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24. Electric Force & Field; Gauss' Law

1

concept

5m

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Hey, guys. So I want to talk about something called electric charge. In this video, you're gonna need to know what for this chapter, but also for other chapters in this course. So let's get to it. But first off, I want to sort of briefly reintroduce you to atoms and atomic structure. So remember that atoms are made of protons, neutrons and electrons, and these protons and neutrons sit inside of this central structure in the atom that we call the nucleus. Whereas the electrons sort of float around on the outside and they orbit this nucleus. Now there's something special about these electrons and this protons. They have a property called electric charge, whereas the neutrons do not. The electric charge is a property of matter is just something that matter has similar to mass. So if you've seen the gravitation chapter, we can actually draw some important analogies between mass and electric charge. For instance, in gravitation, we needed mass in order to create a force and the mawr mass that we had the mortgage gravity or the stronger than that gravitational force. Waas. It's very similar for electric charge. You need charge in order to create an electric force and the mortuaries that you have the Mawr or stronger that electric force becomes now where things start to get a little bit different. Is that in mass and gravitation? We only assume that these numbers were positive. Positive. 5 kg 10 kg. Whatever. You couldn't have a negative mass. Well, physicist a couple of 100 years ago noticed that there was different interactions between charges such that there could be positive or negative. We'll talk about that a little bit later so you could actually have positive and negative charges. One of the other main differences is that in Mass, there was never like a smallest amount of mass that we could have at least physicists that seem to think so. But in electric charges, there is something called the elementary charge. What that means is the smallest amount of charge that something could possibly have. And it's a letter known as E, which is 1.6 times 10 to the minus 19 and the Capital C is the unit for that, which stands for cool OEMs. Now what I wanna do is I wanna make sure that you don't get confused between E and electron, so those were not the same exact thing. In fact, when we're talking about protons and electrons, we said they both have electric charge. Now the charge of a proton is going to be positive. E That's just something that we arbitrarily decided. We just decided to pick it that way. And the charge of an electron is going to be negative. E So this is just sort of like the magnitude and these air actually like these signs positive and negative. So whenever I'm referencing electrons in future videos, I'll try to do with capital letters and I'll write something like electron just so you don't get confused between that. Okay, so we've talked about protons and electrons having charge. So now objects that are not just those things. So Adams and things like that we see every day have charges well, and the net charge of any object is the quantity of imbalance between the number of protons and electrons inside of it. So I want to go ahead and draw a few examples. So we have an atom right here, and all you have to do is just count up the number of protons it has So you've got two protons over here, so that has plus two electric charge. We also have two electrons on the outside. So those two electrons contribute negative to E. So in other words, we have no imbalance between the protons and the electrons. So that means that the charges just zero. That's the net charge in this object. There's no imbalance, whereas over here I've got four protons inside of the nucleus. By the way, the neutrons are also in there somewhere. I just have drawn them and we've got plus four e from those elect from those protons and we've got three electrons on the outside. So that's three electrons, four grand total of minus three. Notice how these things are not equal. There is an imbalance. In fact, this one has one mawr proton. So that means that the total charge is equal to plus E. Now we've got four electrons over here and we've got two protons. So two protons for a total of plus two e, we've got four electrons for a total of minus four e. And so that means the grand total for the imbalance is that there are two more electrons than protons. So that means we're gonna have minus two e. Now, I also want to point out that neutrons neutrons have zero charge, so you don't never have to worry about neutrons or anything like that. Now I want what I also want you to recognize. Is that all three of these examples? These charges, the total number of charge was an entire multiple of E. There's a fancy $5 word you're gonna see for that called charge quantity, ization. And all that word means is that these things have to come into your multiples, e. You can't have half of a neat You can't have negative one quarter of any. It has to be negative one to, you know, 012 things like that. I have to be whole entire multiples and there's an equation they're gonna be using to calculate the total charge of something. It's something that we've used in all three of these examples. Just count the number of protons and the number of electrons. You subtract them and multiply it by the elementary charge. Now, sometimes in this equation, you'll see it in your textbook with ends instead, and all that end just means is the number. So sometimes you'll see it written like this N p minus e. But because it has e and e here, I don't want to say I don't want to confuse you guys, but that's something you definitely should be familiar with in case you see it in textbooks. Great. So most of the material that we're gonna see in physics are gonna be electrically neutral. So that means that the number of protons is perfectly equal to the number of electrons similar to how this example actually worked out. And so the total number of the total net charge of these objects is equal to zero. So you're gonna assume that objects are electrically neutral unless that problems specifically tells you that it's not. And that's it for this video. Guys, let's go ahead and take a look at some examples

2

example

1m

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Hey, guys, hopefully able to figure this one out on your own? So in this problem were asked how What is the total charge of an atom? We're told the amount of protons and the amount of electrons. So let's go ahead and use our charge equation. So we know that charge is equal to we've got the number of protons minus the number of electrons, and we're gonna multiply that by the elementary charge. So the total charge should be We've got 16 protons, minus seven electrons, and that's a that's a seven right there. And we're gonna multiply by the elementary charge, which is 1.6 times 10 to the minus 19. You're gonna need to remember that number. So go ahead and commit it to memory right now. So we've got two. Q is equal to you. Go ahead and work all this out. It should be nine times 1.6 times 10 to the minus 19 and that's a total charge of 1.44 times 10 to the minus 18. Cool. OEMs. So that's the total amount of charge, and what I want you to do is notice that it's also positive and that makes sense because we have more protons, their arm or protons than electrons. So we should end up with a positive number. Let me know if you guys have any questions.

3

Problem

How many electrons make up −1.5 × 10^{−5} C?

A

9.375×10^{13}

B

2.4×10^{−24}

C

1.5×10^{14}

D

9.375×10^{−25}

4

example

4m

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Hey, guys, let's do another example about electric charge. Okay? Waterways. 1 kg per leader has a molecular weight of g per mole and has 10 electrons per molecule. Part A. How many electrons does two liters of water have? And part B. What charges? What charge do these electrons represent? So however many electrons we find in part A what is the charge of those electrons? Okay, so for part a first, what we wanna do is we want to figure out how to get from leaders, which is what we're given were given two liters of water to number of electrons. This will tell us how to solve the problem. We need to create a sort of map to the solution. Okay, let's start with leaders, right, Because that's what's given to us. What can we go to next? Well, we're told that there's a conversion between Kilograms and leaders that we can say for every leader of water it has a mass of 1 kg. So we know how to go from kill a grip from leaders. 2 kg. Next we have grams to moles. Now we don't have kilograms, two moles, but we know right away that 1 kg 1000 g So we can easily go from kilograms 2 g and then using the conversion, go from grams to moles. Now, our last conversion is electrons per molecule. We don't have our number of molecules yet. We haven't moles, but we could use alpha God Rose number to convert moles toe molecules. Now, using our last conversion factor, we can go from molecules to number of electrons. So this right here is our map. That's gonna guide us through this problem. Okay, so let's start doing these conversions. Two liters of water times 1 kg per leader is 2 kg. So our water has a massive 2 kg. Now right away. We know that that's equivalent to 2000 g. So we've done this step and this step. Now we need to go from grams to moles. Okay. 2000 g times g per one. Mole is about 111 moles. So we've done the next step. Now we need to go from moles. Two molecules using avocados number 111 moles times one mole per six times 10 to the 23rd molecules is times 10 to the 25 molecules of water. Okay, so we've done this step. The last step is simply to figure out how many electrons are represented by this much water. As many molecules of water. We know that it's 10 electrons per molecule, so it's very simple. We just multiply this number by 10 6.7 times 10 to the 26 electrons. Okay. And we followed our map successfully from leaders, which was given to us. Two electrons. Okay, now, part B. What charge does this amount of electrons represents? Well, each electron has a charge e the elementary charge, and we have some number of electrons in which we figured out in part a so multiplying. These together will tell us our total charge. Our number is 67 times 10 to the and the elementary charges. What? Remember, guys, you need to know this 16 times 10 to the negative 19. Coghlan's multiplying those. Together we get a total charge of 1.7 times 10 to the eight coolness. Okay,

5

Problem

How many electrons do you have to add to decrease the charge of an object by 16 μC?

A

1.0×10^{-25}

B

1.0×10^{13}

C

1.0×10^{14}

D

1.0×10^{17}

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