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• - 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,

• 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.