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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 amend 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 we'll imagine you had a box and inside of this box I'm going to put some charges so let's say we have a particle here and it's charges 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 I'm not going to 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 if you want a mathematical statement I like math the mathematical statement is 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 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 5 plus 2 is 7 minus 3 is 4 positive 4 coulombs you ever open up this box you're always going to find 4 coulombs in there now this sounds possibly obvious you might be like duh if you don't let these charges go in or out of course you're going to only 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 two these were protons they're not because this is a positive two coulombs 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 an electron you might end up with muons or top quarks or if this is another proton 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 and 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 have to have the same charge maybe this one is 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 charged as 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 uh 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 I don't 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 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 if you don't let any charge in or out the total charge in here has to say 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 is after equal 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 law of conservation of charge says that's equal positive four well negative 7 and negative 4 is negative 11 plus 1 is negative 10 so I get negative 10 coulombs plus you know these cues look like nines sorry about that this is law of conservation of charge if I add a little tail this isn't the law of conservation of nines so there's a little Q this is a little Q not a 9 and so plus Q equals 4 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 no one really does physics in cardboard box so let's say you were doing an experiment and there was some particle X and X particle and it had a certain amount of charge it had say positive 3 coulombs that would be enormous for a particle but for the sake of argument say it has positive 3 coulombs well it decays sometimes particles decay they literally disappear turn into other particles let's say it turns into a Y particle and the 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 1 Coulomb well is this possible no this is not possible if you discover this something went wrong so because of this side over here you start it off with positive 3 coulombs over here you've got to end up according to the law of conservation of charge with positive 3 coulombs but positive two coulombs minus 1 Coulomb that's only one Coulomb you're missing you're missing 2 coulombs over here where the other two coulombs go there had to be there had to be some sort of mystery particle over here that you missed something happened either your detector messed up or just didn't detect a particle that had another amount of charge how much charge should it have this whole sides got to add up to three so if you started off with three over here these two together y&z are only one Coulomb that means the remainder the two coulombs the missing two coulombs has to be here so you must have had some particle or some missed charge that has positive two coulombs is that another why particle maybe that's why physics is fun maybe it is now maybe you miss to 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 have some particle with zero coulombs is it possible to end up with particles that have charge yeah it can't happen in fact if you have a photon that has a 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 got to make sure that whatever charge this gets say positive three coulombs 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 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 antielectrons recalled 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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