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

more mysterious forces
of the universe.

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

fairly mysterious,
so let's talk a

little bit about charge.

And we've all heard of charge.

Charge the battery.

This particle has charge.

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

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

that if something contains a
positive charge-- and calling

it positive is a little
bit arbitrary.

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

We could have called
them negative.

But when something has a
positive charge and when

something else has a positive
charge, that

they repel each other.

We also know that if I had
something else, another

particle that happened to have
a negative charge, and once

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

completely arbitrary.

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

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

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

attracted to a positive
charge.

So what do we know
about charge?

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

enough particles together,
I guess objects have that

property as well.

So it's just a property.

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

know what it is.

And frankly, no one
fundamentally

knows what it is.

Actually, no one really
fundamentally knows anything.

But charge is a property
of particles and

objects, just like mass.

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

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

charge, because our brains
are wired to in some way

comprehend what mass is, but
we're probably comprehending

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

about that at another time.

Charge is a little bit more
abstract because, before we

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

experience much charge unless
we got struck by lightning.

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

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

arbitrarily named positive
and negative.

And we know that like charges
repel and opposite charges

attract, or unlike charges
attract, right?

So what can we do with this?

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

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

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

the coulomb.

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

around a lot with charge.

You could look up more about
him on Wikipedia.

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

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

of elementary particles, just
because, to some degree,

unless you go into quantum
theory and start talking about

quarks and stuff, the elementary
charge is the

charge on a proton
or a neutron.

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

structure of atoms and whatever
else, but let me just

draw a little example.

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

have this charge property.

It'll have some protons
in them, which

have a positive charge.

Once again, that's kind of

arbitrarily defined as positive.

We could have called
a red charge.

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

much, much lighter than the
protons and the neutrons in

the nucleus, and these
are called electrons.

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

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

view them as objects.

Sometimes it's useful
to view them as--

well, not as objects.

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

a negative charge.

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

concerned right now before we
start talking about quarks and

other potentially subatomic
particles, is the charge in an

electron or proton.

And they have the exact same
charge, and that elementary

charge is denoted by e.

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

elementary or e stands
for electron.

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

probably stands for elementary
charge of a proton.

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

negative e is the charge
of an electron.

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

magnitudes are the same.

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

our physics.

That's the fundamental charge.

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

or neutron.

So how does a coulomb
relate to that?

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

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

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

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

the eighteenth e's.

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

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

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

Because if I just say
coulomb, I'm not

really giving a direction.

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

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

1.6 times 10 to the
minus 19 coulombs.

So fair enough.

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

usually be provided for
you in some way.

So what can we do?

We say that these objects have
this property called charge.

Like charges repel.

Unlike charges attract.

If we have enough of these
protons together, then the

whole object has charge.

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

positive charge.

If we have more electrons
than protons, we

have a negative charge.

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

coulomb, which is a bunch of
the fundamental charge.

So let's play around with
this and see if

we can measure charge.

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

definition on what charge is,
I said that like charges

repel, right?

Like charges repel so both
of these are positive.

They're going to repel
each other.

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

they're going to attract
each other, right?

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

particles are going
to accelerate

away from each other.

These two particles are
going to accelerate

towards each other.

The charge between these
particles or the charge in

each of these particles must
be generating some type of

force, right?

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

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

Coulomb's Law, and this
is why we named

charges after Coulomb.

Coulomb figured out that the
force between two charges is

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

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

direction-- is equal to some
constant times the first

charge times the second charge
divided by the distance

between them squared.

And this is pretty neat because
this looks an awful

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

that looks a lot like the
gravitational force equation.

Let me write that down.

The force from gravity between
two masses is equal to the

gravitational constant times
m1 times m2 divided by the

distance between them squared.

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

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

expand this to electromagnetic
force, it seems like they kind

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

forces apply in a vacuum.

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

substances between the two
particles, somehow they are

communicating with each
other, which I find

kind of amazing, right?

You can have nothing between
these two particles, but

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

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

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

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

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

Start moving.

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

think about it and you might.

And it's just like gravity.

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

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

that the other particle's
there.

And when we start learning about
special relativity and

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

maybe the masses are actually
somehow shaping the universe.

And maybe that's happening
with the

electric charges as well.

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

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

to the product of their
respective charges divided by

the square of the distance
between them.

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

What was it?

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

It is 9 times 10 to the ninth.

It's rounded, of course.

That would be amazing
if it was exactly 9.

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

squared per coulomb squared.

And why are those the units?

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

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

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

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

denominator.

We want to cancel out the meter
squared by putting it in

the numerator, and then we'll
end up with the newtons to get

the force, so that's just where
the units come from.

So given that, let's
figure out the

force between two particles.

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

long-winded explanation, but the
actual problems you'll see

in your physics class are pretty
straightforward when it

comes to Coulomb's Law.

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

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

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

coulombs, so that's
a positive charge.

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

that-- I don't know.

How far will I make them?

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

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

10 times 10 to the
minus 2 coulombs.

So what is the force between
these two particles?

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

force due to the electricity.

The electrical force.

Not due to electricity.

We haven't done that yet.

The static electric force
between those two particles is

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

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

second charge-- let me do that
in a different color-- times

minus 10 times 10 to the minus
2-- I just rewrote that,

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

distance squared,
so 0.5 squared.

We just plugged into
this formula.

So that equals-- let me see.

So 9 times 0.5 times 10.

I'm just going to do
the 10 separately.

So that's times minus 10.

This is 0.5 times minus 10 is
minus 5 times 9 is minus 45,

and then 10 to the ninth minus
3, so 10 to the sixth, and

then minus 2, so 10 to the
fourth-- times 10 to the

fourth-- divided by-- and
what's 0.5 squared?

It's 0.25, right?

And this is equal to what?

That's equal to 4 times this
top, 160, plus this is equal

to minus 180 times 10 to
the fourth newtons.

And actually, this might seem
like a large number, but these

charges that I put here are
actually fairly large charges,

and hopefully you'll get a sense
for what's a big or a

small charge later.

But these are reasonably large
charges, and so that's why

there's a relatively large force
exerting between these

two particles.

Now, we got a negative number,
so what does that mean?

Well, we know that unlike
particles attract, right?

Almost by definition.

In this case, we had a positive
and a negative, so

when we end up with a negative
force when we use Coulomb's

Law, that means that the force
will draw the two particles to

each other along the shortest
distance between them.

I mean, it's not going to
make them go in a curve.

That kind of makes sense.

If we had a positive there, that
means that the force was

repelling the two particles.

And if you ever get confused,
just think about it.

If they're both negative,
they're going to repel.

If they're both positive,
they're going to attract.

I will see you in
the next video.