three.
If number three if this is positive and this is positive
and this were negative then this force would be in this
direction, F one, F three two and then the net
force on number two would be the vectorial sum of these two.
Is it obvious that the superposition principal works?
Not at all. It’s not at all obvious.
Do we believe in it? Yes we do.
Why do we believe in it? Because it’s consistent with
all experiments that we have done.
But the superposition principle which is very powerful is really
not a matter of course. But it works.
We can always use it. And we will.
If you compare eight oh one with eight oh two thereby
comparing electricity with gravity you will
see that electric forces are way more powerful than
gravitational forces. And the way I can best show you
that is by taking two protons which are a distance D apart.
Here is a proton and here is a pro- proton and they are
separated by a distance D. They repel each other.
And the force by which they repel each other is of course
extremely easy to calculate. We know Coulomb’s law.
That law is called after Coulomb.
And so the force, the electric force with which
they repel each other, this is just the magnitude now
of the force, is the charge of the proton
which is one point six times ten to the minus nineteen but I have
to square that, I have to multiply it by
Coulomb’s constant, which is nine times ten to the
ninth, and I divide it by D squared.
That’s the electric force. If I want to know the
gravitational force, which is the force with which
they attract each other, these are repelling forces,
but I just want magnitudes here, then I have to take the
mass of the proton, which is one point seven times
ten to the minus twenty-seven I have to square that remember M
one times M two times the
gravitational constant. The gravitational constant in
SI units is six point seven times ten to the minus eleven
and I divide that by D squared. If now I compare the electric
force with the gravitational force, so I divide one by the
other, notice that the D cancels.
They both have D squared downstairs.
And so you will easily be able to
show that this ratio is roughly ten to the thirty-six.
So the electric force is thirty-six orders of magnitude
more potent than the gravitational attraction.
This teaches you some respect perhaps for eight oh two.
If these were the only forces that acted on the protons and
you bring them in the nucleus which has a size
of only ten to the minus twelfth centimeters then the
acceleration that the proton will experience is the electric
force divided by the mass of the proton.
F equals MA. Basis of eight oh one.
And if you take this electric force when you make D ten to the
minus twelfth centimeters which is ten to the minus fourteen
meters and you calculate this ratio you will find
that it is twenty-six orders of magnitude higher than the
gravitational acceleration on earth.
Twenty-six orders of magnitude higher.
So you wonder what the hell holds the nucleus together.
If there is such a tremendous force on these protons.
Well, what is holding them together are the nuclear forces,
which we do not fully understand, but thank goodness
the nuclear forces are not part of eight oh two so I will leave
that alone for now. So what holds our world
together? Well on the nuclear scale ten
to the minus twelve centimeters very important are the nuclear
forces. On an atomic scale up to
thousands of kilometers, it’s really electric forces
that hold our world together. But on a much larger scale,
planets and stars and the galaxy, it is gravity that holds
our world together. And now you may say ah that’s
very inconsistent with what you just told us because didn’t you
tell us that D cancels if you compare gravity
with electricity. Yes, however,
most objects are neutral or very close to neutral and so if
you take the earth it is very unlikely even that the earth as
a whole would have a charge of more than ten coulombs.
That probably is already an exaggeration.
So if I take the earth and I take the moon and I put on both
a charge of ten coulombs, here’s the earth and
here’s the moon, and I put say just arbitrarily
ten coulombs here and that is put on here either minus,
minus ten coulombs, so they will attract each
other, but given their distance, it’s almost nothing.
The force is negligibly small. But of course the force of
gravity, which is proportional to their masses,
wins and in this particular case if you take the earth and
the moon the gravitational force
wins over the electric force by twenty-five orders of magnitude.
So even though our immediate surroundings are dominated by
electric forces, including your own body for
that matter, the behavior of the universe on a large scale is
dictated by gravity. We will use various instruments
to measure charge in a quantitative way
and one of the instruments that you will see we will use it
often in the lectures that are to come, is called an
electroscope. It’s a very simple instrument.
In general it is just a conducting rod.
It could be aluminum, metal, and at the end are two
pieces of tinsel, two pieces of aluminum foil,
and often there is a nice knob here, and if I touch this with a
charged object, then because this can conduct
electricity, this can conduct the fire, as defined by Benjamin
Franklin, if I touch it with an object which is positively
charged, then this object will become positively charged.
If I touch it with an object which is negatively charged it
will become negatively charged. And you see now here these two
very light pieces of aluminum foil will repel each other.
And so you will see that this shows a certain angle,
and the more charge there is the larger that angle.
Sort of gives us a way of doing some quantitative measurements.
There are other electroscopes which are not too different.
There’s one central rod and they would have one leaf hanging
there and when you charge that one up then
this leaf will go out and if the charge is more it will go
out even further. I don’t have an electroscope
now here. But what I want you to see that
if I charge myself up and I hold in my hands these Christmas tree
tinsels, that in a way if I get enough charge on me,
then these tinsels will spread out.
It’s an idea that immediately follows from the fact that you
get a certain amount of charge, whether it’s negative charge
from me, or whether I’m positively charged,
that doesn’t make any difference, these tinsels will
spread out. And of course the best way I
can do that is if I charge myself with the Vandegraaff.
And as I said earlier experiments of this nature are
not entirely without risk. And so there’s always the
possibility of course that I don’t survive this
demonstration. [laughter] But don’t worry
because in that case there will be someone else who will lecture
eight oh two except he is not likely to show this
demonstration again. [laughter] So you might as well
take a close look because this may be the only time you will
ever see it. So I will give you some nice
light on the Vandegraaff and it’s always a
scary moment for me, sleepless nights about the
Vandegraaff. Am I going to turn it on,
Marcos, or you have the courage to turn it on?
You will turn it on? OK, hold it Marcos,
this is too close for comfort. You ready?
Are you nervous? Feel.
[laughter] So look at the tinsels and try not to look at
me please. Go ahead.
I am now a living electroscope. [laughter] If the if the
weather is cooperating today and if I had long hair you might
even see that my hair would start to act like
an electroscope. We can try that too.
Why don’t you throw it. [laughter] [applause]
Is it working? OK, well, this weekend make
sure you take this nylon shirt off in front of the mirror and
enjoy your enjoy the experiment at home.
Don’t try this ever. See you Friday.