- There's a law in physics that has stood the test of time.
Laws come and go.
Sometimes we discover new things.
We have to scrap them, ammend them, adjust them,
tweak them, throw them away,
but there's one law that has been around for a long time
and no one has ever, ever tried to damage this law
or discovered any experiment that has shown it to be wrong,
and it's called the law of conservation of charge.
And this is electric charge, is what we're talking about
in this particular example.
So what does this mean?
Well, imagine you had a box and inside of this box
I'm gonna put some charges.
So let's say we have a particle here
and it's charge is positive two coulombs.
And then we have another charge flying around in here,
and it has a charge of negative three coulombs.
And we have another charge over here
that's got, I don't know, positive five coulombs.
These are flying around.
What the law of conservation of charge says
is if this box is closed up, in the sense that
no charge can enter or exit.
So I'm not going to let any charge come in
and I'm not gonna let any charge go out.
If that's the case, the total charge inside
of this region of space has to be constant
when you add it all up.
So if you want a mathematical statement,
I like math, the mathematical statement is that if you
add up, the sigma is the fancy letter for adding up,
all the charges in a given region,
as long as, here's the asterisk,
as long as no charges are incoming or outgoing,
then the total amount of charge in that region of space
has to be a constant.
This math looks complicated, it's actually easy.
All I'm saying is that if you add up all this charge...
Positive two coulombs plus five coulombs
minus three coulombs, you'll get a number
and what that number represents is the total
amount of charge in there.
Which is going to be, five plus two is seven,
minus three is four.
Positive four coulombs.
You ever open up this box, you're always going to
find four coulombs in there.
Now this sounds possibly obvious.
You might be like, duh.
If you don't let any of these charges go in or out,
of course you're only going to find four coulombs in there
because you've just got these three charges.
But not necessarily.
Physicists know if you collide two particles,
these things don't have to maintain their identity.
I might end up with eight particles in here
at some later point in time.
And if I add up all their charges, I'll still get four.
That's the key idea here.
That's why this is not just a frivolous
sort of meaningless trivial statement.
This is actually saying something useful,
because if these protons, they're not because
this is a positive two coulomb and the proton
has a very different charge,
but for the sake of argument, say this was a proton,
runs into some other particle, an electron, really fast.
If there's enough energy, you might not even end up
with a proton and an electron.
You might end up with muons or top quarks
or if this is another proton,
you end up with Higgs particles or whatever.
And so at some later point in time,
here's why this law is important and not trivial,
because if this really is closed up
and the only stuff going on in there is due to these
and whatever descendants particles they create,
at some later point in time I may end up with, like,
say this one, it doesn't even have to have the same charge.
Maybe this one's positive one coulomb.
And I end up with a charge over here that has
negative seven coulombs.
If these were fundamental particles,
they would have charges much smaller than this,
but to get the idea across, big numbers are better.
And let's say this is negative four coulombs.
And then you end up with some other particle,
some other particle you didn't even have there.
None of these particles were there before.
And some charge q.
Now we end up with these four different particles.
These combined, there was some weird reaction
and they created these particles.
What is the charge of this q?
This is a question we can answer now,
and it's not even that hard.
We know the charge of all the others.
We know that if you add up all of these,
you've got to add up to the same amount of charge
you had previously, because the law of
conservation of charge says is if you don't let any
charge in or out, the total charge
in here has to stay the same.
So let's just do it.
What do we do?
We add them all up.
We say that positive one plus negative seven coulombs
plus negative four coulombs plus whatever charge
this unknown, mystery particle is.
We know what that has to equal.
What does that have to equal?
It has to equal the total charge,
because this number does not change.
This was the total charge before, positive four coulombs.
That means it has to be the total charge afterward in there.
That's what the law of conservation of charge says.
So that has to equal positive four.
Well, negative seven and negative four is negative 11,
plus one is negative 10.
So I get negative 10 coulombs, plus...
Oh, you know what, these q's look like nines,
sorry about that.
This is law of conservation of charge.
I'm gonna add a little tail.
This isn't the law of conservation of nines.
So this is a little q.
This is a little q, not a nine.
And so plus q equals four.
Now we know that charge has to have a charge of
14 coulombs in order to satisfy this equation.
But you don't even really need a box.
I mean, nobody really does physics in cardboard box,
so let's say we're doing an experiment
and there was some particle x, an x particle.
And it had a certain amount of charge,
it had, say, positive three coulombs.
That would be enormous for a particle,
but for the sake of argument,
say it has positive three coulombs.
Well, it decays.
Sometimes particles decay, they literally disappear,
turn into other particles.
Let's say it turns into y particle and z particle.
Just give them random names.
And you discover that this y particle
had a charge of positive two coulombs
and this z particle had a charge of negative one coulomb.
Well, is this possible?
No, this is not possible.
If you discover this, something went wrong
because this side over here,
you started with positive three coulombs.
Over here you've gotta end up,
according to the law of conservation of charge,
with positive three coulombs, but positive two coulombs
minus one coulomb, that's only one coulomb.
You're missing two coulombs over here.
Where'd the other two coulombs go?
Well, there had to be some sort of mystery particle
over here that you missed.
Something happened.
Either your detector messed up or it just didn't
detect a particle that had another amount of charge.
How much charge should it have?
This whole side's gotta add up to three.
So if you started off with three,
over here, these two together, y and z,
are only one coulomb.
That means that the remainder, the two coulombs,
the missing two coulombs, has to be here.
So you must've had some particle or some
missed charge that has positive two coulombs.
Is that another y particle?
Maybe, that's why physics is fun.
Maybe it is in there, maybe you missed another one.
Let me ask you this.
So let's say we get rid of all these charges.
Here's one that freaks people out sometimes.
Take this.
Let's say this had no charge.
No charge, it was uncharged.
You got some particle with zero coulombs.
Is it possible to end up with particles that have charge?
Yeah, it can happen.
In fact, if you have a photon that has no charge,
it's possible for this photon
to turn into charged particles.
How is that possible?
Doesn't that break the law of conservation of charge?
No, but you've gotta make sure that
whatever charge this gets, say positive three coulombs,
then this one's going to have to have
negative three coulombs so that the total amount of charge
over here is zero coulombs just like it was before.
So this is weird, but yeah, photon, a beam of light,
can turn into an electron, but that means
it has to also turn into an anti-electron
because it has to have no total charge over here.
And an anti-electron has the same charge as an electron,
but positive instead of negative.
Which is why it's called a positron.
Anti-electrons are call positrons because they're the same
as electrons, just positive.
You don't really need to know that.
In fact, you don't need to know a lot
about particle physics, that's the whole point here.
Just knowing conservation of charge
lets you make statements about particle physics
because you know the charge has to be conserved
and that's a powerful tool in analyzing these reactions
in terms of what's possible and what's not possible.
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