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Let's talk a little bit about
what I find to be one of the

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more mysterious forces
of the universe.

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Actually, I find all of the
forces of the universe to be

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fairly mysterious,
so let's talk a

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little bit about charge.

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And we've all heard of charge.

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Charge the battery.

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This particle has charge.

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But when you really think about
it, all charge means is

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that there's this property
called charge, and we know

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that if something contains a
positive charge-- and calling

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it positive is a little
bit arbitrary.

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It's not like protons have a
little plus written on them.

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We could have called
them negative.

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But when something has a
positive charge and when

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something else has a positive
charge, that

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they repel each other.

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We also know that if I had
something else, another

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particle that happened to have
a negative charge, and once

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again, the word "negative"
being applied to this is

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completely arbitrary.

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They could have called it blue
charge and red charge, but all

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we know is that when another
object has the other charge--

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in this case, we call it
negative-- that's going to be

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attracted to a positive
charge.

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So what do we know
about charge?

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Charge is a property that
particles have, and if you put

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enough particles together,
I guess objects have that

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property as well.

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So it's just a property.

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And that's a way of saying
that I really don't

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know what it is.

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And frankly, no one
fundamentally

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knows what it is.

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Actually, no one really
fundamentally knows anything.

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But charge is a property
of particles and

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objects, just like mass.

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I mean, if you think about it,
mass is just a property.

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And to some degree, it seems
a little bit more real than

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charge, because our brains
are wired to in some way

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comprehend what mass is, but
we're probably comprehending

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weight and volume more than
mass, but we can think more

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about that at another time.

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Charge is a little bit more
abstract because, before we

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started rubbing amber into our
hair, we really didn't

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experience much charge unless
we got struck by lightning.

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So charge is a property that
particles or objects have, and

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we know that there are two types
of charge, which we've

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arbitrarily named positive
and negative.

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And we know that like charges
repel and opposite charges

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attract, or unlike charges
attract, right?

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So what can we do with this?

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Well, if we have this property,
I think a useful

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thing to do would be to measure
the property, and so

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we came up with units, and so
the unit of charge is called

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the coulomb.

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It's named after a scientist in
the late 1700s, who played

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around a lot with charge.

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You could look up more about
him on Wikipedia.

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But it's called the coulomb,
and the coulomb-- there's a

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bunch of definitions, but I like
to think of it in terms

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of elementary particles, just
because, to some degree,

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unless you go into quantum
theory and start talking about

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quarks and stuff, the elementary
charge is the

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charge on a proton
or a neutron.

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So I'll go into more detail in
the future on actually the

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structure of atoms and whatever
else, but let me just

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draw a little example.

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So an atom tends to have some
neutrons in them, which don't

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have this charge property.

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It'll have some protons
in them, which

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have a positive charge.

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Once again, that's kind of

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arbitrarily defined as positive.

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We could have called
a red charge.

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And then it has these things
floating around that are much,

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much, much lighter than the
protons and the neutrons in

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the nucleus, and these
are called electrons.

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It's not even clear that
they're real objects.

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They're almost like energy, but
sometimes it's useful to

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view them as objects.

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Sometimes it's useful
to view them as--

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well, not as objects.

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And we'll go into all of that
more later, but electrons have

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a negative charge.

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And the fundamental unit of
charge, as far as we are

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concerned right now before we
start talking about quarks and

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other potentially subatomic
particles, is the charge in an

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electron or proton.

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And they have the exact same
charge, and that elementary

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charge is denoted by e.

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And to be frank, I'm not sure
whether e stands for

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elementary or e stands
for electron.

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But actually, e is equal to the
charge of a proton so it

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probably stands for elementary
charge of a proton.

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And the charge of an electron
is the negative of this, so

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negative e is the charge
of an electron.

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But if we didn't care
about sign, then the

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magnitudes are the same.

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So that's the fundamental as
far as we know or so far in

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our physics.

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That's the fundamental charge.

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The fundamental unit of charge
is just the charge in a proton

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or neutron.

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So how does a coulomb
relate to that?

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Well, a coulomb, which we'll
denote by C, is equal to-- and

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this is a bit of an arbitrary
number, but when we start

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doing things with electricity,
we'll see why the coulomb was

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defined the way it is, but a
coulomb is 6.24 times 10 to

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the eighteenth e's.

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Or you can say it's 6.24 times
10 to the eighteenth times the

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charge on an electron--
actually, times the charge on

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a proton, and then, of course,
in terms of magnitude.

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Because if I just say
coulomb, I'm not

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really giving a direction.

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So if you look at it the other
way around, you can say that

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the elementary charge is equal
to-- at least its magnitude--

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1.6 times 10 to the
minus 19 coulombs.

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So fair enough.

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This might be a useful number
to memorize, but it will

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usually be provided for
you in some way.

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So what can we do?

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We say that these objects have
this property called charge.

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Like charges repel.

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Unlike charges attract.

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If we have enough of these
protons together, then the

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whole object has charge.

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If we have more protons than
electrons, then we have a

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positive charge.

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If we have more electrons
than protons, we

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have a negative charge.

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And we know that we've defined
this unit of charge called the

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coulomb, which is a bunch of
the fundamental charge.

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So let's play around with
this and see if

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we can measure charge.

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So part of the initial-- I
guess we could call it--

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definition on what charge is,
I said that like charges

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repel, right?

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Like charges repel so both
of these are positive.

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They're going to repel
each other.

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And unlike charges, if this is
negative, this is positive,

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they're going to attract
each other, right?

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So by definition, if they are
moving each other, these two

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particles are going
to accelerate

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away from each other.

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These two particles are
going to accelerate

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towards each other.

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The charge between these
particles or the charge in

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each of these particles must
be generating some type of

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force, right?

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If there was no force being
generated, then they wouldn't

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repel or attract each other,
and this is where we get to

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Coulomb's Law, and this
is why we named

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charges after Coulomb.

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Coulomb figured out that the
force between two charges is

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equal to-- and this is going to
be a vector quantity, and

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in about 30 seconds, I'll tell
you what happens with the

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direction-- is equal to some
constant times the first

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charge times the second charge
divided by the distance

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between them squared.

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And this is pretty neat because
this looks an awful

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lot like-- so if we call this
the force, the electric force,

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that looks a lot like the
gravitational force equation.

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Let me write that down.

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The force from gravity between
two masses is equal to the

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gravitational constant times
m1 times m2 divided by the

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distance between them squared.

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So far, the two forces that
we've covered, gravity, and

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now we're covering electric
force and we'll eventually

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expand this to electromagnetic
force, it seems like they kind

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of act at distance in a similar
way, and both of these

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forces apply in a vacuum.

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So it doesn't matter if you have
no air, if you have no

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substances between the two
particles, somehow they are

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communicating with each
other, which I find

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kind of amazing, right?

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You can have nothing between
these two particles, but

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somehow, this particle knows
that that particle's there and

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that particle knows that that
particle's there, and they

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start moving without having
any-- it's not like they have

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a wire connected to each other
and someone's telling the

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other particle, hey, there's
a particle there.

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Start moving.

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So I don't know if you find that
as amazing as I do, but

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think about it and you might.

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And it's just like gravity.

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I mean, the two masses are
in no way connected.

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They could be sitting in a
vacuum, but somehow, they know

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that the other particle's
there.

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And when we start learning about
special relativity and

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all of that, we'll learn that
there's nothing there, but

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maybe the masses are actually
somehow shaping the universe.

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And maybe that's happening
with the

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electric charges as well.

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But all we know at this point is
that we have these charges

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and that they exert a force on
each other that's proportional

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to the product of their
respective charges divided by

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the square of the distance
between them.

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And this constant right here,
that is-- I always forget it.

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What was it?

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I think it's 6.-- I always
forget what that constant is.

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It is 9 times 10 to the ninth.

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It's rounded, of course.

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That would be amazing
if it was exactly 9.

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9 times 10 to the ninth, and
the units are newton-meter

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00:10:00,131 --> 00:10:03,629
squared per coulomb squared.

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00:10:03,629 --> 00:10:05,979
And why are those the units?

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Well, pretty much because at
the end, we have coulomb,

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coulomb, so we're going to have
coulomb squared divided

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by meter squared, and we want to
finish with newtons, so we

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want to cancel out the coulomb
squared by putting it in the

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00:10:18,862 --> 00:10:19,535
denominator.

213
00:10:19,535 --> 00:10:21,127
We want to cancel out the meter
squared by putting it in

214
00:10:21,127 --> 00:10:23,859
the numerator, and then we'll
end up with the newtons to get

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00:10:23,859 --> 00:10:26,139
the force, so that's just where
the units come from.

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00:10:26,139 --> 00:10:28,228
So given that, let's
figure out the

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force between two particles.

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So let's say I have-- and I've
spent 10 minutes with a pretty

219
00:10:35,899 --> 00:10:38,429
long-winded explanation, but the
actual problems you'll see

220
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in your physics class are pretty
straightforward when it

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00:10:41,098 --> 00:10:43,331
comes to Coulomb's Law.

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So they'll say, hey, we have a
positive-- we have a particle

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here that has a positive charge
of plus-- let me think

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of a good number-- plus 5
times 10 to the minus 3

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00:11:05,269 --> 00:11:07,226
coulombs, so that's
a positive charge.

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And then we have a negative
charge here, so let's say

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that-- I don't know.

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How far will I make them?

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Let's say that they're half a
meter apart, 0.5 meters apart,

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and then I have a negative
charge here that is 10 minus

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10 times 10 to the
minus 2 coulombs.

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So what is the force between
these two particles?

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So if we just plug them in to
Coulomb's Law, we get the

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00:11:38,762 --> 00:11:42,017
force due to the electricity.

235
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The electrical force.

236
00:11:44,355 --> 00:11:45,342
Not due to electricity.

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00:11:45,342 --> 00:11:46,693
We haven't done that yet.

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00:11:46,693 --> 00:11:49,100
The static electric force
between those two particles is

239
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equal to the constant 9 times
10 to the ninth times the

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first charge times 5 times 10
to the minus 3 times the

241
00:12:01,852 --> 00:12:04,757
second charge-- let me do that
in a different color-- times

242
00:12:04,757 --> 00:12:10,610
minus 10 times 10 to the minus
2-- I just rewrote that,

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although you probably can't
see it-- divided by the

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00:12:12,125 --> 00:12:15,408
distance squared,
so 0.5 squared.

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00:12:15,408 --> 00:12:17,374
We just plugged into
this formula.

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00:12:17,374 --> 00:12:18,837
So that equals-- let me see.

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00:12:18,837 --> 00:12:21,272
So 9 times 0.5 times 10.

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00:12:21,272 --> 00:12:23,584
I'm just going to do
the 10 separately.

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00:12:23,584 --> 00:12:25,207
So that's times minus 10.

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00:12:25,207 --> 00:12:31,840
This is 0.5 times minus 10 is
minus 5 times 9 is minus 45,

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00:12:31,840 --> 00:12:37,826
and then 10 to the ninth minus
3, so 10 to the sixth, and

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00:12:37,826 --> 00:12:41,978
then minus 2, so 10 to the
fourth-- times 10 to the

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00:12:41,978 --> 00:12:46,559
fourth-- divided by-- and
what's 0.5 squared?

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00:12:46,559 --> 00:12:49,511
It's 0.25, right?

255
00:12:49,511 --> 00:12:51,392
And this is equal to what?

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00:12:51,392 --> 00:12:53,562
That's equal to 4 times this
top, 160, plus this is equal

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00:12:53,562 --> 00:13:05,004
to minus 180 times 10 to
the fourth newtons.

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00:13:05,004 --> 00:13:07,474
And actually, this might seem
like a large number, but these

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00:13:07,474 --> 00:13:10,592
charges that I put here are
actually fairly large charges,

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00:13:10,592 --> 00:13:14,459
and hopefully you'll get a sense
for what's a big or a

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00:13:14,459 --> 00:13:15,614
small charge later.

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00:13:15,614 --> 00:13:17,463
But these are reasonably large
charges, and so that's why

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00:13:17,463 --> 00:13:21,411
there's a relatively large force
exerting between these

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00:13:21,411 --> 00:13:22,354
two particles.

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00:13:22,354 --> 00:13:24,557
Now, we got a negative number,
so what does that mean?

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00:13:24,557 --> 00:13:28,073
Well, we know that unlike
particles attract, right?

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00:13:28,073 --> 00:13:29,760
Almost by definition.

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00:13:29,760 --> 00:13:32,194
In this case, we had a positive
and a negative, so

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00:13:32,194 --> 00:13:36,790
when we end up with a negative
force when we use Coulomb's

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00:13:36,790 --> 00:13:40,592
Law, that means that the force
will draw the two particles to

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00:13:40,592 --> 00:13:44,477
each other along the shortest
distance between them.

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00:13:44,477 --> 00:13:46,175
I mean, it's not going to
make them go in a curve.

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00:13:46,175 --> 00:13:47,619
That kind of makes sense.

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00:13:47,619 --> 00:13:50,313
If we had a positive there, that
means that the force was

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00:13:50,313 --> 00:13:52,160
repelling the two particles.

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00:13:52,160 --> 00:13:53,843
And if you ever get confused,
just think about it.

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00:13:53,843 --> 00:13:55,839
If they're both negative,
they're going to repel.

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00:13:55,839 --> 00:13:58,057
If they're both positive,
they're going to attract.

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I will see you in
the next video.