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Concept #1: Conservation of Charge

Should say "Because of charge CONSERVATION" not "quantization".

**Transcript**

Hey guys. In this video we're going to be talking about conservation of charge, conservation of charge is an important law or a rule in physics and it's something that we're going to have to remember going forward, so let's get to it.

The central idea with conservation of charge is that charge cannot be created or destroyed, okay? So, we were to think about the whole universe as being represented in this circle there would be some amount of positive charges and some amount of negative charges in the universe, the reason why charge can neither be created nor destroyed is because in order for that to happen charges would have to leave the universe or they have to enter the universe but that would require something to exist outside of the universe and the universe by definition incorporates everything that is in existence so that thing can't exist outside of it that will just be weird, it wouldn't really make any sense. So, charges are neither created nor destroyed, okay? This fact this law is known as charge conservation, okay? And it's just a rule that we have to remember charges can only be moved from one object to another, that's it, okay? So, one object loses 1 Coulomb of charge the other object gains or not the other object that and other object some other object has to gain that 1 Coulomb of charge that the first object lost, okay? That's all that charge conservation means. So, let's do an example, in the following scenario each pair of conducting spheres is brought into contact and allowed to reach equilibrium, what is the amount of charge transferred and the direction of transfer in each of the cases, okay? So, first I want to mention what equilibrium means, equilibrium simply means that the charges are going to equal, okay? So, if one object has some amount of charge another opposite some amount of charge when they touch and they are allowed to reach equilibrium which takes some amount of time eventually when they do reach equilibrium their charges will be the same, okay? So, we have a negative 1 Coulomb charge a 3 Coulomb charge initially, when they're brought to contact that lacerates equilibrium, how much charge will each of them have, okay? In order to know that we need to know the total charge, well, the total charge is 3 coulombs plus negative 1 Coulomb which is 2 Coulombs. So, how much will they each have? They'll each have 1 Coulomb. So, how do we take our 3 Coulomb charge and make it 1 Coulom? We have to transfer 2 coulombs of charge to the left in this case from the positive to the negative charge, okay?

Now, Part B, same process, what is the total charge here? Well we have negative 5 coulombs on the, right? We have negative 3 coulombs on the left, the total charge is going to be negative 8 coulombs, how much do they each get then? They each get negative 4 coulombs just half of negative 8, how do we make negative 4 coulombs? Well the negative 3 Coulomb charge has to lose 1 Coulomb, if it's already at negative 3 and it loses another Coulomb it's. Now, at negative 4 coulombs, okay? Likewise with the negative 5 Coulomb charge gains 1 Coulomb its number increases to negative 4 coulombs, okay? Now, for this last one Part C, I want you guys to try this on your own, apply the same process, find the total charge find the charge on each of them and find the transfer charge. So, what you should do now is you should pause the video and try this on your own but I'm going to keep going, okay? The total charge is 3 coulombs minus 2 coulombs which is 1 Coulomb so the charged in each of them is half a Coulomb that means that the transfer has to be from the 3 Coulomb charge to the negative 2 Coulomb charge and it has to be 2 and a half coulombs, that's how much it'll take 3 to drop down to half coulomb okay? Now, just as a side note, we can have half of the Coulomb, okay? Don't get this confused with the fact that we cannot have half of an electron or half of an elementary charge. Remember, that was charge, that was called charge quantization, you cannot have half of an electron but half of a Coulomb is a huge amount of electrons. So, in this case you do not have half of an electron, half of a Coulomb perfectly, okay? Don't get that confused with charge quantization, let's do example two, okay?

Two charged metal balls move around inside of an insulated box colliding and randomly exchanging charges they're bouncing around, they are hitting, they're bouncing around, they're hitting, bouncing around hit, each time they hit they randomly exchange some amount of charge, initially one ball has 1 Coulomb of charge while the other has 3 coulombs of charge, after some amount of time you measure you find that one ball is charged to negative 2 coulombs, what is the charge on the other ball at this time, okay? Because of charge quantization whatever the total charge was initially has to be the total charge at any later time. So, let's find what that total charge is. Well, it's just 1 Coulomb from the left charge 3 coulombs from the right charge which is 3 coulombs so the total charge is still 4 coulombs, this is what charge conservation says. So, what I want you guys to think about, okay? Once again you can pause the video is, if the total charge on this box, right up here, has to be 4 coulombs and the charge of this one right here is negative 2 coulombs, what's the charge of our unknown okay? Well it should be positive 6 because positive 6 minus 2 coulombs is 4 coulombs, okay? And, if you want you can represent this as an equation that negative 2 plus our unknown has to equal 4. So, if I add 2 to each side our unknown equals 6 coulombs, this is the idea behind the law of conservation of charge. Remember, that this law is just a rule, okay? And it's very important. So, make sure that you understand it, thanks for watching.

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Concept #1: Conservation of Charge

Consider three identical metal spheres, A, B, and C. Sphere A has a charge of -2μC; sphere B has a charge of -6μC; and sphere C has a charge of +4μC. Spheres A and B are touched together and then separated. Spheres B and C are then touched and separated. Does sphere C end up with an excess or a deficiency of electrons and how many electrons is it?
A) deficiency, 6x1013
B) excess, 3x1013
C) excess, 2x1013
D) deficiency, 3x1012
E) There is no imbalance of electrons.

Two uncharged, conducting spheres, A and B, are held at rest on insulating stands and are in contact. A positively charged rod is brought near sphere A. While the rod is in place, someone moves sphere B away from A. How will the spheres be charged, if at all?
A) A+ and B+
B) A- and B-
C) A+ and B-
D) A- and B+
E) A=0 and B=0

Consider three identical conducting spheres in an equilateral triangle, two with a 4 C charge and one with a -4 C charge. If the spheres are all connected by a thin wire, what is the final charge on the lower left-hand sphere?
A) 0.333333
B) 3.66667
C) 1.33333
D) 2.0

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