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### Course: AP®︎/College Physics 1 > Unit 10

Lesson 2: Conservation of charge# Conservation of charge

The law of conservation of charge states that the total amount of electric charge in a closed system must remain constant. See how this law can be applied to various scenarios, such as when particles collide or decay. Learn how the law of conservation of charge can be used to deduce charges of unknown or undetected particles within a closed system. Created by David SantoPietro.

## Want to join the conversation?

- At8:20, is an anti-electron (or positron) the same as a proton?(63 votes)
- Anti-particles have the same mass, but the opposite charge to their counter-particles. For example, the anti-electron (or positron) has +e charge and same mass as an electron. On the other hand, a proton has +e charge and is 1836 times heavier than the electron (or positron for that matter) .(170 votes)

- It is stated that if there is a neutral particle which breaks up into several charged particles, then the net charge should be 0. But Sal said that positive and negative are just used to describe two different charges. How can they cancel each other out then?

I also read in a book that because the net charge is zero when two differently charged particles with the same magnitude are placed together.This contradicts Sal's statement. Can someone kindly clear up the confusion?(20 votes)- The convention of charges being called 'positive' and 'negative' has been made to make it easier for physicists to deal with charge, and thus this law has been stated in this way. Let me state it as such that it doesn't contradict with any convention being followed
*There are two types of charge. The net total of the charge in existence, provided one type is the counterpart of the other, is constant.*(41 votes)

- After8:00, he said that a photon or a beam of light may turn into an electron and a positron. If a beam of light has no mass, how does it turn into particles that have (a very small amount of) mass?(20 votes)
- great question. I prefer to think about the process in reverse (as a first step in the discussion)

So...

If an electron meets with a positron what happens? and why? The positron is anti-matter and I find it useful to think about it as having the same amount of 'anti' mass as the electron has 'real' mass. So, when they meet, they annihilate one another.... their 'masses' are kind of cancelled out and converted into pure energy. (Good old 'E equals m c squared'...) This energy will now be in the form of radiation or photons.

Second part of the discussion: The reverse is also true...Photons can convert their energy into 'pairs' of particles. If the energy of the photon is high enough, then it might form an electron and a positron.

Can you work out what the wavelength of the original photon must be if it is going to have enough energy to produce electron-positron pair?(28 votes)

- I'm confused what exactly a Coulomb is and what it represents..(4 votes)
- Measure of how much charge there is.

Similar to kilograms for mass.(17 votes)

- Now I know charge is another property of matter, but it seems similar to energy. So is charge another form of energy?(9 votes)
- charge can be seen as an attractive or repulsive force between two particles while energy in laymans terms can be how fast something vibrates, like magnets attract each other fundamentally due to charges in them.(1 vote)

- Is it the flow of charge or the flow of electrons? I have seen both explanations for current.(5 votes)
- The direction of current is conventionally taken to be opposite to to the direction of flow of electrons.. I'd say flow of charge..(1 vote)

- can the law of conservation of charge be stated as the total amount of charge within a space remains constant if kept under constant physical conditions?

are proton and anti-electron same?(in detail)(2 votes)- The antimatter particle to the electron is the positron.(3 votes)

- Is the foundational concept of Conservation of Charge, paired with the Conservation of Energy, the basis for how the LHC detects new particles? Does it just basically look for missing total mass/charge/energy after a collision and see if the mystery particle proposed would fit that and then try to observe it?(2 votes)
- No - you can't just "look for missing total mass/charge/energy" that easily. Particles like the Higgs Boson will decay* into a set of lighter particles almost immediately. Those are detected and the physicists look for those specific sets.

(*) Particle decay means the particle (usually "Hadrons") spontaneously transforms into other particles. Of course, the conservation laws still apply.(3 votes)

- we say electron and proton have charge negative and positive then how can we define charge. what is charge?(1 vote)
- Charge is a fundamental property of all matter. It determines the electromagnetic force interactions between matter. We don't have a further understanding of charge beyond that.(5 votes)

- Do all the subatomic particles in universe have a charge if 1.6*10^-18 . If not then how is quantization of charge true ?(2 votes)
- Well, the quantization of charge implies that charge is quantized in terms of integral multiples of charge on proton. Quarks are an exception, and to clear up any confusion you may have regarding that, go to this link

http://en.wikipedia.org/wiki/Elementary_charge(2 votes)

## Video transcript

- 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.