class if there is something you didn't follow from last time.

I'm afraid to do that now, because it's a big class and I

don't know how many things you follow or didn't follow.

What I will do first is write down a very quick summary of the

main points from last time.

So you should ask yourself, "Did I follow all those

things?"

And if your answer is yes, then you are fine.

Because I talked about many, many things,

but you don't need all of that.

So what I'm going to write down right now is the absolute

essentials of last lecture, okay?

That's going to be needed for what I do next.

First point was: everything is made of atoms.

You know that.

And the atom has a nucleus.

In the nucleus are some things called protons,

some things called neutrons, and outside are some things

called electrons.

That's all the atomic structure we need.

Then we say certain entities have a property called electric

charge.

The symbol for electric charge is q, and you can put a

subscript to say who you are talking about.

So you can say q for the neutron is 0.

A q for the electron is -1.6 times 10 to the -19,

and it's measured in coulombs.

The q for the proton is really--let me put it this way,

q for the proton is a positive number,

so these minus signs cancel.

Now, the importance of the coulomb is that if anything has

some coulombs on it, it will interact with anything

else that has some coulombs on it.

So that if you have two entities and this one has a

charge of q_1 coulombs,

that one has a charge of q_2 coulombs,

and the distance between them is r,

then the force is q_1q

_2_ over 4Πε

_0r^(2).

I'm purposely not putting all the vector signs on F

because it takes too long, but you all know what the

answer is.

Namely, if you want the force on 2,

due to 1, will be repulsive if q_1 and

q_2 are of the same sign and point to the

direction joining them.

Yep?

Student: Shouldn't it be 1 over r^(2)?

Prof: Yes, thank you.

There is another force law which is r^(2),

not so famous, called Hooke's Law,

but you're absolutely right.

That's the difference between being Newton and being Hooke.

Hooke is known for the r^(2)^( )law.

Newton is known for the 1 over r^(2)^( )law.

So this is a very important thing.

If you see anything wrong you should stop me,

because when I go home, they're going to play the video

for me to watch, and I'm going to see that

r^(2).

There is nothing I can do until some voice from the back says,

"Hey, send it downstairs",

and I appreciate that a lot, okay?

It's good, so never hesitate to do that, plus sign,

minus sign, symbols; anything that goes wrong.

It also tells me that you're following me.

So for all those reasons you should not hesitate to correct

anything, and you should not think that you don't follow it

because it's your fault.

Probably it is.

Sometimes it's my fault as was demonstrated now.

Okay?

So this is the force law.

You need only one other ingredient.

That's the superposition principle.

You need that ingredient because we're not going to be

talking only about two charges.

We're going to be talking about many charges.

And the question is: what will they do when they're

all present, and it's a great blessing that

we have the principle of superposition that says that if

you've got, say, three charges,

say 1,2 and 3, you want to know the force on 3

due to 2 and 1.

You can find the force that 1 would exert.

You can find the force that 2 would exert.

We have two vectors, and you can add the two vectors

to get the net force.

In other words, the interaction between pairs

of charges is insensitive to the presence of any other charges.

They go about their business exactly the same way.

That is a principle that is not deduced by logic.

You cannot say, "Of course,

it had to be that way."

That's not true.

It doesn't have to be that way.

In fact it is not that way if you make supreme,

I mean, extremely exquisite measurements,

but they occur really at the really quantum level.

For classical electromagnetic theory it is actually an

experimental fact that you can superpose.

All right, if you combine those things you can calculate

anything and everything that we will deal with for sometime,

but that's summary of--this is all I said last time,

okay?

Now, I didn't do one thing, which is to emphasize to you

that the force of gravitation divided by the electric force is

some number like 10 to the -40.

I put this twiddle here meaning not exactly.

There are factors of 1 and 2 or 10 missing,

but 10 to the -40 is roughly the magnitude of this ratio,

and it was done by comparing the force between electron and a

proton.

It didn't matter what the distance was because everything

goes like 1 over r^(2), so when they take the ratio

that cancels out, but this was really the ratio

of things like mass of the electron,

mass of the proton, divided by 1 over

4Πε _0;

q of the electron and q of the proton.

If you put all these numbers in you've got that.

I want to mention one thing.

It may be interesting for you to think about.

Look at this nucleus.

Nucleus has a lot of protons in it, and according to Coulomb's

Law they all repel each other.

And the neutrons, of course, don't do anything

because they have no electric charge.

So you should ask yourself, "Why are all these protons

staying together inside the nucleus if I don't see any

attraction between them?"

I see why the electrons are hanging around,

because they're attracted to the nucleus,

because nucleus is positively charged,

electrons are negatively charged, and Mr. Coulomb tells

you they'll be attracted.

What are the protons doing together in that tiny space?

That space is like 10 to the -13 centimeters.

So have you ever thought of that, or does anybody know why

the protons are together?

Yes?

Student: The strong nuclear force?

Prof: There is a strong nuclear force.

Okay, that's the answer.

In other words, but that answer will lead to

more questions, but I'll first state the

answer.

There's a force even stronger than the electric force.

You see, this gives the impression electric force is

very strong.

It is much stronger than gravity, but there is a force

even stronger than the electric force that is experienced by

protons and by neutrons.

In other words there is another charge which is not electric

charge, which the protons are endowed with and the neutrons

are endowed with.

And the force due to that charge, if you like,

it's not called charge but it's a similar thing,

is much, much stronger.

It had to be, because you have to beat the

electrical repulsion.

So then you can ask yourself, "Well,

in that case, how did we ever find the

electrical force," because here's another force

even stronger than the electrical force,

maybe a thousand times stronger.

Then why wasn't it completely overshadowing the electrical

force?

Yep?

Student: It's irrelevant over larger

distances.

Prof: Yes, so let me repeat what he said.

It has to do with what's called the range of the force.

In other words, look at two different

functions, okay?

One function looks like 1 over 137 times 1 over r^(2).

Other function looks like 10 times e to the -r

over r_0 divided by r^(2);

r_0 is some length, and the length is

roughly 10 to the -13 centimeters, or 10 to -15

meters.

Which force are you more impressed with is the question,

okay?

If r is much bigger than r_0,

say 10 times bigger, you've got e to the -10

on the top.

e to the -10 is a small number.

e to the -3 is like 1 over 20.

e to the -10 is 1 over 20 cubed.

So then what will happen is, this force, even though there's

a number 10 in front of it, will be negligible compared to

this one.

Whereas if r is much smaller than

r_0, say, r is .1 of

r_0, so you can forget this number,

e to the minus point is roughly 1,

then this 10 will dominate the 1 over 100.

So what happens is, if you're sitting inside the

nucleus, the nuclear force is

numerically strong, not only because of the number

in front of it, but also because this

exponential factor has not kicked in.

Therefore, the protons feel an attraction for each other due to

the nuclear force that is stronger than the repulsion due

to the coulomb force.

And the neutrons attract the protons just as much as the

protons attract the protons with respect to the nuclear force.

So neutrons are actually good, because when you throw an extra

neutron into an atom you don't add to the coulomb repulsion,

but you add to the overall attraction that they all feel

for each other due to the nuclear force.

So neutrons are like the glue.

As you add more and more protons, you will find that

you've got to add more and more neutrons to compensate the

coulomb attraction.

But a time will come when the nucleus becomes so big,

that even if you add enough neutrons,

the repulsion between protons from one end of the nucleus to

the other is now becoming comparable to the attraction due

to the nuclear force, because nucleus has become so

big this factor is no longer negligible.

See, over long distances a coulomb force will always

triumph, because no matter what the

prefactors are, the exponential factor in front

of the nuclear force will always weaken it.

That's why you cannot have nuclei beyond some size.

If you make them any bigger, the nuclear electrical

repulsion between the distant parts of the protons,

due to the distant protons in the nucleus,

cannot be compensated by the short-range attraction.

So it's the range of the interaction that is a

significant factor here.

So all the strong forces are strong, but at short distances

the coulomb force is not that strong, but it falls like 1 over

r^(2).

Now gravity, on the other hand,

is exactly 1 over r^(2)^( )with a number

that's much, much, much smaller than this,

but then we saw the other day why gravity managed to survive,

because this is q_1q

_2 and the q's can be added

algebraically and cancel each other.

Whereas if you've got m_1m

_2_ over r^(2)^( )there is no way

to cancel the m.

This is how the different forces manage to survive for the

different reasons, okay?

Nuclear wins in the nuclear zone, but dies very quickly

outside the size of a nucleus.