 So we're looking at static electricity. What's going on when you rub a balloon on something like your hair or a sweater? Well, what you're doing is electrons are free to move. And this is why we said that Ben Franklin named the charges wrong. You're kind of nicer if positives were free to move. That would just mathematically be a little more convenient. But if you rub a balloon on a sweater, it gathers some electrons from the sweater. Now, as I move close to this wall, keep an eye on the charges in the wall. Now, right now the wall is neutral. But like charges a repel, unlike charges a tract. And as I move closer and closer, you're going to notice the electrons want to try and get far away if they can. And the positives technically don't move. But if electrons are moving to the right mathematically, that's the same as positives moving to the left. So we kind of say, and the positives want to get closer, even though that's not quite what's happening. Once again, this is why Ben Franklin should have named the electrons positives anyways. And we end up with the negatives right here being attracted to the positives right here. And the attraction is enough to overcome the repulsion force of the electrons right there. And you can get more electrons, the more you rub. If you get lots of electrons, you notice it very, very, very much. That's the difference between you rub it a couple of times. It barely sticks to the ceiling. You rub it a bunch. It really sticks on the ceiling. And it works better on a really dry day because on a wet day, there are water molecules in the air. And water is a polarized molecule. It can actually snag an electron or two along the way, which is why it's harder to build a static charge on a damp day like today. What if we have two balloons? So I can rub some electrons here. Oh, what's going on now? So here is your static electricity day. If you pulled something out of the dryer, it either has a shortage or an extra number of electrons. And so if there's something else that is either neutrally charged or oppositely charged, it wants to attract, right? The real question is this. All right, Mr. Dewick, I've done this a bunch of times. I've actually played around with this. I've noticed how this works. The question is, what the heck is it that's pulling this thing over? Won't see electrons? Well, no, no, no. They're not touching. There's a big gap between them. And we have something in physics. In physics, we say, you can't have action at a distance. If I want to make Tyler move, I have to somehow come in physical contact with him. So what the heck is going on? Well, this comes back to the same answer for why this golf ball drops. So when I drop this golf ball, what's pulling it to the ground? But it's not touching the earth. How can the earth pull it to the ground? What we said was, between here and here, there's something that we call the gravitational field. It's invisible. But it's the gravitational field that's exerting a force on this golf ball. It's an electric field, an invisible electric field that's exerting a force on the balloon to pull it to either the sweater or the wall. We say, you can't have action at a distance. If a negative and a positive charge are being pulled together, they are touching each other. They're each sending out an invisible electric field. They're touching Kelvin. It's just that our eyes can't see it. But just as though if I'm in a tug of war, I'm pulling on you with a rope, they're pulling on each other with an electric rope, an electric field that's invisible. It's a really key concept. And in fact, that's what today's lesson is going to be about. So since none of you did the homework, I won't take questions about section one. Gee, do you think I'll put questions from this on the test? What, with nobody having done the homework? Would that be kind of a teaching moment that Mr. Dewitt might take advantage of? I'll let you think about that. Or you can certainly on Tuesday, ask me questions from both of these. And we're gonna move on to lesson two, which is electric field. And I get to show you some pretty cool stuff. Maybe my best toy. Just a reminder, we said last day that charge is quantized. That was the fancy word for it comes in chunks. What was the elementary or the fundamental charge? How big was it? Do you remember, it's on your formula sheet, but I'm also encouraging you to practice finding it so you know where it is. What was it? No. What was the elementary charge? 1.6 times 10 to the negative 19. That's the charge on a proton. What's the charge on an electron? Too slow. Tyler, same but negative. Yeah, that's why we call it the elementary charge. It's the charge on a proton or an electron, okay? Now, we said we measure charge in coulombs. One coulomb is huge. One coulomb is so big it would probably kill you if you shocked you. So usually we use micro coulombs. That was that symbol mu times 10 to the negative six. Read along with me, example or lesson two. Gravitational field reflects the effect that a mass has on the space around it. If another mass is placed in that gravitational field, it will experience a force. So here you have, for example, the sun all by itself. It's sending out to the edge of the universe a gravitational field. This gravitational field gets weaker and weaker and weaker the further you get away, but it's pretty strong. I mean, it's enough to hold Pluto in orbit. So it's, you know, pretty strong. The field only becomes a force when you place another mass nearby. The field is what exerts the force on this mass. Let me say that again, because some people were giggling and this is important. The field is what exerts the force on this mass. So fill in the appropriate relationships. Universal gravity was big G, big M, little m all over r squared. What was the definition of gravitational field? It was on your test yesterday. Big G, big M over r squared. What we really said was this, if big G, big M, little m over r squared is the same as mg here on earth, we really said, oh, I guess g is big G, big M over r squared. That was not on your sheet. It was a logical outcome of the universal gravitation formula. But also gravity is also as a ratio. It's also the force divided by the mass. You can get it like that, force divided by mass, or you can get it as an equation. And remember the units for gravitational field were, well, what's force measured in? Newton's, what's mass measured in? So you can do it in Newton's per kilogram. And it was also, because it was also an acceleration, meters per second squared. For example, if you wanted to find the gravitational field strength that far from the earth's center, you would say this. Gravitational field strength is big G, big M over r squared. It's 6.67 times 10 to the negative 11. The earth's mass is 5.98 times 10 to the 24th. This is the big letter M, because it's the planet that's sending out the gravitational field divided by 8.38 times 10 to the sixth squared. What's G that far from the center of the earth? Can someone crunch the numbers please? We're far from the center, far from the earth's surface. So I'm expecting an answer less than 9.8. 5.67, 5.68, which one? 5.68, units, Newton's per kilogram. I can also calculate the gravitational field. This is if I know the planet, but I don't know the force. I can also calculate it if I know the force and I know the little test mass or the satellite mass that we're placing near the planet. In other words, it says find the gravitational field if a 10 kilogram test mass has a weight of 750. Here what they want me to use is this. Here what they want me to use is this. They want me to go 750 divided by 10 and they want me to realize that the gravity field that we're talking about here is 75 newtons per kilogram, probably Jupiter or something like that. So there's two ways, Justin, that I can find the field strength. If I know the great big planet, I use big G, big M over R squared. If I don't know the planet, but I know the satellite at that location, I can figure out the force, if they tell me the force on that satellite, I can figure out its acceleration, which also happens to be G and newtons per kilogram. See the difference between these two approaches? If you know what's causing the field, we use this. If you know what's in the field at that location, we use this. Big deal, huge deal. Next page. We're gonna define electric field in the similar manner. We say that the electric field reflects the effect that a charge has on the space around it. As soon as you put a charge anywhere in the universe, it's sending out an invisible electric field in all directions. And if you place another charge in that field, it will experience a force. If they're like charges, it will experience a force away. If they're unlike charges, it will experience a force toward. In fact, unlike, you can almost think of this as gravity, it wants to fall to the planet. The only thing is because there's two types of charge, it can also fall up away from the planet. We talked about that last class saying, why aren't there two types of gravity? We're looking. Be nice. Says, fill in the appropriate relationships. The force of electricity, we said it was k big q, little q over r squared, where k was nine times 10 to the ninth. In gravity, it was 6.67 times 10 to the negative 11. Big q is the big planetary charge. Little q is the little tiny positive or negative test charge. And r squared would be that distance squared. What was the definition of electric field then? Well, the same way that gravitational field said, there's your little mass, this is your field. For electric field, capital E, it's actually, look up for a second please. We found gravity as a ratio by dividing the force by little m. Sorry, maybe we'll rephrase that. We found gravitational field as a ratio by dividing the force by little m. What's the equivalent of mass when we're talking about electric force? Charge. As a matter of fact, we're gonna say the electric field is f divided by little q. And what we're really saying here, Justin, is that little q would cancel. The electric field and the symbol for electric field is capital E, don't confuse it with energy. It's equal to k big q over r squared, where k is nine times 10 to the ninth. Big q is the charge that's creating the field. And r is the distance from q to any location that we're trying to figure out the strength of the field at, a field point in meters. It's a scalar equation. We're gonna define electric field distance in a bit. Electric field as a ratio, electric field equals f over q. Take a look at your formula sheet and see if you can find this one. It's good to know where it is because all of these equations look the same. So I want you to start training your eyes where to look. Find the electric field. See it? I think it's the very, very right side, yes? I can't remember. Is this one also on there or not? Oh, it is? Oh, okay. A few years ago it wasn't, so they must have added that. Actually, a few years ago, I think all they gave you was this, they didn't give you this one and you had to realize that this was that and when a q cancels, it is that. This is the equivalent for gravity, Jordan, of little g. In other words, the 9.8 we experienced on Earth, that's how you can figure out the equivalent for electricity for electric field strength. What are the units for electric field? Well, what do I measure force in? Newtons per, what do I measure charge in? Coulombs. Units for electric field or newtons for coulombs? Oh, do you remember gravitational field actually had two units? There was newtons per kilogram and meters per second squared. There's gonna be a second unit for electric field as well but that's later on. Turn the page. As was the case with electric force, electric fields cannot be negative. We don't put a negative sign in. Even if your charge is negative, Kellen, we don't put a negative sign in. In fact, a lot of the time in a, probably in a university textbook, you'll see an absolute value sign around the chart to remind you don't put the negative sign in. So, at a certain point in space, a negative 0.5 micro coulomb charge experiences a force that big towards the south. Find the electric field strength at this point. So, Dylan, I've given you two equations for electric field. I've said it's this and I've said it's this. Which one do you use when? And this you'll just have to know. I'm using a big Q. This is the planetary charge that's causing the electric field. Here, little Q. This is the charge that's at that location, the satellite around the earth, if you will. So, what you need to do is read this question very, very, very, very carefully and ask, question begin. These are the two ones we just wrote in the box. So, what you need to do is read this question very, very carefully and you ask yourself, this charge here, is it the planetary charge that's causing the electric field? Or is it the charge that's at this location experiencing the electric field? They use a capital Q, but it's not. They don't distinguish between letters there. Yeah, they use a big Q on theirs. Trust me, it's the test charge that we're talking about. I'm trying to tie into gravity, so I'm gonna say, planet, big charge causing it, satellite. Read this question again. Are we talking this charge here? Is it the big planetary? Or is it the tiny satellite charge? And your hint is, that word there. A test charge is a charge, a tiny charge, placed at that location. It's the satellite charge. For me to find the electric field, I'm gonna use E equals F over Q. Now my other hint is, they gave me the force in this question, see it? It's gonna be 5.2 times 10 to the negative four all over point five and micro, we said, means 10 to the negative six. Why didn't you put a negative in it? We said for electric field, we don't put negatives in for charge. You get 1.04 times 10 to the three. Let me see here, 5.2 negative four divided by point five, negative six, 1,040, units, units, Newton's per Coulomb, right? B, find the electric field strength 2.45 meters to the right of a 2.3 micro Coulomb charge. Now, this charge here is the planetary charge. We're gonna use this one. How do I know? They've told us to find the field strength to the right of this. So we're not actually, this charge is not at the location we're talking about. I also know, cause they didn't give me a force, I have to use this one. The electric field is going to be K cubed over R squared. It's gonna be nine times 10 to the ninth, 2.3 times 10 to the negative sixth, all over 0.45 squared. And you're gonna find electric field answers are usually in the thousands, tens of thousands, or sometimes even hundreds of thousands. How big is the electric field here? 1.02 times 10 to the fifth, just over 100,000. Units Tyler, that's pretty cool. And the next page, we need to talk about direction because electric field is a vector, it's a vector, it's a vector. You see, gravity field direction was not much of an issue cause which way do things always move in gravity? Towards the center of mass, they fall. Unfortunately in electricity, not only do things fall down, they can also fall up, they can repel. So we need to decide what the direction is. And you absolutely need to star or memorize or asterisk or this is hugely important. Pay attention, you need to know this cause you're gonna lose marks if you don't. Here is how we're going to decide the direction of the electric field. The direction of the electric field is the direction that a small positive test charge would want to go if it could. How small a positive test charge? Jordan, so small that it doesn't have its own electric field cause that would change the whole question. Almost imaginarily small, but it's positive. So the direction of an electric field is which way would a positive want to move if it could? It's always from negative to positive. Example five says this. Find the direction of the electric field at some point where this negative 0.5 microcoulomb test charge experiences a force towards the cell. First, let's find the magnitude of the electric field. Did they give me the force in this equation? Then I'm gonna use f divided by q. It's gonna be 5.2 times 10 to the negative 4 divided by 0.5. What's the magnitude of the electric field? Oh, thank you. Times 10 to the negative 6 microcoulomb. I was looking at this and going, this seems awfully small. I was trying to do it in my head. Now, what's the magnitude of this electric field? It should be in the thousands, I think. It's the same number that we did, but now we're gonna add a direction. So, which way would a positive charge here want to move if it could? Well, which way is a negative charge moving? South, so which way would a positive want to move? We get the direction by asking which way would a positive charge want to move if it could? And we have to kind of think and use some logic and reasoning. It says, find the direction of the electric field at 0.45 meters to the right of a 2.3 microcoulomb charge. So, right there. We already calculated the magnitude on the previous page. What was the magnitude on the previous page? Someone turn back and tell me what the magnitude was the previous page. Anyone turn back right now and tell me, what was the, huh? Yeah, a little quicker next time, boys and girls. Times 10 to the fifth? On the same page, whatever. It's on the same piece of paper, but it is on the previous page, right? I just want a little faster reaction than that. What's the direction? All right, put a tiny positive charge right here. Which way would it want to move if it could? Well, this charge here, is it negative or positive according to this question? Positive, so which way would a positive right here want to move if it could? Depending on what they said, well, they said to the right in the question, so to the right. What would the direction of the electric field be right there? Which way would a positive want to move if it could? To the left. C, draw the electric field around a positive charge. The electric field is millions and millions of electric field lines that go out in every direction. What we draw is a model or a representation. We're going to use arrows to represent electric field lines. The direction is going to be the electric field direction, so don't write this down just yet, but which way would a positive want to move right there if it could? What about right here? What about right there? Okay, here is an example of how we would draw electric field lines. Big deal, oh no, actually a very useful model. Sadly, how many lines are there grand total? Count. Eight? That doesn't mean the electric field is eight, but if in this same diagram, you saw another charge with 16 lines, what that would mean is, it's twice as big a charge. Okay, or if you saw another charge with only four lines, that would mean it's half as big. Secondly, we say this, the closer the lines are together, the stronger the field. So, don't write this down, but right here the lines are only that far apart, fairly strong field. What about right here? Are they further apart? Weaker field, use your imagination. What about here? They'd be about that far apart, even weaker a field. So, Dylan, what this is is kind of a visual model of what's going on with electric field. The further apart the lines are, the weaker the field, and the lines are proportional to the strength of each other. I am not saying the electric field is eight, what I'd be saying is if you saw another one on there with 16 lines, it's twice as big, or if you saw another one with eight lines, you'd be saying same magnitude of charge. What would the electric field around a negative be? Well, which way would a positive right here want to move if it could? What about right here? What about right here? What about right here? Now, what could you say about the magnitude of this bottom charge compared to the top charge? Not the same, absolutely not the same. Huh? No, I want the magnitude, not the polarity, the magnitude, Pat, half as big, why? Four lines, that's the significance of the number of lines. It has nothing to do with the, I'm not saying this has a charge of four and eight. What I'm saying is if this was 10 microcoulombs, this would have to be negative five microcoulombs if I've done this diagram correctly. What if I wanted to show these two charges were the same, Gord? How many lines would I put on here? Eight, what if I wanted to show this was twice as big? So the arrow tells you the polarity, negative or positive. The fact that the arrows are pointing inwards, that's a negative. But the number of lines tells you the magnitude compared to something else. Oh, and once again, the further apart the lines, the weaker the field at that location. So right here, the field's pretty weak because these lines are pretty far apart. Right here, it feels pretty strong because these lines are pretty close together. And again, Justin, this is a terrible model. In real life, there aren't eight lines. In real life, it sends out billions of, in fact, an infinite number of lines. Oh, and it's three dimensional as well. There should be lines coming out of the page towards us and going into the page away from us, but we can't draw that. So here's our model. So the direction of the electric field, we ask which way would a tiny, my abbreviation for positive is the plus sign and a VE next to it. What do you think my abbreviation for negative is? Minus sign and a VE. Why don't you just lose a plus and a minus? Because any time I see a plus and minus by itself, I think it's an equation. So this is what I came up with in university. Use whatever you want to, but you're gonna be writing the words positives and negatives quite a bit this unit. I suggest you find an abbreviation. You can also use pause and negative, but that to me looks a little cleaner. Anyways, which way a positive test charge would want to move if it could? Don't capitalize that. Or negative to positive. Because any positive charge wants to, sorry, I've said that exactly backwards, from positive to negative. Because any positive charge wants to move away from positives and towards negatives. So if you see a line that's going from a positive charge to a negative charge, that's the direction of the electric field. How tiny a positive test charge, so tiny that it doesn't have its own electric field, otherwise that would change the whole question. It's mythical. You really can't have a test charge that small, but we can mathematically. So let's start doing some questions. What if we have two charges and I want to find the electric field? We use what we call the principle of superposition. What we do is we find the vector sum of the field of the individual charges. So Dylan, look at example six. Mr. McDermott, how many charges are there in this question? See him? In example six, two. And they want us to find the net overall combined electric field where that black dot field point is. There is no equation to find the electric field from two charges. What I'm going to do, don't write this down, what I'm going to do temporarily is ignore that guy. In fact, I'm gonna call this charge A. Dylan, what do you think I'm gonna call this? Charge? Okay. So I'm gonna find the electric field at A first. Now, which equation am I gonna use? If you look up for a second when you're done writing this. I think these are both planets. Think Earth and Moon and that's the tiny satellite because I don't know the charge at this location. I'm gonna use the one that has the big planetary charge in it. Which equation was that out of the two? KQ. I'm gonna use KQA all over RA squared. It's gonna be nine times 10 to the ninth. One times 10 to the negative six all over one squared. I think you get 9,000. Try it, but this has lots of ones in it. I can do the math in my head. Is it 9,000? But from now on, that's not enough. Now we know how to get the direction. Electric field is a vector. So we're gonna say this, 9,000 Newtons per Coulomb. And if I put a tiny positive charge right there, which way would this guy make it want to move if it could? Right. I'm gonna repeat this procedure for electric field B. And then if they're both to the right, I'll add them up. If ones to the left and ones to the right, I'll go bigger or minus loser. Vector math. So on your own, try finding the electric field for B. I'm gonna freeze the screen. By the way, what's the radius between the field point and B, not four. Three, see it? You get 1,000 Newtons per Coulomb left. So how would I add, do you think 9,000 right plus 1,000 left? What's the answer? What is 1,000 right, sorry, 9,000 right plus 1,000 left? 8,000 to the right. Okay, so we're gonna say this. The electric field is equal to, and I'll do it this way, 9,000 take away 1,000. What I'm really doing for the vector math is saying, oh, left to the right be negative, whatever. I just go bigger minus smaller. Equals 8,000 Newtons per Coulomb to the right. I like that question, I like that question, I like that question, I like that question. I'm gonna ask you to find on your test the electric field between two points, except, you know, between two charges, but I'm gonna make them different numbers than ones. You'll have to do a bit of arithmetic. Example seven. Draw approximately sketch. The resultant electric field at the indicated field points. Both of these charges are positive one microcoulomb so they're the same size. So ignore this one temporarily. Which way would this guy want to move if he could based on this charge? So I'm gonna just kind of temporarily, don't write this down, I'm gonna add a line, we're gonna change our diagram, so don't write this down, but this is pushing that way, don't write this down, don't write this down, we're gonna change the diagram, don't write this down. This guy here, we're gonna temporarily ignore. Which way is this guy pushing or pulling this guy? Which way would he want to move based on this guy? I think this way, but not anywhere near as much because there's a bigger distance. I think the electric field right there though is a combination of those two. I think, and this is what we're gonna write down, I think the electric field probably about like that-ish. That makes sense, it's getting pushed up and it's getting pushed to the left. What about right here, dead center? It's getting pushed this way by this charge, it's getting pushed this way by this charge. What do you think the net or the resultant electric field right there is? There's an equilibrium point, nothing. What about right above it, right here? I think it's getting pushed this way and it's getting pushed that way if I add those two together, what do you think the electric field is, Evan? I heard you say it, I think. Straight up. What about right here? Well, this guy is pushing to the right really strong. This guy is pushing to the left, but not as strong because it's further away. You know what I think my net resultant electric field would be right there? To the right, but not as strong as if that, to the right, but not as strong as if he wasn't there. How about like that, let's say, I don't know. We're sketching. What direction do you think the electric field would be right there? Left. And this is going to bring us to electric field diagrams and I will be asking you to do these on your test. It says, draw the electric field pattern for equal like charges. So Gordon, if the charges are equal, what will you say about the number of lines here compared to the number of lines here? The same. Put your pencils down and watch. Here's how we draw this, okay? Like charges do what? Repel. So electric field lines would look, don't write this down until I'm done, trust me. This would start to head that way, but it would get repelled. This would start to head that way, but it would get repelled. This would start to head that way, but it would get gradually repelled. Gradually repelled. A line would start to head this way. It would also, they'll get repelled by this guy. It would gradually get repelled. A line would start to head straight up, but it would get kind of repelled. And I always do them in pairs to make sure, because if I know the charges are the same, this way I'm guaranteed to get the same number of lines. Remember I said to you the number of lines tells me nothing about how big the charges, it's just a comparison. So even if I end up with a weird number like seven lines, I would still be good with your diagram as long as you had seven on each. Here would head this way and it would get repelled. Here would head this way and it would get repelled. What about right here? It would head this way, it would get repelled. It would get repelled. It would get repelled even further, and even further. Now we would have one line go straight that way, because it's getting repelled by both, and we would have, oh boy, try that again. We would have one line go straight that way, because it's getting repelled by both, okay? Now what about right here? Don't write this down yet. What about right here? It would get forced down, but I think Tyler, dead center, there would be an equilibrium point where a point could sit and be stable, which is why I've kind of left this area blank. I'll do one more line maybe, like that, and like that. So go ahead, you can copy this, or just try and recreate it the way I did, looking up to see if you get something similar. Sally, if your diagram has a different number of lines than mine, I won't freak out as long as both of your points have the same number of lines, so do the lines in pairs. Now on your test, frequently what they'll do is they'll give you an electric field diagram, and they'll ask you to describe the charges. In other words, on the test ebb and what they'll do is this. They'll call this charge one and charge two, and they'll say, first of all, is charge one negative or positive? How do I know that charge one is positive? The arrows, right? Which way does an electric field point from? Which way would a positive want to? So you look at the direction of the arrows, that tells you the polarity, and then they might say, are the charges like or unlike? Well I can tell that they're unlike because they're repelling each other. Let's try doing another one where we have equal and opposite charges. And I'm gonna change colors because mine's gonna end up overlapping with this blue, but pretend these charges are gone. Okay, I think starting right here, if I start moving, which way would I want to move if I could if I'm a positive test charge? In fact, I think you're gonna have a jump straight like that. What about if I start right here? I think I would get pulled into the, boom, negative charge like that. What about if I started here? I think I would get pulled into there like that. What about if I started going this way? I think I would gradually, oh, ran out of this page. Gradually get pulled in like that, okay? You could also argue the same line exists up here, but that's gonna clutter up this diagram too much. But your lines, yeah, it looks kind of like a happy face, okay? But really what you should have is this too, a line like that, a line like that. I'm gonna get rid of them though because they clutter up this diagram way too much. By the way, now that you see this diagram, how can you tell which one's positive and which one's negative? Okay, arrows. These are electric field diagrams. Also again, the further apart the lines, the weaker the electric field. Are these two lines close together? Strong electric field. Are these two lines far apart? Weak electric field because you're far away. So it's a nice diagram system that gives us a lot of information. Turn the page. So the idea of the electric field originated with Michael Faraday. I'll go on a rant about Michael Faraday, one of my all-time favorite scientists on another day. But he used a different way of representing the field. He used lines of force, which showed the direction which a positive test charge would tend to move if placed anywhere in the field. There is the electric field diagram for a positive all by itself. There is the electric field diagram for a negative all by itself. I noticed these two have the same number of lines, the same magnitude. Okay? Here is positive and negative charge, same polarity. How can I tell they're the same polarity? Same number of lines here and here. Here's two positive charges. And these are better diagrams than the one that we free-handed. Someone's done this with computer graphics, but the free-hand ones work just fine too. Here is your area of neutrals. Doesn't mean there's no electric field here or here, by the way, it just makes the diagram too cluttered. So let's summarize. The electric field can be found using the definition if we're told the force on a test charge. The electric field is the force per Coulomb, which is the definition of electric field. And Justin, I always use a lowercase q here to remind myself this is like the satellite in orbit around the earth. It can be found using the point charge equation if we know the big planetary charge that's causing the electric field. Recall, the electric field definition is found by considering, sorry, the electric field direction is found by considering a positive test charge, and it's away from a positive and towards a negative. And you can see that I didn't type that line because I would have put a VE after the plus and a VE after the minus, because a plus and a minus there looks too much to me like an equation. It's just a bad habit I have. So that means we can find the force two ways. The force is either, if I know two charges, k, q1, q2 over r squared, that was last class. Can I not find the force from here? Get the f by itself. Okay, the force is also, if you know the electric field at a location, and you know how big the satellite charge at that location is, that's also the force that that little charge is experiencing. Recall that the direction of electric force is figured out so electric field, which way would a positive want to move if it could? Electric force, like charges, what? Unlike charges, what? Like charges, repel, unlike charges, attract. That, you gotta memorize. Like if you're on test day, go, I can't remember, you're gonna flunk the test. And I'm gonna laugh at you. Homework, number one, three, six. Do you guys have these questions on your sheet, by the way? Did 12 and 13 work? Cause it's the last time some stuff didn't photocopy. You did, you got, okay. I'm gonna go 13. 13 is between two charges, 17. And at the bottom here, it says to Google something. Does it say that on yours? That's actually gonna be the bonus video game. So I'll send that out as a link, okay? We're gonna temporarily stop there, but I get to show you a very cool toy.