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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,

  • 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