- [Voiceover] Let's talk a little bit about one of the,
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 can could've called them negative.
But that when something has a positive charge
and when something else has a positive charge
that they repel each other.
And we also know that if I had something else,
another particle that happened
to havea negative charge
and once again the word negative being applied
to this is completely arbitrary.
They could've 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.
All right, 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.
I actually didn't.
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 in our brains are wired
to in some way comprehend what mass is
but we're probably more 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...
like charges repel
and opposite charges...
opposite charge attract or unlike charges attract.
All 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 unity of charge is called the Coulomb.
It's named after a scientist
in the late 1700s who played around a lot with charge.
You can 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, well, unless you go
and start going into quantum theory
and start thinking about quirks 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 on atoms and whatever else,
but let me just draw a little example.
So, a atom tends to have some neutrons in them
which don't have this charge property.
It'll have some protons in 'em
which have a positive charge and once again
that's kind of arbitrarily defined as positive.
We could've called it it has a red charge.
And then it has these things floating around
that are much lighter than, the much, much, lighter
than the, than the protons and the neutrons in the nucleus.
And these are called electrons.
It's not even clear that they,
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.
Charge of electron.
But if we didn't care about size,
about sign than the magnitudes are the same.
So, that's the fundamental as far as
we know as 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 a 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 six point two four
times ten to eighteenth Es.
Or you could say six point two four
times ten 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 it direction.
So, if you look at the other way around
you could say the elementary charge, the elementary charge,
is equal to, at least its magnitude,
one point six times ten to the minus nineteen 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 do?
We've, 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, let's say, protons than electrons
and 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, in part of the initial,
I guess we can call it definition on what charge is
I said that like charges repel.
Right, like charges repel, so if those, both
of these are positive they're going to repel each other.
And unlike charges, if this is negative, this is positive,
they're gonna attract each other, right?
So, by definition, if they are moving each other,
they're, 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 particules
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 name 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 thirty seconds I'll tell you which,
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.
Force from gravity between two masses is
equal to the gravitational constant
times M one times M two divided
by the distance between them squared.
So, so far the two forces that we 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 into gravity, in a vacuum.
So, it doesn't matter if you have no air,
if you have no substances between the two particles,
somehow they're 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 this particle is there
and that particle knows that that particle is there,
and they start moving without having any,
It's not like they have a wire connecting 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 is there
and when we start learning about
special relativity and all of that
we'll learn that, oh, maybe there's nothing there
but maybe the masses are somehow shaping the universe,
and maybe that's happening with,
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 six point...
I always forget what that constant is.
It is nine times ten to the ninth.
So, K, that's, it's rounded of course.
That would amazing if it was exactly nine.
Nine times ten to the ninth
and the units are newton meters squared per Coulomb squared,
and why are the...
Why are those the units?
Well, pretty much because at the end we have,
we have Coulomb, Coulombs.
We're gonna have Coulomb squared divided by meters squared
and we wanna finish with newtons
so we wanna cancel out the Coulomb square
by putting in the denominator.
We wanna cancel out the meters square
by putting 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, I have,
and I've spent ten 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,
let's call it, I don't know, plus,
I don't know, let me think of a good number.
I don't know, plus five times ten
to the minus three Coulombs.
So, that's a positive charge.
And then we have a negative charge here.
And let's say that, I don't know, how far will I make them.
Let's say that they're half a meter apart,
point five meters apart,
and then I have a negative charge here that is,
let's say that this is ten minus ten times
ten to the, I don't know, minus two Coulombs.
So, what is the force between these two particles?
So, if we just plug them in to Coulomb's law
we get the electric, the force due to electricity,
due to 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, nine times ten to the ninth.
Nine times ten to the ninth times the first chage
times five times ten to the minus three
times the second charge.
Let me do that in a different color.
Times minus ten times ten to the minus two.
I just rewrote that although you probably can't see it.
Divided by the distance squared, so point five squared.
We just plugged into this formula.
So, that equals, let me see.
So, nine times point five times ten.
I'm just gonna do the ten separately.
So, that's times minus ten.
So, it's minus, this is point five times
minus ten is minus five, times nine is minus forty five,
and then ten to the ninth minus three,
so ten to the sixth and then minus two.
So, ten to the fourth times ten to the fourth
divided by, and what's point five squared is point two five.
All right, and this is equal to what?
It's equal to four times is not one sixty
plus this is equal to minus one hundred and eighty
times ten 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 we'll, hopefully you'll get a sense for
what's a big or 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 negative.
So, when we have a negative...
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 their,
the shortest distance between them.
I mean, it's not it's gonna make them go in a curve.
It kinda makes sense.
If we had a positive there, then that means
that the force was repelling the two particles.
And if you ever get confused,
just think about it.
If they've both negative, they're gonna repel.
If they're both positive, they're going to attract.
I will see you in the next video.