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, calculators,
televisions, 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 second
class. [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. [applause]