 This next unit that we're starting is electrostatics. It's looking at static electricity. If you're asking me what's the level of difficulty with this unit, I find kids that do the homework do pretty good. Kids that try and cram are in for some ugly. And the reason is not that the physics is tough, but the reason I said get your formula sheet out is these are the electrostatics formulas right here. And you may notice that this equation looks an awful lot like this equation, but it's a bit different. And this equation looks an awful lot like this equation. So you kq over r, kqq over r, kqq over r squared, which looks an awful lot like this equation. What I found is the students who can remember what to use, what it's plug and chug. But if you try and cram this, you're going to have to be having a tough time. You really are. Keep up with the homework is my advice. Also, we have a bit of a problem because electricity was discovered or determined to be. It was discovered kind of piece by piece by scientists who didn't quite know what was going on, and they named things poorly. This E here stands for potential energy. This V stands for voltage, which is also called potential. We have potential energy. We have potential to keep those straight. I'll be doing a big song and dance when we get close. This E here stands for electric field, not energy, even though E for energy, and you got to keep stuff straight. I find the kids that do that, this test is really plug and chug. But the kids that, again, try and learn this the night before, I don't have much sympathy for. Let's begin. Matter is made up of atoms. And as best as we can tell, we believe that atoms have a central nucleus that has protons and neutrons, and it has orbiting electrons. When atoms bond together to form solids, the electrons can be tightly bound to the atoms, as in covalent solids like glass. These materials will be insulators because the electrons are not free to move. Or they can be free to move around as in metals. These will be conductors. So in a metal series of atoms, if you're looking at a solid metal, the electrons are nearly free to get past from atom to atom to atom. Not completely free. We need to supply a tiny bit of outside energy. But the best conductors, we need to supply very, very little outside energy. We have learned that subatomic particles like protons, electrons, and neutrons, they have a property that we call charge. And it is this property called charge that is responsible for both electricity and magnetism. What are the basic facts about charge? I think you've seen this before, but I'll teach it as though it's brand new. There are two basic types of charges that we call, what do we call the two basic types of charges, positive and negative. Ben Franklin named them positive and negative, and that was our first mistake. We named them backwards. We really should have called the electrons positive and the protons negative because it's the electrons that move. And in math, we like to think about positive numbers moving. It's the protons that are locked in the nucleus. But whenever we set up a circuit, we're going to talk about positive charges moving even though they don't. They were named wrong. Charge is measured in units of, you know what the unit for charge is? Jacob Coulombs named after a scientist whose last name was and the symbol is capital C. Now, charge is represented by the letter. Unfortunately, we can't use the letter C because first of all, capital C is the unit and lowercase C is the speed of light. And those were assigned long before we did charges. We use the letter Q. Upper for big charge, lower for little charge. We're going to do the same notation as we did for gravity. If we're talking about a great big gravitational planetary charge, we'll use big Q. If we're talking about a little tiny, small orbiting satellite charge, we'll use little Q. Why do we use the letter Q? Another important fact about charge is that it is, here's the fancy word, quantized, which is why we use Q. Quantized means that charge comes in individual quantities. It's not like a bucket of water or a liquid that you can take as much, any size you want to out of a bucket of water. If you have one cup of water, you can pull out a millionth of a cup if you really, really want to if you have small enough measuring drum. Charge comes in chunks, in quantities. It's quantized. And this means that charge is sort of like money. You can't have half a penny. You can on a computer, but in the real world, we don't pay for things with half a penny. The smallest unit of money is a penny. The smallest unit of money is a cent. Any larger unit is how many pennies times the number of pennies that you have is how much money you have. With respect to charge, the smallest unit of charge is called the elementary or fundamental charge. This is the amount of charge on a proton or an electron. How much charge is there? What's the penny equivalent of the electricity world? The smallest unit is it's on your formula sheet under elementary charge. I could tell you, but you need to know where it is when you're looking it up, which is why I'm having you find it. You see it there, elementary charge. It's on the same page as the masses of the planets and all the other stuff. It's part of your data sheet. 1.6 times 10 to the negative 19 coulombs, yes? Positive for a proton, negative for an electron. Protons and electrons have the same amount of charge, just an opposite quantity. All other charges are multiples of E. In other words, if you want to find the overall charge Q, it's the number of electrons or protons times the charge on one electron. In fact, frequently we'll use E minus for electron and E plus for the charge on a proton. Elementary negative charge, elementary positive charge. What's the charge on a neutron, by the way? Zero. A little technical. This is what we thought until about the 1930s. And then we started realizing that electrons and protons, which we thought were the smallest chunks out there, as it turns out, are not the smallest chunks out there. So even though I've said that they're the penny of the electricity world, as it turns out, they're not. So technical comment, some of you might be aware of particles called quarks. And they have charges of 2 thirds and 1 third. So as it turns out, the elementary charge is not the smallest, but we're not going to rewrite the science books for that. Also, because quantum theory is so weird, it's almost frightening. Seriously. So in this course, you're going to get a data page. You've seen it already. And it has the masses of the subatomic particles and the fundamental charge. So your formula sheet has the elementary charge, electron mass, very small, 9.11 times 10 to the negative 31. Proton mass, 1.67 times 10 to the negative 27. Yes, very small still, but 4, sorry, not 4. 10 to the fourth, or 10,000 times larger, roughly. And the neutron mass, almost but not quite the same mass as a proton. Now, however, the data page does not specifically list the charges of the particles. It only gives you the elementary charge. So you will have to remember the charge on electron is negative 1.6 times 10 to the negative 19 coulombs. You will have to remember the charge on a proton is positive 1.6 times 10 to the negative 19 coulombs. And you'll have to remember the charge on a neutron is 0. But I think all of you have that. It's sort of become part of our culture. You learn a little bit of electricity, even if you never do science, because you all have electronic devices and things. You learn batteries have positive and negative ends, for example, when you're putting them in. Turn the page. It turns out charge is distributable. I have here a plastic rod, a little piece of plastic. I can do it with a ruler, but vinyl picks up electrons a little bit better. And I have a piece of cloth that has lots of expert electrons. And I can physically, especially on a nice dry day like this, rub electrons onto this cloth. I've given it some extra charge. And you'll be able to very clearly notice in the forward, you can see, little static electricity. Now, I just touched the paper. I may have grounded it. Nope. And you've all noticed this on a dry day with laundry, or especially on a really wintry dry day, your clothing might even crackle when you're pulling it out of the closet or something like that. All sorts of lovely things you could do with electricity. So the thing is plastic or vinyl is an insulator. What was going on there? So for a conductor, the electrons flow freely and easily. But for an insulator, the electrons cannot flow, but the electron orbits can shift slightly. This is a phenomenon known as polarization. Example four. A negative rod is brought close to an insulating ball. The ball is at first attracted and then repelled by the negative rod. Explain why this happens. So we're going to use a little model here. This rod is negative. So I'm going to give it 1, 2, 3, 4, 5 negative charges. It really has millions. But we're going to do simplified models, Dan. And this insulating ball is neutral. I'm going to give it two positive and two negative charges. I know it's kind of small. I put two pluses and two minuses on it. You're going to want to. As you bring this rod close to this ball, two things occur. First of all, the positives are attracted to the negatives. And the negatives are repelled from the negatives. In fact, what happens here is, so we still have 1, 2, 3, 4, 5. The positives get pulled to the left, and the negatives get pushed to the right. Because like charges repel and unlike charges attract. And what we've really done is we've polarized this insulating ball. Even though it's still neutral, we've managed to separate the charges. In fact, later on, we're going to say, we've done work on the charges. And we'll start to bring in some of our energy stuff. And so we'll calculate how much energy certain electric devices have. Now, what's also going to happen then is these two negative charges, which are free to move, because this is a conductor, they want to get close to these positive charges. So they are going to jump. For a split second, we're going to have this. 1, 2, 3, two positives. But two of the negatives, and again, Evan, the numbers are arbitrary. It's going to be millions and millions, because we're talking about electrons. But I'm using two as a nice, easy one to wrap around. We already had two electrons, and two more are going to jump. So you want to put four electrons onto that little ball. And what now happens, Matt, for a split second, the insulating ball gets attracted, because the positives want to get closer. As soon as they touch, though, the electrons jump the gap, because they want to get closer to those positives. And now, what's the charge on this ball overall? And now, we're going to have negatives repelling. I didn't have a chance to set this up. I wanted to, but I've been too busy today. Let's see if we can make a prediction here. Example five, two uncharged metal spheres are fixed onto supports and are touching. So uncharge means neutral charge. And again, our standard, if we're not sure, I usually go two positive, two negative, maybe three and three, but two and two, I can usually figure out what's going on. So we have neutral charges. A charged negative rod is brought in close to the spheres. So let's go like this. One, two, three, four, five. What's going to happen right now? Well, right now, the positives want to get close to the negative. And the negatives want to get far away from the negatives. We'll say that the positives are now four of them are on the left side. The negatives, four of them are on the right side. Now, what's the overall charge of these two spheres? Still neutral, OK? But if we now separate these, still keeping this rod there, we'll end up with one, two, three, four, five. If we pull these two spheres apart, although the overall charge on those two spheres when they were touching was neutral, you can see what I've managed to do is I've managed to actually create a charge, separating charges. So once the rod is removed, we end up with one positively charged sphere and one negatively charged sphere. We call this charging by induction rather than conduction. So charging by conduction is the previous example where the rod actually touched the insulating ball. You can see here, Zach, we were able to charge two objects without touching them. That's induction charging. And if you have an electric toothbrush, that's how it works inside there. A different mechanism, but it's an induced charge because you don't want to have conducting surfaces around water. Water and electricity, not good. So if you have any kind of a waterproof device that you recharge somehow, there'll be an induction charge. This is what they're talking about the next generation of cell phones having. Ideally, what they would like to have is a little mat next to your computer, and anything you drop onto that mat will get an induced charge. You want to plug it in just anywhere on that mat, it'll get charged like this. And that way you could have the mat, you could drop your mouse, you could drop your iPhone, your iPod, your camera, it would all just be sitting there charging happily away, no need for wires. That's out already. It's in its infancy though. Probably, I would expect within about five years though, you'll see that become the standard. How many of you have an electronic camera, digital camera? How many have a digital phone? How many of you have an iPod that's separate from your phone? How many get frustrated with having all those different cords, none of which fits into the other one? Like, there's a clear demand for it. Honestly, for something like that, if it worked for all of my devices, I'd pick 50 bucks for the non-hassle of not having to plug stuff in, and also only one power outlet required instead of 12 or a power bar or whatever. I think I would. So variations on this, very trendy right now. Okay, induction induced because you're not actually having to physically touch the object to get the charge to occur. Conduction, you have to, went too far, you have to physically touch the object to distribute the charge and create a negative or positive. Since we have charges moving, there must be a force acting on them, and there is. The force is given by Coulomb's law. Coulomb was a scientist, and he found that like gravity, electricity was an inverse square law. In fact, you don't need to write this down, but I'm gonna write gravity right here. Here's Coulomb's law. Electrical force equals the equivalent of mass in gravity is charge. He noticed that it depended on how big Q1 and how big Q2 were. He noticed also that it was once again the inverse square of the radius. And then just like Newton needed to find g 6.67 times 10 to negative 11 to end up with an answer in Newtons starting in kilograms, kilograms, meters squared. Coulomb found what we call Coulomb's constant. We use the letter K, lowercase K. That's the number that we need to put there so that Coulomb's, Coulomb's per meters squared ends up in Newtons. And how big is K? It's on your formula sheet. Dan, can you find it for me? I noticed you were looking. It's a fairly easy one to. Nope. Is that harder? Coulomb's constant. Oh, Coulomb's constant. Little K, universal constant. Oh yeah, nine times 10 to the ninth. It's an easy one to remember. It is, yeah, there's the units. It's an easy one to remember. It's nine times 10 to the ninth. Much nicer than the 6.67 times 10 to the negative 11. But do you notice, Taylor, these look pretty similar. A constant, a constant. Mass, mass, charge, charge. Radius squared, radius squared. This begs the question. How many types of charge are there? Two, what do we call them? Positive and negative. Here's the question. One of the many things they're trying to find at the Large Hadron Collider. If there's two of these charges, why isn't there two gravity charges? Is there an anti-gravity charge? We're not sure. Mathematically, Dan, it looks like there could be. And there are plenty of other examples where mathematically it sure looks like there should be. It would be neat. It would be anti-gravity. That would certainly take care of many of our space travel issues if we could find it. Yeah. In theory, that would, instead of having masses attract, masses repel in theory. But right now, it's all purely theory. Except, geez, those look an awful lot alike. And I mean, we've done enough math to notice that often if stuff looks alike, there is some symmetry involved somewhere there. We're working on it. Pardon me? Wow. No, that's a different phenomenon. Back here, boys and girls. Now, you'll notice, although I put a force and force is a vector, I left the vector sign off because we're gonna have to figure out the direction ourselves. To figure out the direction of the force, we're gonna use these ideas from science 10. I think it's science nine now, actually on the new curriculum. Like charges will what? Repel. Unlike charges will what? Attract. So that you'll have to know. You need to know that unlike charges attract, that like charges repel, because that's gonna give you the direction of your force. Example two. Says find the direction of the electrical forces on the positive Q charge. So here's the charge. And if that's what they want me to find the direction of the forces in, what I'm imagining is all four of these are thumbtacked to the ground or there's little invisible angels holding them all in place because this system here is not stable. If it was real life, instantly they'd be repelling and attracting and things are moving. We're saying Zach right now that we're freezing all of this temporarily. So here's my first question. We have three charges. We have no four counting the one we're looking at. We have no physics that can deal with three or four bodies. In fact, the three body problem in gravity is still unsolved. It says, can you come up with a mathematical equation that will deal with three masses? Nope, we got nothing. Haven't found it yet. This bottom charge here, negative or positive. We're good? Good note. Do I need to come read it? No? Okay, we're back. This bottom charge here, negative or positive. Negative, here. So which way would this guy like to move if he could ignoring these two temporarily? We do one charge at a time. Which way would this guy like to move towards the negative or away from the negative? Okay, so I would say this. There's force one. For me? And you said it, I don't know which it you mean. What I said, remember was pretend these are thumbtacked to the ground or the invisible angels are holding them. Because this is not a stable system, Taylor. You're right. If this was real life, as soon as we let stuff go all of them would be moving, but for the purposes of not driving our brains crazy. If they say, what are the forces on one charge? Assume the other ones are magically frozen. We're only on one charge at a time. That's the first one. Okay, ready? Ignore this one. Look at this one, Taylor, you're correct. Which way would this charge like to move based on this guy if he could? To the right, I'm gonna do that. I'll call that force two. Which way would this guy like to move based on this charge? Repel, right? I would need to know the magnitudes, but to find the net force, I would add these three together, tip to tail. I would also need some kind of an angle here too. Okay? But I would go like this. Force one. Force two. I don't think it's an equilibrium. I don't think as I'm doing the math in my head that this guy actually cancels out both of those. I think the net force would be slightly down to the right a little bit. Eventually it would find an equilibrium point, but this is where again, Taylor, this is why I said let's pretend all this is thumbtacked to the ground because as soon as stuff starts to move, all of these forces start to change. Up to wrap our brain around it. The point here is this. If they give you three points, you never deal with three points, two at a time. Cover up one in your mind. Deal with the two you're dealing with and then ignore the first one. Deal with the two you're dealing with. Ignore the next one. Deal with the two you're dealing with. Make sense? We call that the principle of superposition. What that's the fancy word for saying. Go one at a time. So to solve force problems, we will express the charges in Coulombs if they're not already. Substitute charges and distance into Coulombs law to find the force, except because we're deciding the direction, we never put negatives and positives in. We decide the direction based on like charges repel, unlike charges attract. So use the concept of like repel, unlike attract, attract to find the direction of the force. So technical comment. If we have unlike charges, one positive and one negative, the answer we get for the force will be negative. The significance of the negative is to indicate attraction. This doesn't mean that the force itself is negative. In fact, we drop the minus sign when we state our answer. We state the force as positive, left or positive, right or north or south or whatever frame of direction they give us. In fact, some people write Coulombs law with absolute value signs around the charges. I don't. What I'm saying to you is we're not gonna use negatives and positives. We're going to decide the direction after. Example three. Find the force on an electron in a helium plus ion, which has a radius of two times 10 to the negative 11 meters. They want us to find the electrical force, so let's write out Coulombs law. F E equals K, Q 1, Q 2 over R squared. Equals K is nine times 10 to the ninth. That's the universal constant for Coulombs law. Nine times 10 to the ninth. Q, that's the center charge. I think it says there's two protons. What was the charge on one proton? The elementary charge. So you know what? I'm just gonna go like this. Two times 1.6 times 10 to the negative 19. Little Q, and I'm trying to use the same notation as we did for gravity. Can you see Taylor? Little Q is like a satellite. That's why I'm using lowercase. So it's one electron. What was the charge on one electron? Technically negative. Are we gonna put the negative in here? No, no, we're gonna decide the direction. You know what? I'm running out of room, so I'm gonna do this. 1.6 times 10 to the negative 19. All divided by R squared. Two times 10 to the negative 11 squared. Mr. Duk, yes, Kyle. Is this also gonna be a unit where our calculators are gonna be tricky and we're gonna be typing in a lot? Yes. Is this also a unit where I'd be smart to try these in class to follow? Yes. Is this also a unit where on the test you see a lot of kids have all the right numbers and get the wrong answers? Yes! So try this, please. Can you get that? 1.152 times 10 to the negative six? See if you get that. Nick, did you get that? I think next time I might move you to the front, my friend. Be with me here in the back corner there. Is that right, by the way? Yes, okay. To two sig figs, 1.15 times 10 to the negative six. Now that force may seem very small. 1.15 times 10 to the negative six, Newtons. Except we need to realize we're dealing with electrons which have a very, very small mass. If you were to find the acceleration, it would be 1.15 times 10 to the negative six divided by the mass. You find that the acceleration is 1.26 times 10 to the 24th meters per second squared. Which I'm going to suggest is fairly quick. Troy, my friend, I thought I was going to have to lead you to that. Troy, after your question, as a matter of fact, Troy, what path is this electron tracing out? A circle. So where is the net force on it? Toward the center, which is FE. But you know what? It seems to me I could also say this. The circular acceleration is V squared over R, the centripetal acceleration. Which it seems to me that if I use that number there and R, I should be able to get V squared. Let's see. How fast is that electron moving as it spins around this helium ion nucleus? I think we're going to get V equals the square root of A times R. Now I happen to have the force if I divide that by 9.11 times 10 to the negative 31, like we did right here. So that's the acceleration times the radius, two times 10 to the negative 11 square root. That electron's moving pretty fast. 5.03 times 10 to the one, two, three, four, five, six. Oh, very fast. Well, let's be honest. Do we notice any kind of a delay in any kind of our electronic devices at all? No. So in atomic terms, Troy, and yes, by the way, we're going to bring some circular motion stuff in here too, because you know, it's kind of like an orbit. In fact, don't they call them orbits in chemistry? Why they do? Orbital shells, I think they call them. We see that this force is huge, which also makes sense because the energy required to split an atom for the atomic bomb was off the scale. And once that energy gets released, it's off the scale. So yeah, it's a huge force holding atoms in their nuclei, electrons in their nuclei and in their orbits. Example four. And this is to answer Taylor's question. So Taylor was wondering when we did that four, that rectangular set of atoms. And Taylor, a rectangular one with vectors, I won't give you one like that on the written. It might be fair game as a multiple choice. I like this question. I like this question. I like this question. This is totally fair game on the written. It says, find the net electric force, magnitude, and direction on the, and then I need to introduce a new symbol to you. I have to go get a drink of water and come back when you need to, my friend, okay? Thank you. You're gone for a while. Okay? Matt, you gotta help him. Back here. Are you done? Sorry, I was gonna give you some hints if you wanna stay, I can, but if you're done, what block are you? G, can you put it face down, top of block G? Thank you, kind sir. Taylor, what do they want me to find the force on? No, which of these charges, first, second, or third, do they want me to find the force on? So read the question. What's in front, okay. I'm gonna call this in my high-tech numbering naming system, charge A, charge B, and charge C. Now, I need to introduce some new terminology to you. A coulomb is so small, it's essentially useless to do any physics with. So most of the time, we're going to give you a charge in micro-coulombs. That's that symbol there, that's that symbol there, that's that symbol there, that's that symbol there. And even though it's on your formula sheet, it comes up so often, you'll do yourself a favor if you memorize this. Micro-coulombs is times 10 to the negative six. In other words, whenever I see this symbol on my calculator, I would type in two scientific notation buttons, negative six. One scientific notation button, negative six. One scientific notation button, negative six. You're gonna get your charges in micro-coulombs quite often. That's a much more convenient measure. Yes, yeah, but it is micro-coulombs. Oh, sorry, on the metrics, if you look at your formula sheet where the metric chart is, where they have kilo and giga and all those on there, you'll find the symbol mu is actually abbreviated as a micro, okay? Like a micrometer, a micrometer is actually mu M. Can't use lowercase M because that's milli, right? So Taylor has identified this as what we're trying to find the force on. What I'm gonna do then is I'm gonna find the force between A and B, magnitude and direction. I'm gonna try and find the force between B and C, magnitude and direction. Then I'll add them together. I don't care about A and C because it says it wants the force on this guy. I'm sure A and C are pushing on each other. Who cares? Who cares? So you ready? The force between A and B is gonna be K, QA, QB over R squared. K is nine times 10 to the ninth. The charge on A is one micro-coulom, one times 10 to negative six. I'm ignoring the negative. I don't put that on the equation. I'll use that to figure out the direction. The charge on B is also one times 10 to the negative six, one micro-coulom, all divided by, how far apart are A and B centimeters? Sorry, how many meters? A point two squared. That's the force between those two and then I'll add the direction when I think about whether they'll repel or attract. Nine times 10 to the ninth times one times 10 to the negative six times one times 10 to the negative six divided by point two squared. Do you get point 225? Point 225 newtons. Yep, now the direction. Pretend that this charge is not there. Okay, I'm gonna bring it back, but in your mind, pretend you scribbled it out. Which way would this guy want to move if he could based only on this charge here? Would he want to move towards to the left or away to the right? I heard both, which one? Unlike charges, what? Attract. So this force is gonna be to the left. Now we're gonna do this question again, but Jasmine, this time we're going to ignore this charge. We're only gonna find the force between these two, magnitude and direction. And then to find the net overall force, we'll add them together. So we're gonna find the force between B and C, which is gonna be K, QB, QC over a different R squared. I guess if I wanted to be really fussy, I would call the first R, RAB, and the second R, RBC, whatever, I'm not that fussy. Nine times 10 to the ninth, one times 10 to the negative six, two times 10 to the negative six, all over 0.1 squared this time. And if I'm lucky, I think I can go second function, enter and just change my numbers. Change that to a two, change that to a one. You get 1.8, yeah, very large force. 1.8 Newtons. Direction based only on this charge here, which way would this guy want to move if he could? To the right, because once again, unlike charge is a track, is that okay? How will I figure out the net force if I want to add right plus left? What am I really gonna do here? I think I'm gonna go bigger minus smaller and bigger direction wins. What if it was right plus right? Straight attic, so we're doing vectorial math, but because it's in a nice straight line and I already told you, Taylor, on the written, I won't give you non-linear questions. I've seen this before, where is it? I've seen something like this before with numbers as a nasty multiple choice, but I'll be honest, only with two charges at angles. I've never seen a third one in there, and so you had to just add two vectors tip to tail and it was always right angle so you could go straight so katoa. You know what, multiple choice, I think that would be fair game. Written, f net equals 1.8 minus 0.225. Right take away left. 1.8 minus 0.225. And I get 1.58. Neutrons, that's the magnitude, direction. Who's winner? Because we are doing winner minus loser, technically, right? To the right. So a little bit more interesting than gravity because gravity, everything only acts in one direction. Here, now you can also repel. Turn the page. Example 4C, at which point approximately could we place a one, a positive one micro-cool-ohm charge so that it would experience no net force so that the net force would be zero. Select one of A, B, C, D, or E and explain your answer. Well, let's look at the polarity of both of these. Are they both negative, both positive, or one of each? Both negative, okay. Are they the same magnitude? Oh, see it there? So you have to look a little bit in my high-tech drawings. On your test, on provincial exam questions, it'll be really clear but I just kind of, we just kind of stuck these in there. My friend would take this up. All right, let's go process of elimination. Suppose we put a tiny positive charge, don't write this down. Suppose we put a tiny positive charge right there. Which way would this pull it? Left or right? Which way would this pull it? Left or right? Is right plus right zero? Can't be there. How about right here? Which way would this charge pull it? Left or right? Left? Which way would this charge pull it? Left or right? Okay, so I can get left plus right. Here's the question. What's the difference between these two locations? Which of these would pull stronger? The bigger charge or the smaller charge? The bigger charge. So if I'm closer to the bigger charge, this is really pulling right? Fairly pulling left. I don't think that's in balance. Where right here, reasonably pulling left, reasonably pulling right. I think it's this one, but let's double check and do a process of elimination for the rest. If you put a charge right here, which way is this pulling it? That way. Which way is this pulling it? Down right. Can you add that plus that and get zero? No, you're gonna have a net force that way. So I don't think C can possibly be the answer. And I don't think E can be, because here they're both pulling, I think to the left, you would have left plus left. I think for the same reason that A doesn't work, E doesn't work. So it is one of these two, and I think you'd have to be a little bit closer to the smaller charge, and a little bit further away from the bigger charge to find equilibrium. It is B. Q1 is bigger than Q2. So R1, sorry, Q1 is not bigger than Q2. Q1 is smaller than Q2. I'll call this Q1 and Q2 in my high-tech numbering system. So if you have a smaller charge, we also need a smaller radius. R1 has to be smaller than R2. Otherwise you can't be in balance. So, Taylor, in all honesty, that's why I use those. Therefore, because it never looks like a number. Example five is about as tough as it'll get, Eric. And in fact, I've already told you, as I've written, no, as I've written, I've already told you which one I like this question, like this question, like this question. This one here, though, makes a good multiple choice. Here's what I think we're saying. It says, find the electrical force, magnitude, and direction on the electron. And again, we're imagining that little invisible angels, little invisible thumbtacks, something is holding this all in place. It's straining to go, but it's being held where it is. So we don't have to worry about things moving. Also, going back to your comment, Taylor. If things are moving, we need calculus. Can't do it. Cover this one up in your mind. I'm not gonna scribble it out. If that's an electron and this charge is here, which way does this electron wanna move down or up? If that's a negative charge and this is an electron, which way does this electron want to move down or up? Is it positive on your screen? Hang on, let me look. Holy smokes, I barely got that. It is positive. I stand corrected. Sorry. The glare on my screen, I got nothing. Wow. Oh, there it is. Okay, I'm not teaching like this though. Oh, okay. So down. What about here? I better look carefully. Which way does this electron want to move? Left or right? Left. So here's what we're going to get. We're gonna get two forces added tip to tail. We're gonna get this plus that. I just need to figure out what numbers go on this and I need to figure out how to draw a bit of a better line. Once again, I'm gonna call this charge A and I'll call this charge B. Let's find the force from charge A. It's gonna be K QA Q over R squared. I'll call the second Q, QE for electron. There's my high tech naming system. And yes, I'll use QP for a proton as my high tech naming system. Will I ever use QN for a neutron? No, because what's the charge on a neutron? Zero, it would really make a pointless question. So we're gonna have this, nine times 10 to the ninth. The charge on A is two micro coulombs, two times 10 to the negative sixth. The charge on the electron is the elementary charge, 1.6 times 10 to the negative 19, all divided by R squared, which is two micrometers. What does micromean? 10 to the negative six, two times 10 to the negative six squared. Okay. Calculator. Nine times 10 to the ninth times two times 10 to the negative six, oops, times 10 to the negative six times 1.6 times 10 to the negative 19 divided by two times 10 to the negative six squared. You get 7.2 times 10 to the negative four? I get, what did I get again? 7.2 times 10 to the negative four, that's that force. Let's also find the force from charge B. That's gonna be KQB on QE all over R squared. It's gonna be nine times 10 to the ninth, one micro coulomb, one electron, all over two times 10 to the negative six squared. Oh, the distances are identical, that's very convenient, because I think that means I can just go second function, enter, and instead of having a two times 10 to the negative six, I'm just gonna put a one times 10 to the negative six squared, and I get 3.6 times 10 to the negative four. Yeah, it's half as big. Same distance, half the charge, half as big. In fact, my diagram is a bit yucky. Really, I should draw this much more like that, I guess, if I'm gonna be really, really technical. About half as long. But here's the point. There's my resultant. How can I find the magnitude of my net force? Yeah, this is a nice right triangle. I'll take the Pythagoras here. It's gonna be this squared plus 7.2 times 10. To the negative four squared, square root of that. I get 8.05 times 10 to the negative four. Newtons, then they want the direction. Uh-oh, we're at angles now, so it's gonna be at. We're gonna have to find the theta. And I think I'm gonna use this angle here. Now, if I use that angle there, it's gonna be what of what? But you know what, let's put a compass on here. Step south of west. I'll add a little space here, south of west. Oh, which trig function to find angle theta tan? Tan theta equals opposite over adjacent. In fact, I can take a real shortcut. You know what 3.6 times 10 to the negative four divided by 7.2 times 10 to the negative four is? Not 2.5. I'm just gonna go inverse tan of 0.5. There we go, 0.5. That's what that big fraction's gonna work out to. So the angle is, oh, math 12s, what am I in? It's not a special triangle. Yeah, but two is the hypotenuse, not one root two, it's one over two, right? We have a root two is the hypotenuse, we have a two is the hypotenuse, but we don't have a two is the side. 26.6 degrees. Yo, Troy said for the previous question, because it's the inverse square law, would it be four times closer? Let me think, you're doubling the mass, sorry, doubling the charge so you have twice as much force. So two times closer, I think. I think it would be one third of the way. So you'd have one third of the distance and then two thirds of the distance so that it was twice as close as the other one. That was gonna be really, really fussy, right? It would be one of those should make one, two of those. Since you asked, good nerd question. Very nice, hold my shirt. I always do this lesson before circular motion because hopefully you're seeing at least some of this is the same calculator practice just about, which I've learned over the years is something you're gonna need for everything. So your homework is to study for the test, but I also see you a week from today. This is the homework you wanna have done by a week from today and some of you I realize that means getting organized and having to think about things. I think I would like to assign if you're okay with that even if you're not. Number one, two, four. So number seven I like, here's where you have three charges all in a straight line and they're adding a little compass. They're saying up as north and right as east. Eight I like as well, same idea. You don't have another page? Okay, I've been having trouble printing these and I didn't realize the photocopier, I'm guessing some diagram on here, the photocopier couldn't handle. Okay, well then I guess one, two, four, five, seven. And then on Monday we're gonna look at electric fields and I will show you a way nerdly cool toy. Also reminder tutorial today after school.