WEBVTT

00:02.550 --> 00:05.560
Prof: So,
I've got to start by telling

00:05.558 --> 00:09.108
you the syllabus for this
term--not the detailed one,

00:09.113 --> 00:10.963
just the big game plan.

00:10.960 --> 00:14.770
The game plan is:
we will do electromagnetic

00:14.772 --> 00:15.572
theory.

00:15.570 --> 00:19.340
Electromagnetism is a new force
that I will introduce to you and

00:19.336 --> 00:21.066
go through all the details.

00:21.070 --> 00:24.860
And I will do optics,
and optics is part of

00:24.863 --> 00:26.583
electromagnetism.

00:26.580 --> 00:30.740
And then near the end we will
do quantum mechanics.

00:30.740 --> 00:34.710
Now, quantum mechanics is not
like a new force.

00:34.710 --> 00:36.490
It's a whole different ball
game.

00:36.490 --> 00:40.640
It's not about what forces are
acting on this or that object

00:40.637 --> 00:43.447
that make it move,
or change its path.

00:43.450 --> 00:46.320
The question there is:
should we be even thinking

00:46.316 --> 00:47.566
about trajectories?

00:47.570 --> 00:49.550
Should we be even thinking
about particles going on any

00:49.552 --> 00:50.032
trajectory?

00:50.030 --> 00:53.010
Forget about what the right
trajectory is.

00:53.010 --> 00:57.970
And you will find out that most
of the cherished ideas get

00:57.966 --> 00:59.006
destroyed.

00:59.010 --> 01:03.990
But the good news is that you
need quantum mechanics only to

01:03.991 --> 01:08.131
study very tiny things like
atoms or molecules.

01:08.129 --> 01:10.279
Of course the big question is,
you know, where do you draw the

01:10.281 --> 01:10.531
line?

01:10.530 --> 01:12.960
How small is small?

01:12.959 --> 01:15.999
Some people even ask me,
"Do you need quantum

01:15.998 --> 01:18.848
mechanics to describe the human
brain?"

01:18.849 --> 01:21.639
And the answer is,
"Yes, if it is small

01:21.637 --> 01:22.607
enough."

01:22.610 --> 01:25.290
So, I've gone to parties where
after a few minutes of talking

01:25.289 --> 01:29.059
to a person I'm thinking,
"Okay, this person's brain

01:29.058 --> 01:33.118
needs a fully quantum mechanical
treatment."

01:33.120 --> 01:36.640
But most of the time everything
macroscopic you can describe the

01:36.638 --> 01:39.708
way you do with Newtonian
mechanics, electrodynamics.

01:39.709 --> 01:42.569
You don't need quantum theory.

01:42.569 --> 01:46.799
All right, so now we'll start
with the brand new force of

01:46.796 --> 01:48.226
electromagnetism.

01:48.230 --> 01:51.710
But before doing the force,
I've got to remind you people

01:51.705 --> 01:55.235
of certain things I expect you
all to understand about the

01:55.242 --> 01:58.752
dynamics between force,
and mass, and acceleration that

01:58.747 --> 02:00.627
you must have learned last term.

02:00.629 --> 02:01.949
I don't want to take any
chances.

02:01.950 --> 02:10.980
I'm going to start by reminding
you how we use this famous

02:10.982 --> 02:14.312
equation of Newton.

02:14.310 --> 02:16.200
So you've seen this equation,
probably,

02:16.199 --> 02:18.909
in high school,
but it's a lot more subtle than

02:18.913 --> 02:21.313
you think,
certainly a lot more subtle

02:21.307 --> 02:23.717
than I thought when I first
learned it.

02:23.720 --> 02:27.490
So I will tell you what I
figured out over these years on

02:27.491 --> 02:30.321
different ways to look at F =
ma.

02:30.318 --> 02:33.318
In other words,
if you have the equation what's

02:33.324 --> 02:34.244
it good for?

02:34.240 --> 02:37.640
The only thing anybody knows
right away is a stands

02:37.644 --> 02:40.454
for acceleration,
and we all know how to measure

02:40.450 --> 02:40.870
it.

02:40.870 --> 02:44.400
By the way, anytime I write any
symbol on the board you should

02:44.400 --> 02:46.890
be able to tell me how you'd
measure it,

02:46.889 --> 02:49.599
otherwise you don't know what
you're talking about as a

02:49.598 --> 02:50.198
physicist.

02:50.199 --> 02:53.099
Acceleration,
I think I won't spend too much

02:53.102 --> 02:55.062
time on how you measure it.

02:55.060 --> 02:57.610
You should know what
instruments you will need.

02:57.610 --> 03:00.920
So I will remind you that if
you have a meter stick,

03:00.921 --> 03:04.821
or many meter sticks and clocks
you can follow the body as it

03:04.819 --> 03:05.469
moves.

03:05.468 --> 03:08.448
You can find its position now,
its position later,

03:08.454 --> 03:10.834
take the difference,
divide by the time,

03:10.830 --> 03:12.110
you get velocity.

03:12.110 --> 03:15.140
Then find the velocity now,
find the velocity later,

03:15.143 --> 03:17.223
take the difference,
divide by time,

03:17.223 --> 03:18.893
you've got acceleration.

03:18.889 --> 03:22.639
So acceleration really requires
three measurements,

03:22.639 --> 03:25.529
two for each velocity,
but we talk of acceleration

03:25.532 --> 03:28.722
right now because you can make
those three measurements

03:28.721 --> 03:32.091
arbitrarily near each other,
and in the limit in which the

03:32.092 --> 03:34.992
time difference between them
goes to zero you can talk about

03:34.988 --> 03:37.588
the velocity right now and
acceleration right now.

03:37.590 --> 03:40.290
But in your car,
the needle points at 60 that's

03:40.292 --> 03:41.822
your velocity right now.

03:41.819 --> 03:43.749
It's an instantaneous quantity.

03:43.750 --> 03:45.870
And if you step on the gas you
feel this push.

03:45.870 --> 03:47.840
That's your acceleration right
now.

03:47.840 --> 03:50.810
That's a property of that
instant.

03:50.810 --> 03:55.660
So we know acceleration,
but the question is can I use

03:55.656 --> 03:59.676
the equation to find the mass of
anything.

03:59.680 --> 04:03.080
Now, very often when I pose the
question the answer given is,

04:03.078 --> 04:05.508
you know, go to a scale,
a weighing machine,

04:05.513 --> 04:06.763
and find the mass.

04:06.758 --> 04:09.238
And as you know,
that's not the correct answer

04:09.235 --> 04:12.475
because the weight of an object
is related to being near the

04:12.479 --> 04:16.079
earth due to gravity,
but the mass of an object is

04:16.083 --> 04:17.483
defined anywhere.

04:17.480 --> 04:20.450
So here's one way you can do it.

04:20.449 --> 04:23.609
Now you might say, "Well,
take a known force and find the

04:23.607 --> 04:26.897
acceleration it produces,"
but we haven't talked about how

04:26.901 --> 04:28.551
to measure the force either.

04:28.550 --> 04:30.750
All you have is this equation.

04:30.750 --> 04:36.840
The correct thing to do is to
buy yourself a spring and go to

04:36.841 --> 04:43.341
the Bureau of Standards and tell
them to loan you a block of some

04:43.338 --> 04:45.758
material,
I forgot what it is.

04:45.759 --> 04:48.219
That's called a kilogram.

04:48.220 --> 04:51.060
That is a kilogram by
definition.

04:51.060 --> 04:53.010
There is no God-given way to
define mass.

04:53.009 --> 04:55.739
You pick a random entity and
say that's a kilogram.

04:55.740 --> 04:57.480
So that's not right and that's
not wrong.

04:57.480 --> 04:59.650
That's what a kilogram is.

04:59.649 --> 05:03.619
So you bring that kilogram,
you hook it up on the spring,

05:03.624 --> 05:07.464
and you pull it by some amount,
maybe to that position,

05:07.456 --> 05:09.086
and you release it.

05:09.088 --> 05:12.558
You notice the acceleration of
the 1 kilogram,

05:12.562 --> 05:15.652
and the mass of the thing is
just one.

05:15.649 --> 05:18.079
Then you detach that mass.

05:18.079 --> 05:21.809
Then you ask--Then the person
says, "What's the mass of

05:21.807 --> 05:23.257
something else?"

05:23.259 --> 05:25.149
I don't know what the something
else is.

05:25.149 --> 05:26.989
Let's say a potato.

05:26.990 --> 05:32.250
And you take the potato or
anything, elephant.

05:32.250 --> 05:33.750
Here's a potato.

05:33.750 --> 05:38.670
You pull that guy by the same
distance, and you release that,

05:38.666 --> 05:41.286
and you find its acceleration.

05:41.290 --> 05:44.580
Since you pulled it by the same
amount, the force is the same,

05:44.581 --> 05:45.501
whatever it is.

05:45.500 --> 05:47.890
We don't know what it is,
but it's the same.

05:47.889 --> 05:51.819
Therefore we know the
acceleration of 1 kilogram times

05:51.815 --> 05:55.365
1 kilogram is equal to the
unknown mass times the

05:55.369 --> 05:58.109
acceleration of the unknown
mass.

05:58.110 --> 06:03.860
That's how by measuring this
you can find what the mass is.

06:03.860 --> 06:05.940
In principle you can find the
mass of everything.

06:05.939 --> 06:11.139
So imagine masses of all
objects have been determined by

06:11.141 --> 06:12.561
this process.

06:12.560 --> 06:17.230
Then you can also use F =
ma to find out what forces

06:17.226 --> 06:21.086
are acting on bodies in
different situations,

06:21.089 --> 06:23.779
because if you don't know what
force is acting on a body you

06:23.783 --> 06:24.973
cannot predict anything.

06:24.970 --> 06:27.580
So you can go back to the
spring and say,

06:27.581 --> 06:31.371
"I want to know what force
the spring exerts when it's

06:31.370 --> 06:33.330
pulled by various amounts.

06:33.329 --> 06:36.059
Well, you pull it by some
amount x.

06:36.060 --> 06:40.090
You attach it to a non-mass and
you find the acceleration,

06:40.091 --> 06:41.721
and that's the force.

06:41.720 --> 06:45.460
And if you plot it,
you'll find F as a

06:45.461 --> 06:50.391
function of x will be
roughly a straight line and it

06:50.392 --> 06:53.712
will take the form F =
-kx,

06:53.709 --> 06:56.199
and that k is called a
force constant.

06:56.199 --> 07:01.129
So this is an example of your
finding out the left hand side

07:01.125 --> 07:02.625
of Newton's law.

07:02.629 --> 07:06.569
You've got to understand the
distinction between F =

07:06.567 --> 07:08.607
-kx and F = ma.

07:08.610 --> 07:10.380
What's the difference?

07:10.379 --> 07:14.239
This says if you know the force
I can tell you the acceleration,

07:14.237 --> 07:17.907
but it's your job to go find
out every time what forces might

07:17.910 --> 07:19.380
be acting on a body.

07:19.379 --> 07:22.129
If it's connected to a spring,
and you pull the spring and it

07:22.132 --> 07:24.782
exerts a force,
someone's got to make this

07:24.783 --> 07:28.153
measurement to find out what the
force will be.

07:28.149 --> 07:31.519
All right, so that's one kind
of force.

07:31.519 --> 07:35.799
Another force that you can find
is if you're near the surface of

07:35.797 --> 07:38.447
the earth,
if you drop something,

07:38.446 --> 07:41.976
it seems to accelerate towards
the ground,

07:41.980 --> 07:48.080
and everything accelerates by
the same amount g.

07:48.079 --> 07:51.049
Well, according to Newton's
laws if anything is going to

07:51.052 --> 07:53.702
accelerate, it's because there's
a force on it.

07:53.699 --> 07:58.109
The force on any mass m
must be mg,

07:58.105 --> 08:03.515
because if I divide by m
I've got to get g.

08:03.519 --> 08:06.769
So the force on masses near the
earth is mg.

08:06.769 --> 08:09.749
That's another force.

08:09.750 --> 08:12.540
Something interesting about
that force is that unlike the

08:12.543 --> 08:15.243
spring force where the spring is
touching the mass,

08:15.240 --> 08:18.070
you can see it's pulling it,
or when I push this chair you

08:18.067 --> 08:22.247
can see I'm doing it,
the pull of gravity is a bit

08:22.250 --> 08:24.780
strange,
because there is no real

08:24.779 --> 08:28.249
contact between the earth and
the object that's falling.

08:28.250 --> 08:31.630
It was a great abstraction to
believe that things can reach

08:31.634 --> 08:34.614
out and pull things which are
not touching them,

08:34.610 --> 08:39.270
and gravity was the first
formally described force where

08:39.273 --> 08:40.633
that was true.

08:40.629 --> 08:46.169
And another excursion in the
same theme is if this object

08:46.168 --> 08:50.378
gets very far,
say like the moon over there,

08:50.375 --> 08:54.115
then the force is not given by
mg,

08:54.120 --> 09:01.520
but the force is given by this
law of gravitation.

09:01.519 --> 09:03.109
For every r near the
surface of the earth,

09:03.110 --> 09:06.390
if you put r equal to
the surface of the earth you

09:06.386 --> 09:09.426
will get a constant force that
is just mg,

09:09.428 --> 09:11.768
but if you move far from the
center of the earth you've got

09:11.769 --> 09:14.729
to take that into account,
and that's what Newton did and

09:14.731 --> 09:17.721
realized the force goes like 1
over r^(2).

09:17.720 --> 09:23.160
So every time things accelerate
you've got to find the reason,

09:23.155 --> 09:25.915
and that reason is the force.

09:25.918 --> 09:28.758
Many times many forces can be
acting on a body,

09:28.759 --> 09:30.949
and if you put all the forces
that are acting on a body and

09:30.952 --> 09:33.192
that explains the acceleration,
you're done,

09:33.190 --> 09:35.090
but sometimes it won't.

09:35.090 --> 09:38.430
That's when you have a new
force.

09:38.428 --> 09:42.708
And the final application of
F = ma is this one.

09:42.710 --> 09:46.100
If you knew the force,
for example,

09:46.102 --> 09:49.802
on a planet,
and here's a planet going

09:49.796 --> 09:53.186
around the sun and it is here.

09:53.190 --> 09:55.840
This is the sun,
and you know the force acting

09:55.841 --> 09:59.021
on it given by Newton's Law of
Gravity you can find the

09:59.024 --> 10:02.564
acceleration that will help you
find out where it will be one

10:02.561 --> 10:06.341
second later,
and you repeat the calculation,

10:06.337 --> 10:08.767
you will get the trajectory.

10:08.769 --> 10:10.559
So F = ma is good for
three things,

10:10.558 --> 10:13.728
that's what I want you to
understand: to define mass,

10:13.730 --> 10:17.410
to calculate forces acting on
bodies by seeing how they

10:17.413 --> 10:20.063
accelerate,
and finally to find the

10:20.062 --> 10:23.082
acceleration of bodies given the
forces.

10:23.080 --> 10:27.000
This is the cycle of Newtonian
dynamics.

10:27.000 --> 10:32.220
And what I'm going to do now is
to add one more new force,

10:32.215 --> 10:37.705
because I'm going to find out
that there is another force not

10:37.705 --> 10:39.165
listed here.

10:39.168 --> 10:42.688
I'm going to demonstrate to you
that new force,

10:42.692 --> 10:43.232
okay?

10:43.230 --> 10:44.990
Here's my demonstration.

10:44.990 --> 10:48.750
The only demonstration you will
see in my class,

10:48.750 --> 10:52.830
because everything else I've
tried generally failed,

10:52.830 --> 10:55.230
but this one always works.

10:55.230 --> 11:01.150
So, I have here a piece of
paper, okay?

11:01.149 --> 11:05.619
Then I take this trusty comb
and I comb the part of my head

11:05.619 --> 11:08.469
that's suited for this
experiment,

11:08.470 --> 11:13.890
then I bring it next to this,
and you see I'm able to lift

11:13.893 --> 11:14.563
that.

11:14.558 --> 11:18.118
Now, that's not the force of
gravity because gravity doesn't

11:18.116 --> 11:20.646
care if you comb your hair or
not, okay?

11:20.649 --> 11:25.599
And also when I shake it,
it falls down.

11:25.600 --> 11:28.660
So you're thinking, "Okay,
maybe there is a new force but

11:28.655 --> 11:32.225
it doesn't look awfully strong
because it's not able to even

11:32.227 --> 11:35.507
overcome gravity,
because it eventually yielded

11:35.514 --> 11:39.754
to gravity and fell down,"
but it's actually a mistake to

11:39.754 --> 11:40.594
think so.

11:40.590 --> 11:45.880
In fact this new force that I'm
talking about is 10 to the power

11:45.880 --> 11:49.410
of 40 stronger than
gravitational force.

11:49.408 --> 11:52.948
I will tell you by what metric
I came up with that number,

11:52.950 --> 11:55.310
but it's an enormously strong
force.

11:55.308 --> 11:59.738
You've got to understand why I
say it is such a strong force

11:59.736 --> 12:03.036
when, when I shook it the thing
fell down.

12:03.038 --> 12:08.548
So the reason is that if you
look at this experiment,

12:08.548 --> 12:11.148
here's the comb and here's the
paper,

12:11.149 --> 12:13.069
the comb is trying to pull the
paper,

12:13.070 --> 12:17.260
but what is trying to pull it
down?

12:17.259 --> 12:21.219
What is trying to pull it down?

12:21.220 --> 12:24.340
So here is me,
here is that comb,

12:24.337 --> 12:26.187
here's the paper.

12:26.190 --> 12:34.260
The entire planet is pulling it
down: Himalayas pulling it down,

12:34.260 --> 12:38.100
Pacific Ocean,
pulling it down,

12:38.104 --> 12:44.514
Bin Laden sitting in his cave
pulling it down.

12:44.509 --> 12:47.219
Everything is pulling it down,
okay?

12:47.220 --> 12:50.730
I am one of these people
generally convinced the world is

12:50.729 --> 12:53.549
acting against me,
but this time I'm right.

12:53.548 --> 12:57.348
Everything is acting against
me, and I'm able to triumph

12:57.354 --> 13:00.264
against all of that with this
tiny comb.

13:00.259 --> 13:03.169
And that is how you compare the
electric force with the

13:03.166 --> 13:04.346
gravitational force.

13:04.350 --> 13:08.240
It takes the entire planet to
compensate whatever tiny force I

13:08.236 --> 13:11.356
create between the comb and the
piece of paper.

13:11.360 --> 13:13.580
To really get a number out of
this I'll have to do a little

13:13.582 --> 13:17.162
more,
but I just want to point out to

13:17.163 --> 13:23.083
you this is a new force much
stronger than gravitation.

13:23.080 --> 13:27.100
So I want to tell you a few
other experiments people did

13:27.102 --> 13:31.202
without going into what the
explanation is right now,

13:31.200 --> 13:35.590
but let me just tell you if you
go through history what all did

13:35.590 --> 13:36.440
people do.

13:36.440 --> 13:42.680
So one experiment you can do:
You take a piece of glass and

13:42.678 --> 13:49.238
you rub it on some animal that's
passing by, water buffalo.

13:49.240 --> 13:52.580
That's why I cannot do all the
experiments in class.

13:52.580 --> 13:56.460
You rub it on that guy,
then you do it to a second

13:56.456 --> 13:59.466
piece of glass,
and you find out that they

13:59.467 --> 14:02.367
repel each other,
meaning if you put them next to

14:02.366 --> 14:04.326
each other they tend to fly
apart.

14:04.330 --> 14:09.260
Then you take a piece of hard
rubber and you rub that on

14:09.264 --> 14:10.794
something else.

14:10.788 --> 14:14.898
I forgot what,
silk, Yeti, some other thing.

14:14.899 --> 14:15.769
Then you put that here.

14:15.769 --> 14:18.669
So I'll give a different shape
to that thing.

14:18.669 --> 14:20.129
That's the rubber stick.

14:20.129 --> 14:25.339
And you find when you do that
to this, these two attract each

14:25.335 --> 14:26.025
other.

14:26.028 --> 14:30.138
Sometimes they repel,
sometimes they attract.

14:30.139 --> 14:35.049
Here's another thing you can
do: Buy some nylon thread.

14:35.048 --> 14:39.168
You hang a small metallic
sphere, and you bring one of

14:39.166 --> 14:41.026
these rods next to it.

14:41.029 --> 14:42.909
It doesn't matter which one.

14:42.908 --> 14:48.388
Initially they're attracted and
suddenly when you touch it and

14:48.388 --> 14:51.888
you remove it,
they start repelling each

14:51.890 --> 14:52.790
other.

14:52.789 --> 14:53.689
What's going on?

14:53.690 --> 14:56.150
That's another thing you could
do.

14:56.149 --> 15:01.389
Last thing I want to mention is
if you took two of these things

15:01.389 --> 15:05.109
which are repelling each other,
let's say.

15:05.110 --> 15:08.530
Let's say they're attracting
each other like this.

15:08.528 --> 15:12.868
Then you connect them with a
piece of nylon and you take it

15:12.871 --> 15:14.671
away, nothing happens.

15:14.668 --> 15:19.108
If you connect them with a
piece of wire and take away the

15:19.109 --> 15:22.379
wire, they no longer attract
each other.

15:22.379 --> 15:24.159
So these are examples of
different things.

15:24.158 --> 15:26.018
I'm just going to say,
you do this,

15:26.018 --> 15:27.328
you do this,
you do that,

15:27.330 --> 15:30.610
then finally you need a theory
that explains everything.

15:30.610 --> 15:34.310
So that's the theory that I'm
going to give you now.

15:34.308 --> 15:36.808
That's the theory of
electrostatics.

15:36.808 --> 15:40.338
And I don't have time to go
into the entire history of how

15:40.335 --> 15:42.805
people arrived at this final
formula,

15:42.808 --> 15:48.768
so I'm just going to tell you
one formula that really will

15:48.773 --> 15:53.903
explain everything that I've
described so far,

15:53.899 --> 16:00.009
and that formula is called
Coulomb's Law.

16:00.009 --> 16:02.729
Even though Mr. Coulomb's
name is on it,

16:02.727 --> 16:06.907
he was not the first one to
formulate parts of the law,

16:06.908 --> 16:10.988
but he gave the final and
direct verification of Coulomb's

16:10.990 --> 16:14.140
Law that other people who had
contributed.

16:14.139 --> 16:20.589
So Coulomb's Law says that
certain entities have a property

16:20.590 --> 16:22.370
called charge.

16:22.370 --> 16:26.770
You have charge or you don't
have charge, but if you have

16:26.767 --> 16:31.157
charge the charge that you have,
you meaning any of these

16:31.163 --> 16:34.073
objects, is measured in
coulombs.

16:34.070 --> 16:36.470
Remember, that was not
Coulomb's idea to call it

16:36.469 --> 16:36.979
coulomb.

16:36.980 --> 16:39.440
Whenever you make a discovery,
you're breathlessly waiting

16:39.436 --> 16:41.156
that somebody will name it after
you,

16:41.158 --> 16:44.328
but it's not in good taste to
name to after yourself,

16:44.330 --> 16:46.150
but it carries Coulomb's name.

16:46.149 --> 16:48.769
So he didn't say call it
coulomb, okay,

16:48.774 --> 16:51.474
but he certainly wrote down
this law.

16:51.470 --> 16:55.520
The law says that if you've got
one entity which has some amount

16:55.515 --> 16:58.145
of charge called
q_1,

16:58.149 --> 17:01.409
and there's another entity that
has some amount of charge

17:01.408 --> 17:04.728
q_2 they will
exert a force on each other

17:04.726 --> 17:06.696
which is given by
q_1q

17:06.704 --> 17:09.734
_2 times this
constant which is somehow

17:09.731 --> 17:11.711
written as 1 over
4Πε

17:11.711 --> 17:13.691
_0.

17:13.690 --> 17:17.010
That's 1 over r^(2).

17:17.009 --> 17:18.889
But r is the distance
between them,

17:18.887 --> 17:21.217
and you can ask in this
picture, what do you mean by

17:21.223 --> 17:21.823
distance?

17:21.818 --> 17:24.528
I mean, is it from here to
there, or is it from center to

17:24.525 --> 17:24.955
center?

17:24.960 --> 17:28.840
We're assuming here that the
distance between them is much

17:28.837 --> 17:31.217
bigger than the individual
sizes.

17:31.220 --> 17:33.420
For example,
you say, how far am I from Los

17:33.422 --> 17:34.792
Angeles, well,
3,225 miles,

17:34.786 --> 17:37.876
but you can say are you taking
about your right hand or your

17:37.880 --> 17:38.720
left hand?

17:38.720 --> 17:41.870
Well, I'm a point particle for
this purpose so it doesn't

17:41.873 --> 17:42.383
matter.

17:42.380 --> 17:45.590
So here we're assuming that
either they're mathematically

17:45.585 --> 17:48.955
point charges or they're real
charges with a finite size but

17:48.961 --> 17:52.111
separated by a distance much
bigger than the size,

17:52.108 --> 17:53.988
so r could stand,
if you like,

17:53.990 --> 17:55.550
for center to center.

17:55.549 --> 17:58.629
It doesn't matter too much.

17:58.630 --> 18:00.930
So this is what Coulomb said.

18:00.930 --> 18:03.060
Now, if you look at this number
here,

18:03.058 --> 18:05.858
1 over 4Πε
_0,

18:05.858 --> 18:12.008
its value is 9 times 10 to the
9^(th).

18:12.009 --> 18:16.309
What that means is the
following: If you take one body

18:16.307 --> 18:20.647
with 1 coulomb of charge,
another body with 1 coulomb of

18:20.653 --> 18:23.563
charge and they're separated by
1 meter,

18:23.558 --> 18:27.258
then the force between them
will be this number,

18:27.259 --> 18:28.879
because everything else is a 1.

18:28.880 --> 18:32.440
It'll be 9 times 10 to the 9
newtons.

18:32.440 --> 18:35.000
That's an enormous force,
and normally you don't run into

18:34.998 --> 18:37.508
1 coulomb of charge,
but the reason why a coulomb

18:37.507 --> 18:40.727
was picked is sort of historical
and it has to do with currents

18:40.732 --> 18:41.412
and so on.

18:41.410 --> 18:45.050
But anyway, this is the
definition.

18:45.048 --> 18:49.168
But if you want to be more
precise, I should write a

18:49.170 --> 18:53.290
formula more carefully because
force is a vector.

18:53.288 --> 18:58.118
Also I should say force on whom
and due to what.

18:58.118 --> 19:01.358
So let's say there are two
charges,

19:01.358 --> 19:05.338
and say q_1 is
sitting at the origin and

19:05.339 --> 19:09.819
q_2 is sitting
at a point whose position is the

19:09.817 --> 19:11.237
vector r.

19:11.240 --> 19:17.340
Then the force on 2 due to 1 is
given by q_2q

19:17.336 --> 19:22.786
_1 over
4Πε_0

19:22.790 --> 19:27.070
times 1 over
r^(2).

19:27.068 --> 19:30.278
That's the magnitude of the
force, but I want to suggest

19:30.281 --> 19:33.441
that the force is such that
q_1 pushes

19:33.436 --> 19:35.186
q_2 away.

19:35.190 --> 19:38.130
So I want to make this into a
vector, but I've got the

19:38.127 --> 19:39.567
magnitude of the vector.

19:39.568 --> 19:42.578
As you know,
to make a real vector you take

19:42.580 --> 19:47.100
its magnitude and multiply it by
a vector of unit length in that

19:47.096 --> 19:48.456
same direction.

19:48.460 --> 19:51.150
The unit vector we can write in
many ways.

19:51.150 --> 19:53.290
One is just to say
e_r,

19:53.286 --> 19:56.646
e_r_
is a standard name for a

19:56.654 --> 19:59.784
vector of length 1 in the
direction of r.

19:59.779 --> 20:01.299
But I'll give you another
choice.

20:01.298 --> 20:04.478
You can also write it as
r divided by the length

20:04.483 --> 20:05.313
of r.

20:05.308 --> 20:08.058
That also would be a vector of
unit length parallel to

20:08.058 --> 20:08.628
r.

20:08.630 --> 20:11.800
So there are many ways to write
the thing that makes it a

20:11.799 --> 20:12.309
vector.

20:12.308 --> 20:24.268
And F_21 is
minus of F_12.

20:24.269 --> 20:28.989
Now, how do we get attraction
and how do we get repulsion?

20:28.990 --> 20:30.300
We get it because
q_1 and

20:30.300 --> 20:32.510
q_2,
if they're both positive and

20:32.509 --> 20:35.669
you if you use the formula,
you'll find they repel each

20:35.665 --> 20:38.255
other, but if they're of
opposite signs,

20:38.259 --> 20:40.829
you'll do the same calculation,
but you'll put a minus sign in

20:40.830 --> 20:41.970
front of the whole thing.

20:41.970 --> 20:46.670
That'll turn repulsion into an
attraction.

20:46.670 --> 20:50.110
So you must allow for the
possibility that q can be

20:50.105 --> 20:53.045
of either sign;
q can also be 0.

20:53.048 --> 20:55.938
There are certain entities
which don't have any electric

20:55.942 --> 20:59.102
charge, so if you put them next
to a million coulombs nothing

20:59.097 --> 20:59.727
happens.

20:59.730 --> 21:00.900
So some things have plus charge.

21:00.900 --> 21:02.290
Some things have minus charge.

21:02.288 --> 21:09.338
Some things have no charge,
but they're all contained in

21:09.337 --> 21:12.027
this Coulomb's Law.

21:12.028 --> 21:16.308
Now, again, skipping all the
intermediate discoveries,

21:16.307 --> 21:21.227
I want to tell you a couple of
things we know about charge.

21:21.230 --> 21:30.360
First thing is - q is
conserved.

21:30.358 --> 21:34.508
Conserved is a physics terms
for saying--does not change with

21:34.506 --> 21:34.986
time.

21:34.990 --> 21:36.670
For example,
when you say energy is

21:36.674 --> 21:39.074
conserved,
it means particles can come and

21:39.069 --> 21:41.159
collide and do all kinds of
things,

21:41.160 --> 21:44.280
but if you add that energy
before, you'll get the same

21:44.281 --> 21:47.101
answer afterwards,
and whenever that happens,

21:47.098 --> 21:48.738
the quantity is conserved.

21:48.740 --> 21:52.300
The claim is electrical charge
is conserved.

21:52.298 --> 21:55.698
So electrical charge may
migrate from A to B or B to A,

21:55.700 --> 21:57.030
but if you add up the total
charge,

21:57.029 --> 22:00.249
say the chemical reaction of
any process,

22:00.250 --> 22:02.910
including in big particle
accelerators where things

22:02.913 --> 22:05.633
collide and all kinds of stuff
comes flying out,

22:05.630 --> 22:08.990
the charge of the final
products always equal to the

22:08.990 --> 22:11.230
charge of the incoming products.

22:11.230 --> 22:16.280
But charge conservation needs
to be amended with one extra

22:16.278 --> 22:18.758
term, extra qualification.

22:18.759 --> 22:22.279
It's called local.

22:22.278 --> 22:26.328
Suppose I say the number of
students in the class is

22:26.327 --> 22:27.277
conserved?

22:27.278 --> 22:31.078
That means you count them any
time, you've got to get the same

22:31.078 --> 22:31.638
number.

22:31.640 --> 22:33.880
Well, here's one possibility.

22:33.880 --> 22:39.590
Suddenly one of you guys
disappears and appears here at

22:39.589 --> 22:41.599
the same instant.

22:41.598 --> 22:44.608
That's also consistent with
conservation of student number

22:44.611 --> 22:46.461
because the number didn't
change.

22:46.460 --> 22:50.350
What disappeared there,
appeared here.

22:50.348 --> 22:53.168
But that is not a local
conservation of charge because

22:53.174 --> 22:56.374
it disappears in one part of the
world and appears in another

22:56.373 --> 22:56.803
one.

22:56.798 --> 23:03.038
And it's not even a meaningful
law to have in the presence of

23:03.038 --> 23:04.388
relativity.

23:04.390 --> 23:09.810
Can any of you guys think of
why that might be true,

23:09.808 --> 23:13.568
why a charge disappearing
somewhere and appearing

23:13.568 --> 23:17.718
somewhere else cannot be a very
profound principle?

23:17.720 --> 23:18.650
Yes?

23:18.650 --> 23:19.240
Student:
>

23:19.240 --> 23:20.980
Prof: Yep?

23:20.980 --> 23:22.800
Student:  Well,
if it's in the same instant

23:22.799 --> 23:24.839
disappearing from one place and
appearing another place,

23:24.844 --> 23:26.224
it's traveling faster than
light?

23:26.220 --> 23:29.500
Prof: Well,
we don't know that it was the

23:29.503 --> 23:31.743
same thing that even traveled.

23:31.740 --> 23:33.630
It may not have traveled.

23:33.630 --> 23:36.840
It may even be--Here's another
thing.

23:36.838 --> 23:40.048
Suppose an electron,
suppose a proton disappears

23:40.049 --> 23:42.509
there and a positron appears
here.

23:42.509 --> 23:45.659
That still conserves charge,
but we don't think that the

23:45.661 --> 23:48.471
proton traveled and became the
positron, right?

23:48.470 --> 23:51.960
So it is not that it has
traveled.

23:51.960 --> 23:52.390
You are right.

23:52.390 --> 23:53.510
I hadn't thought about that.

23:53.509 --> 23:56.879
It's a good point that it
implies it traveled infinitely

23:56.882 --> 24:00.012
fast, but that's not the reason
you object to it.

24:00.009 --> 24:00.809
Yep?

24:00.808 --> 24:03.978
Student:  It's not
necessarily simultaneous.

24:03.980 --> 24:05.160
Prof: That is the
correct answer.

24:05.160 --> 24:10.370
The answer is it is not
simultaneous in every frame of

24:10.369 --> 24:11.549
reference.

24:11.548 --> 24:14.648
You must know from the special
theory that if two events are

24:14.645 --> 24:16.845
simultaneous in one frame of
reference,

24:16.848 --> 24:19.598
if you see those same two
events in a moving train,

24:19.598 --> 24:23.598
or plane, or anything they will
not be simultaneous.

24:23.598 --> 24:26.288
Therefore, in any other frame
of reference,

24:26.288 --> 24:29.488
either the charge would have
been created first and then

24:29.491 --> 24:32.231
after a period of time
reappeared somewhere,

24:32.230 --> 24:35.530
I mean, destroyed somewhere and
appeared after a delay,

24:35.529 --> 24:38.559
or the appearance could take
place before the destruction,

24:38.558 --> 24:41.488
so suddenly you've got two
charges.

24:41.490 --> 24:48.130
So conservation of charge,
which is conserved non-locally,

24:48.130 --> 24:50.800
cannot have a significance
except in one frame of

24:50.797 --> 24:52.857
reference,
but if you believe that all

24:52.862 --> 24:55.842
observers are equivalent and you
want to write down laws that

24:55.844 --> 24:58.284
make sense for everybody it can
only be local.

24:58.279 --> 25:01.909
So electrical charge is
conserved and it is local,

25:01.914 --> 25:03.404
locally conserved.

25:03.400 --> 25:05.330
In other words,
stuff doesn't just disappear.

25:05.329 --> 25:07.209
Stuff just moves around.

25:07.210 --> 25:10.680
You can keep track of it,
and if you add it up you get

25:10.681 --> 25:11.861
the same number.

25:11.858 --> 25:19.738
The second part of q,
which is not necessary for any

25:19.740 --> 25:27.620
of these older phenomena,
is that q is quantized.

25:27.618 --> 25:32.968
That means the electrical
charge that we run into does not

25:32.971 --> 25:36.541
take a continuum of possible
values.

25:36.538 --> 25:38.278
For example,
the length of any object,

25:38.279 --> 25:40.489
you might think at least in
classical mechanics,

25:40.490 --> 25:41.760
is any number you like.

25:41.759 --> 25:45.549
It's a continuous variable,
but electric charge is not

25:45.549 --> 25:46.479
continuous.

25:46.480 --> 25:50.190
As far as we can tell,
all the charges we have ever

25:50.189 --> 25:54.639
seen are all multiples of a
certain basic unit of charge,

25:54.640 --> 26:04.050
which turns out to be 1.6 times
10 to the -19 coulombs.

26:04.048 --> 26:07.028
Every charge is either that or
some multiple of it.

26:07.028 --> 26:11.258
Multiple could be plus or minus
multiple.

26:11.259 --> 26:16.649
So charge is granular,
not continuous.

26:16.650 --> 26:22.070
Okay, so I'm going to give you
a little more knowledge we have

26:22.067 --> 26:27.037
had since the time of Coulomb
that sort or explains these

26:27.041 --> 26:28.021
things.

26:28.019 --> 26:31.199
I mean, what's really going on
microscopically?

26:31.200 --> 26:32.950
We don't have to pretend we
don't know.

26:32.950 --> 26:37.600
We do, so we might as well use
that information from now on.

26:37.598 --> 26:42.038
What we do know is that
everything is made up of atoms,

26:42.040 --> 26:46.400
and that if you look into the
atom it's got a nucleus,

26:46.400 --> 26:48.950
a lot of guys sitting here.

26:48.950 --> 26:53.440
Some are called protons and
some are called neutrons,

26:53.440 --> 26:58.880
and then there are some guys
running around called electrons.

26:58.880 --> 27:02.900
Of course we will see at the
end of the semester that this

27:02.903 --> 27:06.223
picture is wrong,
but it is good enough for this

27:06.221 --> 27:07.071
purpose.

27:07.068 --> 27:11.318
It's certainly true that there
are charges in an atom which are

27:11.316 --> 27:15.216
near the center and other light
charges which are near the

27:15.220 --> 27:17.070
periphery, are outside.

27:17.068 --> 27:21.018
All things carrying electric
charge in our world in daily

27:21.019 --> 27:23.769
life are either protons or
electrons.

27:23.769 --> 27:26.909
You can produce strange
particles in an accelerator.

27:26.910 --> 27:29.610
They would also carry some
charge which would in fact be a

27:29.608 --> 27:32.308
multiple of this charge,
but they don't live very long.

27:32.308 --> 27:36.098
So the stable things that you
and I are made of and just about

27:36.096 --> 27:39.626
everything in this room is made
of, is made up of protons,

27:39.634 --> 27:41.314
neutrons and electrons.

27:41.308 --> 27:46.128
The charge of the neutron,
as you can guess,

27:46.125 --> 27:46.905
is 0.

27:46.910 --> 27:51.800
The charge of the electron,
by some strange convention,

27:51.804 --> 27:55.434
was given this minus sign by
Franklin.

27:55.430 --> 28:04.210
And the charge of the proton is
plus 1.6 times into -19

28:04.211 --> 28:06.001
coulombs.

28:06.000 --> 28:10.930
There are a lot of amazing
things I find here.

28:10.930 --> 28:14.080
I don't know if you've thought
about it.

28:14.078 --> 28:18.398
The first interesting thing is
that every electron anywhere in

28:18.402 --> 28:21.452
the universe has exactly the
same charge.

28:21.450 --> 28:24.830
It also has exactly the same
mass.

28:24.829 --> 28:27.399
Now, you might say, "Look,
that's a tautology,"

28:27.403 --> 28:30.643
because if it wasn't the same
charge and if it wasn't the same

28:30.636 --> 28:32.806
mass you would call it something
else.

28:32.808 --> 28:36.428
But what makes it a non-empty
statement is that there are

28:36.431 --> 28:39.081
many, many, many,
many electrons which are

28:39.083 --> 28:40.703
absolutely identical.

28:40.700 --> 28:43.430
Look, you try to manufacture
two cars.

28:43.430 --> 28:45.560
The chance that they're
identical is 0,

28:45.560 --> 28:46.010
right?

28:46.009 --> 28:49.089
I got one of those cars so I
know that.

28:49.089 --> 28:50.079
It doesn't work.

28:50.079 --> 28:51.529
It's supposed to.

28:51.529 --> 28:56.249
So despite all the best efforts
people make, things are not

28:56.251 --> 28:57.231
identical.

28:57.230 --> 29:01.370
But at the microscopic level of
electrons and protons,

29:01.368 --> 29:05.508
every proton anywhere in the
universe is identical.

29:05.509 --> 29:08.149
And they can be manufactured in
a collision in another part of

29:08.150 --> 29:08.800
the universe.

29:08.798 --> 29:11.918
This can be manufactured in a
collision in Geneva,

29:11.922 --> 29:14.282
the stuff that comes out
identical.

29:14.278 --> 29:17.328
That is a mystery,
at least in classical mechanics

29:17.330 --> 29:18.390
it's a mystery.

29:18.390 --> 29:22.170
Quantum Field Theory gives you
an answer to at least why all

29:22.170 --> 29:25.180
electrons are identical,
and why all protons are

29:25.182 --> 29:26.082
identical.

29:26.078 --> 29:29.178
The fact that they're
absolutely identical particles

29:29.179 --> 29:30.759
is very, very important.

29:30.759 --> 29:34.509
It also makes your life easy,
because if every particle was

29:34.509 --> 29:38.069
different from every other
particle, you cannot make any

29:38.065 --> 29:39.095
predictions.

29:39.098 --> 29:42.498
We know that the hydrogen atom
on a receding galaxy is

29:42.499 --> 29:45.449
identical to the hydrogen atom
on the Earth.

29:45.450 --> 29:48.020
That's why when the radiation
coming from the atom has a

29:48.016 --> 29:50.906
shifted wavelength of frequency,
we attributed to the motion of

29:50.910 --> 29:51.610
the galaxy.

29:51.608 --> 29:55.268
From the Doppler Shift we find
out its speed.

29:55.269 --> 29:58.079
But another explanation could
be, well, that's a different

29:58.079 --> 29:58.869
hydrogen atom.

29:58.868 --> 30:01.058
Maybe that's why the answer's
different.

30:01.058 --> 30:04.108
But we all believe it's the
same hydrogen atom,

30:04.112 --> 30:06.172
but it's moving away from us.

30:06.170 --> 30:10.310
Therefore, one of the
remarkable things is that all

30:10.309 --> 30:13.539
electrons and all protons are
equal,

30:13.538 --> 30:17.448
but a really big mystery is why
is the charge of the electron

30:17.450 --> 30:20.970
exactly equal and opposite the
charge of the proton.

30:20.970 --> 30:22.060
They are not the same particle.

30:22.059 --> 30:23.789
Their masses are different.

30:23.788 --> 30:25.588
Their other interactions are
different.

30:25.588 --> 30:29.688
But in terms of electrical
charge these two numbers are

30:29.692 --> 30:32.962
absolutely equal as far as
anybody knows.

30:32.960 --> 30:34.230
That's another mystery.

30:34.230 --> 30:38.750
Two different particles,
not related by any manifest

30:38.746 --> 30:42.376
family relationship,
have the same charge,

30:42.376 --> 30:44.056
except in sign.

30:44.058 --> 30:46.898
And there are theories called
Grand Unified Theories which try

30:46.895 --> 30:49.795
to explain this,
but certainly not part of any

30:49.799 --> 30:53.939
standard established theory,
but it's key to everything we

30:53.935 --> 30:58.445
see in daily life because that's
what makes the atom electrically

30:58.452 --> 30:59.232
neutral.

30:59.230 --> 31:03.390
Okay, now we can understand the
quantization of charge,

31:03.390 --> 31:05.860
because charge is carried by
these guys and these guys are

31:05.855 --> 31:09.045
either there or not there,
so you can only have so many

31:09.048 --> 31:09.808
electrons.

31:09.808 --> 31:14.548
We cannot have a part of an
electron, or part of a proton.

31:14.548 --> 31:19.978
Now, let's try to understand
all these experiments in terms

31:19.976 --> 31:21.656
of what we know.

31:21.660 --> 31:24.730
First of all,
when you take this piece of

31:24.733 --> 31:29.043
glass, and you rub it,
the atoms in glass are neutral.

31:29.038 --> 31:31.558
They've got equal number of
protons and electrons,

31:31.560 --> 31:33.880
but when you rub it,
the glass atom loses some

31:33.876 --> 31:36.086
electrons to whatever you rubbed
it on.

31:36.088 --> 31:39.518
Therefore, it becomes
positively charged,

31:39.520 --> 31:43.210
because some negative has been
taken out.

31:43.210 --> 31:47.410
In the case of the rubber
stick, it gains the electrons

31:47.413 --> 31:52.323
and whatever animal you rubbed
it on, it loses the electrons.

31:52.318 --> 31:55.508
So actually real charge
transfer takes place only

31:55.509 --> 31:56.839
through electrons.

31:56.838 --> 31:59.438
Protons carry charge,
but you are never going to rip

31:59.442 --> 32:01.742
a proton out unless you use an
accelerator.

32:01.740 --> 32:04.730
It's really deeply bound to the
nucleus.

32:04.730 --> 32:07.690
Electrons are the ones who do
all the business of electricity

32:07.690 --> 32:08.480
in daily life.

32:08.480 --> 32:11.870
The current flowing in the
wire, in the circuit,

32:11.866 --> 32:14.386
it's all the motion of
electrons.

32:14.390 --> 32:19.920
So from this and Coulomb's Law,
can you understand the

32:19.916 --> 32:23.146
attraction between these two?

32:23.150 --> 32:26.700
How many people think you can,
from Coulomb's Law,

32:26.702 --> 32:30.402
understand the attraction
between these two rods?

32:30.400 --> 32:33.280
Nobody thinks you can?

32:33.279 --> 32:36.569
Well, why do you think you
cannot?

32:36.569 --> 32:37.679
You know why?

32:37.680 --> 32:40.640
Student:  Because
they're not point charges?

32:40.640 --> 32:46.590
Prof: Okay,
any other reason why Coulomb's

32:46.589 --> 32:49.069
Law is not enough?

32:49.068 --> 32:52.108
Well, how will we apply
Coulomb's Law to understand the

32:52.105 --> 32:54.125
attraction between these two
rods?

32:54.130 --> 32:55.910
What will you have to do?

32:55.910 --> 33:00.520
Student:  You'd have to
apply it to F = ma.

33:00.519 --> 33:01.749
Prof: No.

33:01.750 --> 33:04.370
Once you got the F, the
a will follow,

33:04.371 --> 33:06.891
but can you compute the force
between two rods?

33:06.890 --> 33:08.900
One of them has got a lot of
positive charge.

33:08.900 --> 33:10.940
One of them has a lot of
negative charge given Coulomb's

33:10.936 --> 33:11.156
Law.

33:11.160 --> 33:12.220
Yes?

33:12.220 --> 33:13.270
Student:  You don't know
the exact quantities of the

33:13.269 --> 33:13.429
charges..

33:13.432 --> 33:13.852
Prof: Pardon me?

33:13.847 --> 33:14.897
Student:  You don't know
the exact quantities of the

33:14.897 --> 33:15.167
charges.

33:15.170 --> 33:16.870
Prof: Suppose I tell you.

33:16.868 --> 33:18.788
I tell you how many charges
there are.

33:18.789 --> 33:19.749
Yes?

33:19.750 --> 33:21.860
Student:  You don't
which direction the attraction

33:21.861 --> 33:22.051
is.

33:22.048 --> 33:25.258
Prof: No,
we do know, because the plus

33:25.258 --> 33:28.538
and minus will be drawn towards
each other.

33:28.539 --> 33:29.959
Okay, I'll tell you what it is.

33:29.960 --> 33:32.890
It's an assumption we all make,
but you're not really supposed

33:32.894 --> 33:33.524
to make it.

33:33.519 --> 33:36.019
It's not a consequence of any
logic.

33:36.019 --> 33:41.009
Coulomb's Law talks about two
charges, two point charges.

33:41.009 --> 33:45.299
What if there are three charges
in the universe?

33:45.298 --> 33:49.718
What is the force this one will
experience due to these two?

33:49.720 --> 33:50.880
This is q_1.

33:50.880 --> 33:51.610
This is q_2.

33:51.609 --> 33:53.929
This is q_3.

33:53.930 --> 33:56.150
Coulomb's Law doesn't tell you
that.

33:56.150 --> 34:02.480
It tells you only two at a
time, but we make an extra

34:02.479 --> 34:10.029
assumption called superposition
which says that if you want the

34:10.025 --> 34:14.395
force on 3 (should read 1),
when there is

34:14.396 --> 34:16.156
q_1 and
q_2,

34:16.159 --> 34:20.619
you find the force due to
q_2 and you

34:20.619 --> 34:25.079
find the force due to
q_3 and you add

34:25.079 --> 34:26.089
them up.

34:26.090 --> 34:34.140
The fact that you can add these
two vectors is not a logical

34:34.139 --> 34:36.049
requirement.

34:36.050 --> 34:39.800
In fact, it's not even true at
an extremely accurate level that

34:39.800 --> 34:43.610
the force between two charges is
not affected by the presence of

34:43.612 --> 34:44.582
a third one.

34:44.579 --> 34:46.169
But it's an excellent
approximation,

34:46.168 --> 34:48.748
but you must realize it is
something you've got to find to

34:48.753 --> 34:49.983
be true experimentally.

34:49.980 --> 34:53.820
It's not something you can say
is logical consequence.

34:53.820 --> 34:57.580
Logically there is no reason
why the interaction between two

34:57.577 --> 35:01.717
entities should not be affected
by the presence of a third one.

35:01.719 --> 35:05.929
But it seems to be a very good
approximation for what we do,

35:05.929 --> 35:08.909
and that's the reason why
eventually we can find the force

35:08.911 --> 35:12.121
between an extended object,
another extended object by

35:12.121 --> 35:15.851
looking at the force on everyone
of these due to everyone of

35:15.846 --> 35:18.116
those and adding all the
vectors.

35:18.119 --> 35:21.739
Okay, so superposition plus
Coulomb's Law is what you need.

35:21.739 --> 35:24.989
Then you can certainly
understand the attraction.

35:24.989 --> 35:29.639
How about the comb and the
piece of paper?

35:29.639 --> 35:32.329
That's a very interesting
example and it's connected to

35:32.331 --> 35:32.881
this one.

35:32.880 --> 35:35.980
See, the piece of paper is
electrically neutral.

35:35.980 --> 35:39.280
So let me do paper and comb
instead of this one.

35:39.280 --> 35:40.910
It's got the same model.

35:40.909 --> 35:42.639
Here's the piece of paper.

35:42.639 --> 35:43.559
Here's the comb.

35:43.559 --> 35:47.559
The comb is positively charged.

35:47.559 --> 35:49.639
The paper is neutral.

35:49.639 --> 35:52.359
So anyway, there's nothing here
to be attracted to this one,

35:52.360 --> 35:56.840
but if you bring it close
enough, there are equal amount

35:56.838 --> 35:59.768
of positive and negative
charges,

35:59.768 --> 36:03.868
but what will happen is the
negative charges will migrate

36:03.869 --> 36:07.529
near these positive charges from
the other end,

36:07.530 --> 36:11.050
leaving positive charges in the
back,

36:11.050 --> 36:13.640
so that the system will
separate into a little bit of

36:13.643 --> 36:17.833
negative closer to the positive,
and the leftover positive will

36:17.827 --> 36:19.207
be further away.

36:19.210 --> 36:22.910
Therefore, even though it's
neutral the attraction of plus

36:22.911 --> 36:26.941
for this minus is stronger than
the repulsion of this plus with

36:26.940 --> 36:27.850
this plus.

36:27.849 --> 36:29.379
That's called polarization.

36:29.380 --> 36:32.510
So polarization is when charge
separates.

36:32.510 --> 36:34.710
Some materials cannot be
polarized, in which case no

36:34.706 --> 36:37.116
matter how much you do this with
a comb it won't work.

36:37.119 --> 36:39.089
Some materials can be polarized.

36:39.090 --> 36:42.510
The piece of paper is an
example of what can be

36:42.507 --> 36:43.397
polarized.

36:43.400 --> 36:44.960
We can understand that too.

36:44.960 --> 36:47.750
And in this example,
if you bring a lot of plus

36:47.748 --> 36:50.368
charges here,
and you look at what's going on

36:50.367 --> 36:52.617
here,
the minus guys here will sit

36:52.617 --> 36:55.967
here and the plus will be left
over in the back,

36:55.969 --> 36:59.049
and then this attraction
between plus and minus is bigger

36:59.045 --> 37:02.875
than this repulsion,
so it will be attracted to it.

37:02.880 --> 37:06.160
But once it touches it,
this rod touches that,

37:06.155 --> 37:09.865
then what you have is a lot of
plus charges here.

37:09.869 --> 37:11.639
They repel each other.

37:11.639 --> 37:12.989
They want to get out.

37:12.989 --> 37:14.179
Previously they couldn't get
out.

37:14.179 --> 37:17.369
They were stuck on the rod,
but now that you've made

37:17.365 --> 37:20.235
contact, some of them will jump
to that one.

37:20.239 --> 37:23.499
Then when you separate them,
you will have a ball with some

37:23.500 --> 37:25.790
plus charges,
and you will have a rod with

37:25.793 --> 37:31.883
more plus charges,
and they will repel each other.

37:31.880 --> 37:35.430
And finally I said if you take
two of these spheres,

37:35.431 --> 37:39.121
suppose one was positively
charged, one was negatively

37:39.123 --> 37:42.123
charged, they're attracting each
other.

37:42.119 --> 37:45.329
If you connect them with a
nylon wire or a wooden stick

37:45.329 --> 37:48.229
nothing happens,
but if you connect them with an

37:48.231 --> 37:51.041
electrical wire,
what happens is that the extra

37:51.043 --> 37:53.723
negative charges here will go to
that side,

37:53.719 --> 37:59.559
and then when you are done they
will both become electrically

37:59.556 --> 38:00.526
neutral.

38:00.530 --> 38:02.430
Okay, so that's why.

38:02.429 --> 38:06.039
So the point of this one is:
electric charges can flow

38:06.036 --> 38:09.436
through some materials,
but not other materials.

38:09.440 --> 38:11.710
If it can flow through some
materials, it's called a

38:11.706 --> 38:12.236
conductor.

38:12.239 --> 38:15.269
If it cannot flow through them,
it's called an insulator.

38:15.269 --> 38:17.339
So real life you've got both.

38:17.340 --> 38:19.350
So when you're changing the
light bulb,

38:19.349 --> 38:21.939
if you don't want to get an
electric shock you're supposed

38:21.943 --> 38:24.813
to stand on a piece of wood
before you stick your finger in,

38:24.809 --> 38:26.789
unless you've got other
intentions.

38:26.789 --> 38:31.269
Then, you will find that you
don't get the shock because the

38:31.271 --> 38:33.931
wood doesn't conduct
electricity.

38:33.929 --> 38:37.519
But if you stand on a metallic
stool, on a metallic floor and

38:37.516 --> 38:41.036
put your hand in the socket,
you'll be part of an electrical

38:41.041 --> 38:41.761
circuit.

38:41.760 --> 38:44.440
The human body is a good
conductor of electricity,

38:44.436 --> 38:47.706
but what saves you is that it
cannot go from your feet to the

38:47.713 --> 38:48.263
floor.

38:48.260 --> 38:49.600
Now, there are also
semiconductors,

38:49.599 --> 38:52.499
which are somewhere in between,
but in our course either we'll

38:52.501 --> 38:54.821
talk about insulators,
which don't conduct

38:54.822 --> 38:57.092
electricity, and perfect
conductors,

38:57.090 --> 38:59.920
which conduct electricity.

38:59.920 --> 39:05.540
Okay, so a summary of what I've
said so far is that there's a

39:05.539 --> 39:07.599
new force in nature.

39:07.599 --> 39:11.649
To be part of that game you
have to have charge.

39:11.650 --> 39:13.130
If you have no charge,
you cannot play that game.

39:13.130 --> 39:16.100
Like neutrons cannot play this
game.

39:16.099 --> 39:19.959
Nothing's attracted or repelled
by neutrons and neutrons cannot

39:19.963 --> 39:21.713
attract or repel anything.

39:21.710 --> 39:23.370
So you've got to have electric
charge.

39:23.369 --> 39:26.329
It happens to be measured in
coulombs.

39:26.329 --> 39:28.419
So let me ask you another
question.

39:28.420 --> 39:36.820
Suppose I tell you,
here is Coulombs Law.

39:36.820 --> 39:41.210
Let me just write the number 1
over 4Πε

39:41.213 --> 39:43.413
_0.

39:43.409 --> 39:47.099
How are we going to test that
this law is correct?

39:47.099 --> 39:47.969
Okay, I'm giving you a bonus.

39:47.969 --> 39:49.069
You don't have to discover the
law.

39:49.070 --> 39:50.620
I'm giving you the law.

39:50.619 --> 39:55.399
All you have to do is to verify
it, and don't use any other

39:55.400 --> 39:58.780
definitions other than this law
itself.

39:58.780 --> 40:00.670
How will you know it depends on
q_1 and

40:00.668 --> 40:02.008
q_2 in this
fashion?

40:02.010 --> 40:04.080
How will you know it depends on
r in that fashion?

40:04.079 --> 40:06.979
That's what I'm asking you.

40:06.980 --> 40:16.220
Can anybody think of some
setup, some experiment you will

40:16.215 --> 40:17.035
do?

40:17.039 --> 40:18.189
Let me ask an easier question.

40:18.190 --> 40:23.670
How will you know it goes like
1 over r^(2)?

40:23.670 --> 40:25.180
Yep?

40:25.179 --> 40:26.829
Student:  Vary the
distance between them,

40:26.827 --> 40:28.087
and show that the force falls
off.

40:28.090 --> 40:30.750
Prof: Well,
you're right that if you vary

40:30.751 --> 40:34.061
the distance between them and
show the force falls like that,

40:34.059 --> 40:40.389
but how do you know what the
force is?

40:40.389 --> 40:41.099
Yes?

40:41.099 --> 40:42.629
Student:  Could you use
a spring here?

40:42.630 --> 40:43.740
Prof: What was your plan?

40:43.739 --> 40:46.559
Student:  Observe
acceleration.

40:46.559 --> 40:47.109
Prof: You are right.

40:47.110 --> 40:49.320
Both of you are right.

40:49.320 --> 40:53.260
You can maybe hold this guy
fixed, and let this go,

40:53.262 --> 40:55.552
and see how it accelerates.

40:55.550 --> 40:59.430
And if you knew the mass of
this guy then you know the

40:59.425 --> 41:00.005
force.

41:00.010 --> 41:02.750
Then you can vary the distance
to another distance,

41:02.753 --> 41:04.183
maybe half the distance.

41:04.179 --> 41:07.199
At half the distance if you get
four times the force you

41:07.197 --> 41:09.117
verified 1 over r^(2
)law.

41:09.119 --> 41:11.109
The other one is with the
spring.

41:11.110 --> 41:12.420
You can take a spring.

41:12.420 --> 41:17.120
Say maybe there are two metals,
uncharged objects,

41:17.119 --> 41:20.549
then you dump some charge on
this and some charge on that,

41:20.550 --> 41:24.040
and then the spring will
expand, and you can see what

41:24.039 --> 41:28.179
force the spring expands,
exerts, and see if it is

41:28.177 --> 41:31.657
proportional to 1 over
r^(2).

41:31.659 --> 41:34.759
That's how Newton deduced the 1
over r^(2) force law.

41:34.760 --> 41:38.590
He found the acceleration of
the apple is 3,600 times the

41:38.592 --> 41:41.742
acceleration of the moon towards
the earth,

41:41.739 --> 41:44.449
and the moon was 60 times
further than the apple,

41:44.449 --> 41:46.699
and 60 squared is 3,600.

41:46.699 --> 41:49.319
That's how he found 1 over
r^(2).

41:49.320 --> 41:50.350
Now, he was very lucky.

41:50.349 --> 41:54.459
It could have been 1 over
r to the 2.110 or 1.96,

41:54.463 --> 41:58.283
but it happens to be exactly 1
over r^(2).

41:58.280 --> 42:00.840
Anyway, that's how we can find
even if it's not 1 over

42:00.844 --> 42:01.574
r^(2).

42:01.570 --> 42:04.670
If it's 1 over r^(3),
or 1 over r^(4),

42:04.668 --> 42:07.828
whatever it is you can find by
taking two charges.

42:07.829 --> 42:09.819
See, we don't have to know what
q_1 and

42:09.822 --> 42:10.802
q_2 are.

42:10.800 --> 42:12.600
That's what I'm trying to
emphasize here.

42:12.599 --> 42:15.089
If all you're trying to see is
does it vary like 1 over

42:15.090 --> 42:17.120
r^(2),
keep everything the same except

42:17.119 --> 42:17.719
r.

42:17.719 --> 42:20.399
Double the r and see
what happens.

42:20.400 --> 42:21.990
And best way is what you said.

42:21.989 --> 42:25.459
Watch the acceleration,
and if it falls to one fourth

42:25.460 --> 42:28.860
of the value for doubling the
distance, it is 1 over

42:28.864 --> 42:30.004
r^(2).

42:30.000 --> 42:32.870
All right, suppose I got 1 over
r^(2).

42:32.869 --> 42:35.569
I want to know it depends on
the charges as the first power

42:35.565 --> 42:37.655
of q_1 and the
first power of

42:37.657 --> 42:38.817
q_2.

42:38.820 --> 42:41.900
So how should we do that?

42:41.900 --> 42:45.210
And don't say put 10 electrons
once and then 20 electrons

42:45.210 --> 42:47.870
because you cannot see electrons
that well.

42:47.869 --> 42:52.139
In the old days people did not
even know about electrons,

42:52.143 --> 42:54.893
and yet they managed to test
this.

42:54.889 --> 42:58.509
So how will you vary the charge
in a known way?

42:58.510 --> 42:59.300
Yep?

42:59.300 --> 43:01.460
Student:  You could have
many identical spheres,

43:01.460 --> 43:03.260
and maybe keep touching them to
each other.

43:03.260 --> 43:05.460
Prof: Ah!

43:05.460 --> 43:07.600
Okay, many identical spheres.

43:07.599 --> 43:10.439
Student:  And then put
charge on one and then touch it

43:10.438 --> 43:12.708
to the second one and you'll get
half as much.

43:12.710 --> 43:13.700
Prof: Very good.

43:13.699 --> 43:15.469
Let me repeat what she said.

43:15.469 --> 43:17.339
First you take many identical
spheres.

43:17.340 --> 43:20.700
Well, I not going to even try
to draw identical spheres

43:20.704 --> 43:23.764
because I haven't learned how to
draw spheres,

43:23.760 --> 43:27.000
but let's imagine you've got a
whole bunch of these guys.

43:27.000 --> 43:29.150
You put some charge on this.

43:29.150 --> 43:32.010
You don't know what it is, okay?

43:32.010 --> 43:32.970
We don't know what q is.

43:32.969 --> 43:34.319
We're trying to find out.

43:34.320 --> 43:35.560
You don't have to know what
q is.

43:35.559 --> 43:37.789
So let this be one of the
objects.

43:37.789 --> 43:39.569
That's my q.

43:39.570 --> 43:43.170
For the other object,
keep a fixed-object containing

43:43.173 --> 43:44.733
some other q.

43:44.730 --> 43:45.790
This has got charge q.

43:45.789 --> 43:47.579
Don't vary the r.

43:47.579 --> 43:50.259
Question is,
can you change q to

43:50.260 --> 43:52.330
q/2,
and her answer was:

43:52.329 --> 43:55.089
if it's got some charge,
maybe a plus,

43:55.090 --> 44:00.410
bring it in contact with the
second identical sphere.

44:00.409 --> 44:04.149
If it really is identical,
you have to agree that when you

44:04.146 --> 44:07.356
separate them they must exactly
have half each.

44:07.360 --> 44:08.780
That's a symmetry argument.

44:08.780 --> 44:11.190
Because for any reason you give
me for why one of them should

44:11.188 --> 44:13.758
have more, I will tell you why
the other one should have more.

44:13.760 --> 44:18.140
You cannot, so they will split
it evenly and therefore charge

44:18.141 --> 44:22.451
will split evenly to q/2
here and q/2 here.

44:22.449 --> 44:27.009
Then you can take this and put
it there--you've got q/2.

44:27.010 --> 44:29.980
Then you can do other
combinations.

44:29.980 --> 44:33.270
For example,
you can take this q/2

44:33.273 --> 44:37.643
and connect it to the ground so
it becomes neutral.

44:37.639 --> 44:39.519
So this has got 0 again.

44:39.518 --> 44:42.918
You can touch that with the
q/2 and separate them.

44:42.920 --> 44:47.470
Then each will have q/4.

44:47.469 --> 44:50.389
So in this way you can vary the
charge in a known way,

44:50.387 --> 44:52.037
maybe half of it,
double it.

44:52.039 --> 44:55.239
I give you some homework
problem where you want to get

44:55.240 --> 44:56.450
5/16 of a coulomb.

44:56.449 --> 44:58.789
By enough spheres you can do
that.

44:58.789 --> 45:02.539
Again, what I want you to
notice is that you did not know

45:02.541 --> 45:05.001
what q was,
but all you knew is that

45:04.996 --> 45:07.476
q went to q/2 when
you brought two identical

45:07.481 --> 45:08.791
spheres and separated them.

45:08.789 --> 45:10.819
That's how we can find that it
depends linearly on

45:10.818 --> 45:11.768
q_1.

45:11.768 --> 45:14.378
Of course, it also depends
linearly on q_2

45:14.375 --> 45:16.705
because it's up to you to decide
who you want to call

45:16.710 --> 45:19.620
q_1,
and who you want to call

45:19.617 --> 45:21.207
q_2.

45:21.210 --> 45:27.720
Okay, so I want you people to
understand all the time that you

45:27.721 --> 45:33.061
should be able to tell me how
you measure anything,

45:33.059 --> 45:34.019
okay?

45:34.019 --> 45:35.349
That's very, very important.

45:35.349 --> 45:36.389
That's why you should think
about it.

45:36.389 --> 45:39.659
If you think in those terms
you'll also find you're doing

45:39.664 --> 45:41.364
all the problems very well.

45:41.360 --> 45:43.990
If you're thinking of pushing
symbols and canceling factors of

45:43.994 --> 45:46.634
Π you won't get the
feeling for what's happening.

45:46.630 --> 45:50.640
So everything you write down
you should be able to measure.

45:50.639 --> 45:52.239
If you say, "Oh,
I want to measure the

45:52.244 --> 45:54.544
force," you've got to be
sure how you'll measure it,

45:54.539 --> 45:57.439
and one way is like you said,
find m times a.

45:57.440 --> 45:59.480
If you knew the m you
can measure the force.

45:59.480 --> 46:02.710
For everything make sure you
can measure it.

46:02.710 --> 46:05.730
If I give you a sphere charged
with something,

46:05.733 --> 46:08.223
then of course we've got to
decide.

46:08.219 --> 46:09.439
Suppose I give you a sphere.

46:09.440 --> 46:12.220
It's got some charge,
and I want you to find how much

46:12.224 --> 46:13.674
charge is on that sphere.

46:13.670 --> 46:16.000
This time I want you to tell me
how many coulombs there are.

46:16.000 --> 46:19.840
What will you do?

46:19.840 --> 46:27.720
What process will you use?

46:27.719 --> 46:31.809
Well, then you have a problem
because you are not able to

46:31.806 --> 46:34.546
figure out,
but if I tell you here's an

46:34.547 --> 46:36.147
object,
it is 3 meters long,

46:36.152 --> 46:39.142
you can test it because you'll
go and bring the meter stick

46:39.144 --> 46:42.194
from the Bureau of Standards and
measure it three times.

46:42.190 --> 46:46.630
I'm asking you,
if I give you a certain charge

46:46.632 --> 46:52.062
and say how much charge is
there, by what process can we

46:52.063 --> 46:54.633
calibrate the charges?

46:54.630 --> 46:55.690
Yep?

46:55.690 --> 46:57.400
Student:  Put it in the
vicinity of a reference charge

46:57.402 --> 46:58.432
and then measure the
acceleration.

46:58.429 --> 47:01.159
Prof: That's correct.

47:01.159 --> 47:04.859
If you knew one standard
charge, somehow or other we knew

47:04.862 --> 47:08.042
its value, then bring the
unknown one next to it,

47:08.036 --> 47:10.546
put it at a known distance,
right?

47:10.550 --> 47:11.180
You know the r.

47:11.179 --> 47:12.059
You know the 4Π.

47:12.059 --> 47:13.409
You know the ε
_0.

47:13.409 --> 47:15.439
You find the force,
you can find this charge.

47:15.440 --> 47:19.210
So all we need to know is how
to get a reference charge,

47:19.210 --> 47:19.760
right?

47:19.760 --> 47:24.590
So how do I know something has
a coulomb?

47:24.590 --> 47:28.880
How do I get 1 coulomb of
charge just to be sure?

47:28.880 --> 47:31.760
You know what you could do,
because you haven't defined yet

47:31.764 --> 47:34.054
the reference,
so you should think about how

47:34.054 --> 47:38.454
will I get a coulomb charge,
or any other charge?

47:38.449 --> 47:41.699
So I could take these two
spheres that she talked about,

47:41.702 --> 47:43.892
each with the same charge
q.

47:43.889 --> 47:45.339
We don't know what it is.

47:45.340 --> 47:48.430
I put them at 1 meter distance
and I measure the force,

47:48.432 --> 47:51.702
namely how hard should I hold
one from running away to the

47:51.697 --> 47:52.497
other one.

47:52.500 --> 47:54.750
Once I got the force,
the only thing unknown in the

47:54.751 --> 47:56.331
equation is q times
q.

47:56.329 --> 47:57.229
I know r.

47:57.230 --> 47:59.920
I know 1 over 4Πε
_0.

47:59.922 --> 48:00.952
I can get q.

48:00.949 --> 48:03.529
So every time you write
something think about how you'll

48:03.530 --> 48:06.250
measure it, because in that
process you're learning how the

48:06.251 --> 48:07.191
physics is done.

48:07.190 --> 48:09.910
If you try to avoid that you'll
be just juggling equations,

48:09.909 --> 48:12.769
and that doesn't work for you
and that doesn't work for me.

48:12.768 --> 48:15.588
Anybody who wants to do good
physics should be constantly

48:15.592 --> 48:17.712
paying attention to physical
phenomena,

48:17.710 --> 48:22.010
and not to the symbols that
stand for physical objects.

48:22.010 --> 48:27.450
All right, so the final thing I
want to do in this connection is

48:27.454 --> 48:32.764
to give this number I mentioned,
F_gravity over

48:32.757 --> 48:34.887
F_electric.

48:34.889 --> 48:38.619
I said gravity is 10 to the -40
times weaker.

48:38.619 --> 48:41.889
Well, you have to precise on
how you got the number.

48:41.889 --> 48:45.439
See, it's not like selling
toothpaste where you can say it

48:45.438 --> 48:46.808
is 7.2 times whiter.

48:46.809 --> 48:49.859
I don't know how those guys
measure whiteness in a unit with

48:49.856 --> 48:52.436
two decimal places,
but that's a different game.

48:52.440 --> 48:56.530
It's not subject to any rules,
but here you have to say how

48:56.529 --> 48:58.009
you got the number.

48:58.010 --> 49:01.400
In what context did you make
the comparison?

49:01.400 --> 49:04.590
It turns out the answer does
depend on what you choose.

49:04.590 --> 49:08.710
There'll be some variations,
but those tiny variations are

49:08.708 --> 49:11.958
swamped by this enormous ratio I
would get.

49:11.960 --> 49:14.620
So what you could do is take
any two bodies,

49:14.623 --> 49:17.723
and find the ratio of gravity
to electric force.

49:17.719 --> 49:21.129
One option is to take two
elementary particles,

49:21.134 --> 49:22.994
whichever two you like.

49:22.989 --> 49:25.629
So I will take an electron and
a proton, but you can take an

49:25.626 --> 49:27.946
electron and a positron,
or a proton and a proton.

49:27.949 --> 49:29.689
It doesn't matter.

49:29.690 --> 49:35.310
These two guys attract each
other gravitationally and

49:35.309 --> 49:36.929
electrically.

49:36.929 --> 49:39.399
So I will write the force of
gravitation,

49:39.400 --> 49:42.320
which is G, mass of the
proton,

49:42.320 --> 49:46.050
mass of the electron,
over r^(2 )divided by

49:46.050 --> 49:51.040
q_electron,
q_proton over

49:51.043 --> 49:55.263
4Πε
_0 times 1

49:55.255 --> 49:57.095
over r^(2).

49:57.099 --> 49:59.009
Notice in this experiment,
in this calculation,

49:59.010 --> 50:03.690
r^(2 )does not matter,
so you don't have to decide how

50:03.692 --> 50:06.082
far you want to keep them,
because they both go like 1

50:06.083 --> 50:08.633
over r^(2 ),so you can
pick any r.

50:08.630 --> 50:14.190
So whatever you pick is going
to cancel and you will be left

50:14.188 --> 50:15.978
with this number.

50:15.980 --> 50:19.850
A q_1,
q_2 and the 1

50:19.846 --> 50:22.326
over
4Πε_0

50:22.326 --> 50:25.386
is 9 times 10 to the
9^(th).

50:25.389 --> 50:27.659
So now we put in some numbers.

50:27.659 --> 50:31.149
So G is 10 to the -11
with some pre-factors,

50:31.146 --> 50:32.746
maybe 6 in this case.

50:32.750 --> 50:34.940
I'm not going to worry about
pre-factors.

50:34.940 --> 50:38.990
But the mass of the proton is
10 to the -27 kilograms,

50:38.994 --> 50:42.594
the mass of the electron 10 to
-30 kilograms.

50:42.590 --> 50:45.250
So don't say how come they all
have these nice round numbers.

50:45.250 --> 50:45.950
They are not.

50:45.949 --> 50:47.739
There are factors like 1 and 2.

50:47.739 --> 50:51.329
I'm not putting them because
I'm just counting powers of 10.

50:51.329 --> 50:56.389
q_1 is 1.6
times 10 to the -19,

50:56.393 --> 51:01.353
so two of those q's is
10 to the -38.

51:01.349 --> 51:06.059
Then 9 times 10 to the 9^(th)
is roughly 10 to the 10^(th).

51:06.059 --> 51:10.869
If you do all of that you will
find this is 10 to the -40,

51:10.865 --> 51:14.655
if it is some typical situation
that you took,

51:14.661 --> 51:17.951
and you found this ratio of
forces.

51:17.949 --> 51:19.429
If there are two elementary
particles,

51:19.429 --> 51:22.249
which are like the building
blocks of matter,

51:22.250 --> 51:25.930
and you brought them to any
distance you like you compare

51:25.934 --> 51:29.754
the electric attraction to the
gravitational attraction.

51:29.750 --> 51:33.820
So one question is:
if gravity is so weak,

51:33.817 --> 51:38.477
how did anyone discover the
force of gravity?

51:38.480 --> 51:41.180
If all you had was electrons
and protons, you'd have to

51:41.179 --> 51:42.829
measure the force between them.

51:42.829 --> 51:46.399
Suppose you knew only about
electricity, didn't know about

51:46.402 --> 51:47.282
gravitation.

51:47.280 --> 51:51.710
One way to find there is an
extra force is to measure the

51:51.711 --> 51:55.671
force to an accuracy good to 40
decimal places,

51:55.670 --> 51:58.390
and in the 40th decimal place
you find something is wrong.

51:58.389 --> 52:00.939
You fiddle around and figure
out the correction comes from

52:00.938 --> 52:03.398
m_1m_2
over r^(2),

52:03.400 --> 52:05.390
but that's not how it was done,
right?

52:05.389 --> 52:07.299
You guys know that.

52:07.300 --> 52:10.430
So how did anyone discover the
force of gravity when it's

52:10.427 --> 52:11.207
overwhelmed?

52:11.210 --> 52:12.040
Yes?

52:12.039 --> 52:13.029
Student:  Most things
are neutral?

52:13.030 --> 52:14.080
Prof: Yes.

52:14.079 --> 52:17.359
Most things are electrically
neutral.

52:17.360 --> 52:20.140
In other words,
electric force,

52:20.143 --> 52:25.713
even though it's very strong,
comes with opposite charges.

52:25.710 --> 52:29.730
It can occur with a plus sign
or with a minus sign.

52:29.730 --> 52:32.970
Therefore, if you take the
planet Earth,

52:32.971 --> 52:36.881
it's got lots and lots of
charges in every atom,

52:36.876 --> 52:39.366
but every atom is neutral.

52:39.369 --> 52:43.919
You've got the moon,
ditto, lots and lots of atoms,

52:43.922 --> 52:46.292
but they're all neutral.

52:46.289 --> 52:50.559
But the mass of the electron
does not cancel the mass of the

52:50.557 --> 52:51.207
proton.

52:51.210 --> 52:55.730
So mass can never be hidden,
whereas charge can be hidden.

52:55.730 --> 52:57.430
Mass never cancels.

52:57.429 --> 53:00.439
That's the reason why,
in spite of the incredible

53:00.438 --> 53:04.008
amount of electrical forces
they're potentially capable of

53:04.012 --> 53:07.062
exerting,
they present to each other

53:07.063 --> 53:08.573
neutral entities.

53:08.570 --> 53:12.590
Therefore, this remaining force
which is not shielded is what

53:12.585 --> 53:16.255
you see, and has a dramatic role
in the structure of the

53:16.264 --> 53:18.344
universe, force of gravity.

53:18.340 --> 53:20.890
But in most cosmological
calculations you can forget

53:20.889 --> 53:22.289
mainly the electric force.

53:22.289 --> 53:23.849
It's all gravitational force.

53:23.849 --> 53:27.309
That's because electricity can
be neutralized.

53:27.309 --> 53:29.769
So you cannot hide gravity.

53:29.769 --> 53:31.099
Everything has mass.

53:31.099 --> 53:33.039
Even photons which have no mass
have energy.

53:33.039 --> 53:35.979
They're also attracted by
gravitation.

53:35.980 --> 53:42.420
So gravity cannot be hidden,
and that's the origin of

53:42.420 --> 53:46.260
something called dark matter.

53:46.260 --> 53:50.550
So how many of you guys heard
about dark matter?

53:50.550 --> 53:51.320
Okay?

53:51.320 --> 53:53.080
Anyone want to volunteer?

53:53.079 --> 53:58.439
Someone whose name begins with
T, anybody's name begins with T

53:58.436 --> 54:01.596
and also knows the answer to
this?

54:01.599 --> 54:04.859
The trouble is,
you people are plagued with one

54:04.855 --> 54:08.105
quality which is not good for
being in physics,

54:08.110 --> 54:09.880
namely you're modest.

54:09.880 --> 54:11.530
So you don't want to tell me
the answer.

54:11.530 --> 54:15.850
So I have to give an excuse for
whoever gives the answer.

54:15.849 --> 54:24.809
If your seat has a number 142,
anybody in seat 142?

54:24.809 --> 54:27.879
Maybe they're not even numbered.

54:27.880 --> 54:32.490
Look, anybody with a red piece
of clothing knows the answer to

54:32.494 --> 54:33.784
this--go ahead.

54:33.780 --> 54:35.070
Yes?

54:35.070 --> 54:37.480
Student:
>

54:37.480 --> 54:38.260
Prof: Pardon me?

54:38.260 --> 54:47.360
Student:
>

54:47.360 --> 54:47.910
Prof: Right.

54:47.909 --> 54:51.889
Basically there's no way you
can see it, and there's dark

54:51.885 --> 54:54.295
matter right in this room,
okay?

54:54.300 --> 54:58.270
And there's dark matter
everywhere, but the reason,

54:58.273 --> 55:01.853
the way people found out there
is dark matter,

55:01.849 --> 55:05.029
do you know how that was
determined?

55:05.030 --> 55:06.130
Yep?

55:06.130 --> 55:09.270
Student:  The rotation
of galaxies didn't line up with

55:09.266 --> 55:11.146
the matter that was visible,
so...

55:11.150 --> 55:12.370
Prof: So yes.

55:12.369 --> 55:16.209
Maybe one example I can talk is
about our own galaxy.

55:16.210 --> 55:22.700
So here's our visible galaxy,
okay, the old spiral.

55:22.699 --> 55:27.309
Now, if something is orbiting
this galaxy just by using

55:27.306 --> 55:30.766
Newtonian gravity,
by knowing the velocity of the

55:30.773 --> 55:34.913
object as it goes around,
you can calculate how much mass

55:34.905 --> 55:37.105
is enclosed by the orbit.

55:37.110 --> 55:39.850
That's a property of
gravitation--from the orbit,

55:39.849 --> 55:42.419
you can find out how much mass
is enclosed.

55:42.420 --> 55:45.420
So what you will find is,
if you found something orbiting

55:45.418 --> 55:48.578
the center of the galaxy at that
radius, you'll enclose some

55:48.577 --> 55:49.057
mass.

55:49.059 --> 55:51.619
If you take objects at bigger
and bigger radius,

55:51.617 --> 55:54.767
you'll enclose more and more
mass, until you find orbits as

55:54.771 --> 55:55.971
big as the galaxy.

55:55.969 --> 56:00.499
Then the mass enclosed as a
function of radius should come

56:00.498 --> 56:04.868
and stop, because after that the
orbit's getting bigger,

56:04.869 --> 56:07.729
but not enclosing any more
mass.

56:07.730 --> 56:11.420
But what people found,
that even after you cross the

56:11.418 --> 56:16.248
nominal size of the galaxy,
you still keep picking up mass,

56:16.250 --> 56:20.370
and that is the dark matter
halo of our galaxy.

56:20.369 --> 56:23.769
So it's dark to everything,
but you cannot escape gravity.

56:23.769 --> 56:24.859
That's what I meant to say.

56:24.860 --> 56:27.820
You cannot avoid gravitational
force.

56:27.820 --> 56:30.550
So people are trying to find
dark matter.

56:30.550 --> 56:33.570
People at Yale are trying to
find dark matter.

56:33.570 --> 56:36.360
The thing is,
you don't know exactly what it

56:36.364 --> 56:36.694
is.

56:36.690 --> 56:39.540
It's not any of the usual
suspects, because then they

56:39.538 --> 56:41.618
would have interacted very
strongly.

56:41.619 --> 56:44.439
So you're trying to find
something not knowing exactly

56:44.438 --> 56:45.128
what it is.

56:45.130 --> 56:47.710
And you've got to build
detectors that will detect

56:47.708 --> 56:48.338
something.

56:48.340 --> 56:50.970
And you go through it everyday
in your lab,

56:50.969 --> 56:54.619
and you're hoping that one of
these dark matter particles will

56:54.617 --> 56:57.187
collide with the stuff in your
detector,

56:57.190 --> 56:59.750
and trigger a reaction.

56:59.750 --> 57:02.610
Of course there will be lots of
reactions everyday,

57:02.610 --> 57:05.070
but most of them are due to
other things.

57:05.070 --> 57:06.060
That's called background.

57:06.059 --> 57:08.419
You've got to throw the
background out,

57:08.423 --> 57:11.913
and whatever is left has got to
be due to dark matter.

57:11.909 --> 57:15.129
And again, how do you know it's
dark matter?

57:15.130 --> 57:17.260
How do you know it's not
something else?

57:17.260 --> 57:20.730
Well you can see that if you're
drifting through dark matter in

57:20.731 --> 57:23.281
a moving Earth,
you will be running into more

57:23.275 --> 57:26.185
of them in the direction of
motion and less in the other

57:26.188 --> 57:28.568
direction,
because you're running into the

57:28.572 --> 57:28.892
wind.

57:28.889 --> 57:32.009
So by looking at the direction
dependence, you can try to see

57:32.007 --> 57:33.147
if it's dark matter.

57:33.150 --> 57:37.760
Anyway, dark matter was
discovered by simple Newtonian

57:37.760 --> 57:38.980
gravitation.

57:38.980 --> 57:42.070
The particles that form dark
matter are very interesting to

57:42.074 --> 57:43.254
particle physicists.

57:43.250 --> 57:46.660
There are many candidates in
particle theory,

57:46.655 --> 57:50.755
but the origin of the
discrepancy came from just doing

57:50.757 --> 57:52.457
Newtonian gravity.

57:52.460 --> 58:04.820
All right, the final thing
today before we break is that

58:04.817 --> 58:14.027
there's one variation of
Coulomb's Law.

58:14.030 --> 58:18.320
By the way, I do not know your
mathematical training and how

58:18.320 --> 58:21.070
much math you know,
so you have to be on the

58:21.070 --> 58:22.840
lookout, say,
if I write something that looks

58:22.835 --> 58:25.515
very alien to you,
you've got to go take care of

58:25.523 --> 58:27.113
that,
in particular,

58:27.105 --> 58:31.325
how to do integrals in maybe
more than one dimension.

58:31.329 --> 58:34.569
Anyway, what I wanted to
discuss today is the following:

58:34.567 --> 58:37.917
we know how to do Coulomb's Law
due to any number of point

58:37.922 --> 58:38.632
charges.

58:38.630 --> 58:41.560
So if you put another charge
q here you want the force

58:41.563 --> 58:43.083
on this guy due to all these.

58:43.079 --> 58:45.359
You draw those lines,
you take the 1 over r^(2

58:45.360 --> 58:47.400
)due to that,
1 over r^(2 )due to

58:47.404 --> 58:48.834
that, add all the vectors.

58:48.829 --> 58:50.149
That's very simple.

58:50.150 --> 58:54.150
But we will also take problems
where the charges are

58:54.150 --> 58:55.170
continuous.

58:55.170 --> 58:57.160
So here's an example.

58:57.159 --> 59:01.059
Here's a ring of charge.

59:01.059 --> 59:02.149
The ring has some radius.

59:02.150 --> 59:06.940
You pick your radius r,
and the charge on it is

59:06.943 --> 59:08.123
continuous.

59:08.119 --> 59:10.649
It's not discrete,
or it could be in real life

59:10.650 --> 59:13.460
everything is discrete,
but to a coarse observer it

59:13.460 --> 59:15.430
will look like it's continuous.

59:15.429 --> 59:20.689
So we can draw some pictures
here, charges all over the ring,

59:20.686 --> 59:25.766
and λ is the
number of coulombs per meter.

59:25.768 --> 59:29.498
Let me see, if you snipped one
meter of the wire it'll have

59:29.503 --> 59:31.633
λ coulombs in it.

59:31.630 --> 59:36.200
And you want to find the
electric force on some other

59:36.195 --> 59:39.265
charge q due to this
wire.

59:39.269 --> 59:40.839
So you cannot do a sum.

59:40.840 --> 59:42.280
And you have to do an integral.

59:42.280 --> 59:45.160
That's what I'm driving at,
and I'm going to do one

59:45.159 --> 59:48.269
integral, then we'll do more
complicated ones later.

59:48.268 --> 59:52.148
So I want to find the force on
a charge q here.

59:52.150 --> 59:56.770
So what I will do is,
I will divide this into

59:56.771 --> 1:00:01.081
segments each of length,
say dl.

1:00:01.079 --> 1:00:06.849
Then I will find the force of
the charge here,

1:00:06.851 --> 1:00:08.391
dF.

1:00:08.389 --> 1:00:13.779
I will add the forces due to
all the segments.

1:00:13.780 --> 1:00:16.640
The force of this segment will
be the charge--

1:00:16.639 --> 1:00:19.859
this segment is so small,
you can treat it as a point

1:00:19.860 --> 1:00:22.810
charge,
and the amount of charge here

1:00:22.807 --> 1:00:25.697
is λ times
dl.

1:00:25.699 --> 1:00:27.659
That's the q_1.

1:00:27.659 --> 1:00:30.509
The q_2 is the
q I put there.

1:00:30.510 --> 1:00:31.610
Then there's the
4Πε

1:00:31.610 --> 1:00:33.720
_0,
r^(2),

1:00:33.719 --> 1:00:38.649
r^(2 )will be this
distance z times this

1:00:38.652 --> 1:00:41.992
radius r will be--
maybe I shouldn't call it

1:00:41.987 --> 1:00:42.277
r.

1:00:42.280 --> 1:00:45.910
Let me call it capital
R, and it's R^(2

1:00:45.909 --> 1:00:47.799
)plus z^(2).

1:00:47.800 --> 1:00:50.530
That's the distance.

1:00:50.530 --> 1:00:54.310
But now that force is a vector
that's pointing in that

1:00:54.311 --> 1:00:57.321
direction,
but I know that the total force

1:00:57.322 --> 1:01:01.092
is going to point in this
direction because for every guy

1:01:01.088 --> 1:01:05.048
I find in this side I can find
one in the opposite direction

1:01:05.052 --> 1:01:06.602
pointing that way.

1:01:06.599 --> 1:01:08.839
So they will always cancel
horizontally.

1:01:08.840 --> 1:01:13.040
The only remaining force will
be in the z direction.

1:01:13.039 --> 1:01:16.589
So I'm going to keep only the
component of the force in the z

1:01:16.590 --> 1:01:17.300
direction.

1:01:17.300 --> 1:01:20.620
I denote it by dF in the
z direction.

1:01:20.619 --> 1:01:25.169
For that, you have to take this
force and multiply by cosine of

1:01:25.166 --> 1:01:26.776
that θ.

1:01:26.780 --> 1:01:29.290
I hope you know how to find the
component of a force in a

1:01:29.291 --> 1:01:29.831
direction.

1:01:29.829 --> 1:01:32.399
It's the cosine of the angle
between them.

1:01:32.400 --> 1:01:37.010
That angle is equal to this
angle, and cosine of this is

1:01:37.005 --> 1:01:41.695
z divided by R^(2
)plus z^(2 )on the

1:01:41.695 --> 1:01:42.445
root.

1:01:42.449 --> 1:01:45.649
That is the dF due to
this segment,

1:01:45.648 --> 1:01:50.178
and the total force in the z
direction is integral of this,

1:01:50.175 --> 1:01:52.355
and what that integrate.

1:01:52.360 --> 1:01:54.220
λ,
q, all these are

1:01:54.215 --> 1:01:56.305
constant, R,
z, everything is a

1:01:56.311 --> 1:01:56.931
constant.

1:01:56.929 --> 1:02:01.299
You have to add all the
dl's, if you add all the

1:02:01.298 --> 1:02:04.938
dl's you will get the
circumference.

1:02:04.940 --> 1:02:07.720
In other words,
this is going to be

1:02:07.722 --> 1:02:11.982
λqz divided
by 4Πε

1:02:11.980 --> 1:02:16.810
_0R^(2
)plus z^(2 )to the

1:02:16.809 --> 1:02:19.429
3/2 integral of dl.

1:02:19.429 --> 1:02:25.339
Integral of dl is just
2ΠR.

1:02:25.340 --> 1:02:27.210
In other words,
every one of them is making an

1:02:27.213 --> 1:02:29.313
equal contribution,
so the integrand doesn't depend

1:02:29.306 --> 1:02:32.196
on where you are in the circle,
so you're just measuring the

1:02:32.195 --> 1:02:33.475
length of the circle.

1:02:33.480 --> 1:02:34.660
That's the answer.

1:02:34.659 --> 1:02:38.189
The force looks like
λ times

1:02:38.192 --> 1:02:41.382
2ΠR,
what is that?

1:02:41.380 --> 1:02:44.180
λ is the charge
per unit length.

1:02:44.179 --> 1:02:47.719
That, times the length of the
loop, is the charge on the loop.

1:02:47.719 --> 1:02:51.609
It's the charge you're putting
there divided by

1:02:51.614 --> 1:02:55.684
4Πε
_0 divided

1:02:55.679 --> 1:02:59.829
by R^(2) plus
z^(2) to the 3/2.

1:02:59.829 --> 1:03:04.889
That's an example of
calculating the force which will

1:03:04.891 --> 1:03:07.131
be in this direction.

1:03:07.130 --> 1:03:10.640
Now, once you've done this
calculation you may think maybe

1:03:10.644 --> 1:03:13.984
I missed a factor of Π
or factor of e,

1:03:13.976 --> 1:03:14.836
something.

1:03:14.840 --> 1:03:19.560
Can you think of a way to test
this?

1:03:19.559 --> 1:03:22.939
What test would you like to
apply to this result?

1:03:22.940 --> 1:03:24.020
Yep?

1:03:24.018 --> 1:03:27.268
Student:  Put the
z equal to 0 and have it

1:03:27.273 --> 1:03:28.223
in the middle.

1:03:28.219 --> 1:03:29.579
There should be no forces on it.

1:03:29.579 --> 1:03:30.509
Prof: Very good.

1:03:30.510 --> 1:03:33.160
What he said is,
if you pick z equal to 0

1:03:33.163 --> 1:03:35.763
you're sitting in the middle of
the circle,

1:03:35.760 --> 1:03:38.000
and you're getting pushed
equally from all sides,

1:03:38.000 --> 1:03:40.240
and you better not have a
force, and that's certainly

1:03:40.239 --> 1:03:40.669
correct.

1:03:40.670 --> 1:03:43.790
This vanishes when z
goes to 0.

1:03:43.789 --> 1:03:47.469
Anything else?

1:03:47.469 --> 1:03:57.079
Any other test?

1:03:57.079 --> 1:03:58.099
Yep?

1:03:58.099 --> 1:03:59.969
Student:  You could put
it underneath by negative

1:03:59.965 --> 1:04:00.335
z.

1:04:00.340 --> 1:04:03.570
The force should be negative.

1:04:03.570 --> 1:04:07.250
Prof: Yes,
it will point down and be

1:04:07.253 --> 1:04:08.223
negative.

1:04:08.219 --> 1:04:12.109
That's correct,
but how about the magnitude of

1:04:12.114 --> 1:04:16.534
the force itself,
rather than just the direction?

1:04:16.530 --> 1:04:17.470
Yep?

1:04:17.469 --> 1:04:19.859
Student:  If you go
infinitely far away it should

1:04:19.864 --> 1:04:21.044
look like a point charge.

1:04:21.039 --> 1:04:22.479
Prof: Yes.

1:04:22.480 --> 1:04:24.700
If you go very,
very far, someone's holding a

1:04:24.704 --> 1:04:26.984
loop, you cannot see that it's
even a loop.

1:04:26.980 --> 1:04:29.690
It's some tiny spec,
and it should produce the

1:04:29.688 --> 1:04:30.168
field.

1:04:30.170 --> 1:04:31.930
So what field should it produce?

1:04:31.929 --> 1:04:34.629
It should produce the coulomb
force q_1q

1:04:34.630 --> 1:04:36.670
_2,
or 4Πε

1:04:36.670 --> 1:04:39.070
_0 times
distance squared.

1:04:39.070 --> 1:04:41.740
And when z is much,
much, much bigger than

1:04:41.737 --> 1:04:44.737
R, this is one kilometer,
this is two inches.

1:04:44.739 --> 1:04:46.409
You forget this.

1:04:46.409 --> 1:04:50.449
You get z^(2) to the 3/2
is then z cubed.

1:04:50.449 --> 1:04:54.679
That means the whole thing here
reduces to 1 over z^(2)

1:04:54.682 --> 1:04:58.572
and it looks like the force
between two point charges.

1:04:58.570 --> 1:05:03.460
So I would ask you whenever you
do a calculation to test your

1:05:03.456 --> 1:05:04.186
result.

1:05:04.190 --> 1:05:07.880
Okay, before going I've got to
tell you something about those

1:05:07.876 --> 1:05:08.856
who come late.

1:05:08.860 --> 1:05:11.850
I realize that you guys come
from near and far,

1:05:11.846 --> 1:05:15.346
so when you come late let me
give you my preference for

1:05:15.351 --> 1:05:16.391
doors, okay?

1:05:16.389 --> 1:05:18.649
Door number one is that one.

1:05:18.650 --> 1:05:21.240
That's the least problematic.

1:05:21.239 --> 1:05:24.999
Door number two is this one,
because in the beginning of the

1:05:24.998 --> 1:05:27.868
lecture I'm usually on that side
of the board,

1:05:27.865 --> 1:05:29.645
so you guys can come in.

1:05:29.650 --> 1:05:33.320
Door number three is that one
where Jude is taking the

1:05:33.315 --> 1:05:36.835
picture, but do not stand in
front of the camera and

1:05:36.842 --> 1:05:38.782
contemplate your future.

1:05:38.780 --> 1:05:42.240
If you do I will make sure you
don't have a future,

1:05:42.235 --> 1:05:42.715
okay?

1:05:42.719 --> 1:05:43.779
So don't do that.

1:05:43.780 --> 1:05:48.090
If you come fashionably late,
never come through that door,

1:05:48.094 --> 1:05:49.364
maybe this one.

1:05:49.360 --> 1:05:52.700
In fact if you come through
that door because I have reached

1:05:52.697 --> 1:05:54.897
this side of the board,
you are very,

1:05:54.900 --> 1:05:57.820
very late, so I think you
should take the day off and

1:05:57.820 --> 1:05:59.920
start fresh next time,
all right?

1:05:59.920 --> 1:06:01.500
Okay, thank you.

1:06:01.500 --> 1:06:07.000