in this video we're going to focus on solving problems associated with electric charge so let's start with this one if 4500 electrons were transferred to a neutral metal rod what would be the electric charge of the metal rod so let's draw a picture let's say this is the metal rod originally it's neutral so its initial charge is zero but then we're going to have 4500 electrons that's going to be transferred to this metal rod so once that happens it's going to acquire a negative charge we need to calculate what that new charge is going to be now what you need to know is that one electron has a charge of negative 1.602 times 10 to negative 19 coulombs now we could use this as our conversion factor so let's start with what we're given which is 4 500 electrons and let's convert it to charge so one electron we're going to put that on the bottom we can equate that to this quantity of charge so we set it up in such a way that the unit electrons will cancel and so we're going to multiply the two numbers so you should get Negative 7.2 times 10 to the negative 16 coulombs so that's going to be the new electric charge of this metal rod now let's move on to the second problem what is the electric charge of 3.6 moles of electrons so what we're going to do in this problem by the way feel free to pause the video if you want to try this problem yourself this is going to be a double conversion problem we're going to convert moles of electrons to number of electrons and then once we have the number of electrons we can convert that to electric charge in coulombs now we know that one electron has a charge of negative 1.602 times 10 to negative 19 coulombs so we're going to use that in the second part of the problem now another conversion factor that you need to know for this problem is Avogadro's number and that is one mole is equal to 6.022 times 10 to the 23. so if you have one mole of atoms that's 6.02 times 10 to the 23 atoms if you have one mole of calculators that's 6 times 10 to the 23 calculators so if we have one mole electrons that's going to be that number of electrons so let's start with what we're given which is 3.6 moles of electrons and let's convert that to the number of electrons using Avogadro's number so we're going to put moles of electrons on the bottom so we could cancel those two units and the other part of the conversion factor is going to go on top of this fraction so now we could use this conversion factor to convert from number of electrons to coulombs so since we have electrons here we're going to put this on the bottom of the third fraction and this is going to go on top of the third fraction now those units cancel and we simply need to multiply by the numbers on top so it's 3.6 times 6.022 times 10 to the 23 times a negative 1.602 times 10 to the negative 19. so you should get Negative 347 000. 300.784 coulombs now we can round that and convert it to kilograms by dividing by a thousand so this is approximately negative 347 kilo coulombs so that is the total electric charge of 3.6 moles of electrons now what about this problem what is the total electric charge of 50 kilograms of protons that's a lot of protons but how would you calculate the electric charge if you're given the mass instead of the number of moles well we could use a conversion process first we know that the charge on one proton is positive instead of negative but positive 1.602 times 10 to the negative 19 coulombs now the second thing that we need to know is the mass of an individual proton and you can look this up in your physics textbook one proton has a mass of 1.6726 times 10 to the negative 27 kilograms so with this information and these two conversion factors we can convert from 50 kilograms to the electric charge in columns so let's start with what we're given we have 50 kilograms of protons we'll use P for protons now let's use this to convert from kilograms to protons so since we have kilograms on top we're going to put kilograms on the bottom so 1.6 726 times 10 to the negative 27 kilograms of protons well that's just the mass of one proton so there's really no point in putting that we can just leave it like this and put one proton on top so one proton has this Mass in kilograms now we can cross out the unit kilograms now all we need to do at this point is use this conversion factor to convert protons into electric charge and we know one proton has a charge of 1.602 times 10 to the negative 19 coulombs so we can cross out the unit protons so we're going to multiply by the numbers on top and divide by the numbers on the bottom so it's 50 times 1.602 times 10 to the negative 19 clones divided by 1.6726 times 10 to the negative 27. so you should get 4.789 and this is approximately the routed answer times 10 to the 9 . let's make sure I have the right number of decimal places and this is columns so we could say that's approximately 4.8 Giga coulombs Giga is 10 to 9. so that is the total electric charge of 50 kilograms of protons it's pretty high now this problem is a lot more involved than the other three problems that we've considered and for those of you who want more difficult problems on electric charge check out my video on column's law I have a free version on YouTube which is about 35 minutes long close to 36 minutes but the full version which is an hour and 40 minutes long you can find that on my patreon page or in my YouTube membership program so I'm going to post a few links in the description section below for those of you who might be interested now for those of you who want to sign up for my patreon membership program you can access it at patreon.com math science tutor now if you click on this link physics it'll give you all my physics videos but I do have other videos on calculus organic chemistry General chemistry precal and more as well but clicking on physics you'll see all my physics topics so these are where you could find the full length version of my YouTube videos what you see on YouTube those are the free versions so some of these videos on YouTube might be 30 minutes long but the full version might be an hour it might be two hours long and it contains worksheets as well but we're going to scroll all the way down until we get to column's law so here it is so this is the full video as you can see it's about an hour and 40 minutes long and here you have the worksheet which contains a printout of all the problems in the full extended video since some of you have been requesting that but in this video you're going to find more problems on electric charge particularly the harder ones now you can also access this video on my YouTube membership program but for those of you who want the worksheet I only currently have it on my patreon membership program now I do have some other physics 2 videos here electric Fields as you can see from this picture a lot of hard problems here electric potential electric potential energy and even on capacitors as well so feel free to take a look at this when you get a chance I'm going to post some links in the description section below this video so you it will take you it'll take you directly to this page but now let's get back to this problem a metal sphere with a charge of positive 20 microklumes is placed in contact with an identical metal sphere carrying a charge of positive four micro plumes what will be the new charge of each sphere after equilibrium is established so let's draw a picture so we have two metal spheres we'll call this we'll say this is number one and this is number two they both carry a positive charge the first sphere has the charge of 20 microcloons the second one has a charge of four micro columns and then the two spheres will be placed in contact with each other so after they've been in contact for some significant time what's going to be the new charge on each sphere now we're dealing with identical spheres so the charges will be the same since each sphere has the same surface area if we want to calculate the new equilibrium charge where they're the same all we need to do is average the two numbers so we're going to add up 20 and 4 and then we'll divide it by 2. so this gives us 24 divided by 2 which is 12. so charge one is going to be 12 micro coulombs charge two I mean this metal sphere 2 will also be 12 microclumes now Part B what type of electric particles were transferred would you say protons or electrons well you need to be familiar with the structure of an atom but more specifically the atoms in the metal so the atoms in a metal the nucleus contains the protons outside of the protons you have the orbitals where you'll find the electrons now the protons they're stuck in the nucleus they don't move but in a metal the electrons they're free to move so when you're dealing with electricity it is the electrons that are moving through the metallic wires that's why Metals conduct electricity is because these charge carriers these electrons they're free to move in a in a metal particularly the valence electrons the core electrons they're stuck in the atom but the outermost Advanced electrons they're free to move in the metal so when electric charge is transferred from one metal sphere to another metal sphere you need to know that it is not the protons that are being transferred it is the electrons so that's the answer to the part B it is the electrons that are being transferred now the next question is for part C how much electric charge was transferred and from where was it transferred initially q1 had a charge of positive 20. and then after some time T it went down to 12. so it lost eight microclumes of charge so its charge went down Q2 initially had four microclobes of charge then it went up to 12. so it gained eight micro coulombs of charge not that again protons again this positive charge through the loss of electrons so electrons are negative and they like to flow towards positive charges so the electrons will flow from spheres two to three or one as that fear one it's going to flow from sphere metal sphere 2 to metal sphere one because metal sphere one is more positive it has a higher positive charge metal sphere 2 is less positive which means it's more negative than metalsphere 1 in a relative sense and electrons they're attracted to positive charges so they're going to go towards the metal sphere with the higher positive charge and so it was transferred from metal sphere to to metal sphere one so we know from where it was transferred and where it went to and we also know how much electric charge was transferred that is eight microklumes since we're dealing with electrons they carry a negative charge so the charge that was transferred is negative eight microclimbs as opposed to positive eight the reason why this gained positive charge is because it lost electrons this lost positive charge because it gained electrons now how many electric particles were transferred we know the electric charge that was transferred we just got to convert that to the number of electrons so first let's convert micro coulombs to coulombs one micro coulomb micro is 10 to negative six so that's one times ten to the minus 6 coulombs and we know that one electron has a charge of negative 1.602 times 10 to the negative 19 cloves so the unit micro coulombs cancel and the unit coulombs cancel giving us the number of electrons so we're going to multiply by the numbers on top and divide by the number on the bottom so it's negative 8 times 1 times 10 to the negative six divided by negative 1.602 times 10 to the negative 19 coulombs so this is equal to 4.99 times 10 to the 13 electrons so that's how many electrons were transferred from metal sphere 2 to metal sphere 1. so hopefully this video gave you a good introduction into the concept of electric charge by the way this particular example problem it illustrates something called the law of conservation of electric charge that is that the total amount of electric charge in a closed system remains constant so before the two metal spheres were brought into contact with each other the total electric charge before the interaction was 20 plus four which is 24 microclumps after contact the total charge Remains the Same 12 plus 12 is 24. so the total electric charge of this closed system we don't have any outside forces acting on it the total electric charge was conserved it remained constant it stayed 24 microclumes so that's the basic idea behind the law of conservation of electric charge the total amount of electric charge in a closed system remains constant