 All right, recall from last lesson, so we did lots of right hand rule stuff, which we're going to be reusing over and over and over and over. So if you think you can get away without learning it, you're going to be out of luck. But we said that when a current carrying wire or a charge moving on its own, as long as it's moving, when it enters a magnetic field, it experiences a force. And the force can be calculated by the magnetic force is equal to QVB, QVB. Oh, except Justin, I said, look, please make sure that your velocity and your magnetic field are perpendicular so that your right hand rule works. Otherwise, your right hand rule won't work and there is no force. If they're parallel, the charge, if the velocity and the magnetic field are parallel, the charge won't experience a force. And I think I said it was Faraday who said, ah, it's when it cuts across the magnetic field lines that it experiences a force. And if you really want to know what's going on, this is where you're getting into quantum physics and you're looking at how electrons spin and when they spin, they give off a certain type of magnetic field and their spin interacts with another. It's quite complicated. And in fact, I don't understand it yet. It's on my list of things to read up on. But I'd like you to consider an electron as follows. So the electron is moving to the right now. It's an electron. We don't do the right hand rule with electrons. What does our right hand rule work with? Protons. But we said there's an easy fix. An electron moving to the right is the same as a proton moving to the... Okay. I'd like to know which direction this electron is going to get deflected. So point your right thumbs to the left. For me, it's that way. For you, it's that way. Which way is the magnetic field? Extend your fingers into the page right down towards your paper. So lift your hand up like this, towards your paper. Extend your fingers. Extend your fingers. Okay? You'll have to figure this out because you were away. Right when it gets right to here, right there, which way will it be deflected? Down the page. So it's going to start to move this way. Now which way is the electron moving this way? Now that's the same as a proton moving this way. So now point your thumbs kind of diagonally up your page, magnetic field still in the page. Which way will it get deflected now? I think in this direction. In fact, I think this electron is going to get deflected in a... This is what's going on in a cyclotron. This is what's going on in a particle accelerator. This is how we can deflect particles into circles. What path is this electron tracing out? A circle. Where must my net force be towards the... One almost thinks that the superintendent walking in earlier today was perfect for reviewing some of those concepts, was it not? In fact, it means we can say this. The magnetic force is what's moving it in a circle. It means we can say qvb equals mv squared over r or qvb equals m for pi squared r over t squared. We don't use this one very much. We're going to use this one quite a bit. You may notice, Connor, that one of the velocities cancels. In fact, this simplifies to qb equals mv over r. With one, two, three, four, five terms, if I know four, I can find the fifth. Not only that. If I really, really wanted to get technical, what is mass times velocity? Do you remember? Oh, boy. What's mass times velocity? What's mv? It's on your formula sheet. It's a big one. It's a major concept. Regan, you guys should be embarrassed. He's learning this on his own, and he's getting the hang of this momentum. You could actually, Justin, if you really wanted to rewrite this as qb equals the momentum divided by the radius, or if you wanted to get the momentum by itself multiplied by r. There's all sorts of different little things that pop out of here. Very nice. Example two. An electron moving at 3.2 times 10 to the 6 meters per second enters a perpendicular 0.545 Tesla magnetic field, and it traces out a circular path. What's the radius of this path? How is this electron moving? It is traveling in A, so equals fc. What force is pushing it in a circle? This time it's not gravity in orbits. This time it's magnetic. In fact, qvb equals mv squared over r. By the way, again, most common mistake, if you look on your formula sheet, mv squared over r never appears. What appears on your formula sheet? v squared over r as the acceleration. Meaghan, you're going to have to remember that force is mass times acceleration. I think a few of us forgot that on the test. Yes, I notice one of my v's cancels. What's this question want me to find? r equals mv over qb. Now it's plug and chug, m mass. Which mass? Mass of what? $10 says that's on my formula sheet somewhere. It's 9.11, but I can never remember the times 10 to the negative 31. What's the velocity of this here electron? 3.2 times 10 to the sixth divided by? What's the charge of this electron? Don't you dare look it up. Please tell me. By this time you haven't memorized. What's the charge on any electron or proton? 1.6 times 10 to the negative 19. And radius, we're doing it as a scalar because the radius is always positive by def, it's a radius. So I'm not worried about the negative or positive charge. Oh, b. What does letter b stand for? Sorry? What did we say letter b stood for? Brandon, magnetic field strength, oh, 0.545 Teslas. What's the radius? Someone else want to double check? 3.3. Anyone else? Yeah. Okay. Where this was really used was in early particle detection and even now, if we know the radius, so we deflect the particle, but we deflect it in a circle on top of a photographic plate or a radioactive plate so that it leaves actually just like an old style film photo. So it leaves a little circular imprint and we carefully measure the radius. If we know the radius, we can either get the mass of the particle or the charge on a particle because we can definitely get the velocity in the magnetic field from external measurements pretty easily. The mass and the charge at the tough ones to get because they're so caught in thick and small. 3. As shown in the above diagram, a proton entered a magnetic field at a. By the way, let's practice our right hand rule to see if this diagram is correct. Which way is the proton moving? When it hits a, look at the diagram, which way is the proton moving? Point your thumbs up the page. Which way is the magnetic field? Into the page. So right when it hits this, which way will the proton get deflected? To the left and then follow the path of the proton. Does your palm always end up pointing towards the center so that it keeps getting deflected more and more in a circle? Yeah, okay. Does work. Like. Right hand rule. Don't curl your fingers though, extend your fingers. So as shown in the above diagram, a proton entered a magnetic field at a. This was a seven mark written question by the way and it does show up occasionally and it's straight cross multiplying if you understand the concept. It's about the easiest seven marks mathematically that will ever show up on the provincial exam. The radius r is that. When the magnetic field strength was that. What's the proton speed? I would say well it's moving in a circle so magnetic equals circular. I would say qvb equals mv squared over r. I would say woohoo, one of the velocities cancels. What's this question want me to find? Speed? Get the v by itself? V equals? Oh yeah, cross multiplying, stuff moves diagonally. Qbr over m, is that right? Qbr over m. So Dylan, I don't memorize this. This is what I've memorized. Moving in a circle, being pushed by a magnet. Magnetic force is circular force and then from here Sally, I derive whatever. What do you want me to find? I'll find it. It really I would argue is almost grade 8 cross multiplying. Okay, we did some canceling. Maybe it's grade 9 cross multiplying. Go to it, what do you get? Let's see proton is 1.6 times 10 to the negative 19. Magnetic field is 0.02, 2 times 10 to negative 2 but that's way easier to write. Radius is 3.25 and I know the mass of a proton is 1.67 but I can never remember Times 10 to the negative what? 27. Ryan what were you suggesting is the answer? Is that right folks? Yeah. Is that reasonable? What would make me nervous that it was times 10 to the 8th? Because that would be faster than light. You know what else would make me nervous? Times 10 to the 4th or 3rd because particles move fast. I mean we don't see them move, they move faster than our eyes can detect. So that seems reasonable. So there's one type of written question they love to throw at you. Curving a particle into a circle, particle accelerometers. And that's why they need the huge magnets at the Large Hadron Collider. But that's what they're doing is they're trying to get the magnetic field just right. The radius just right so that the particles going in opposite directions actually collide in midair nearly at light speed. Tougher than it sounds but still this is the math. That's on a single charge. If we have a wire carrying current perpendicular to an external magnetic field it will experience a force. Basically a wire is a bunch of charges holding hands. It's a bunch of charges holding hands. They're stuck together. So we originally said this, yeah? Where V is really distance over time. So you could rewrite this as Q distance. Now instead of the letter D I'm going to use the letter L for length of wire. B over and I'm going to be really really clever. Instead of putting the T in the middle I'm going to put the T right there under the Q. Because on our formula sheet we do have an expression for Q over T. What is Q over T from the last unit? Current. This is current. In fact you want the force on a wire. It's built. It's how big your magnetic field is. Question Jordan? Velocity is distance over time, right? If it's constant. And then I said instead of distance Jordan I'm going to use the letter L for length of wire. So that's where the L came from and I put the T there. You don't need to worry about the derivation. I always try and show you where the equations come from because I'm a nerd. I like to know where they're from. This is what you need to, oh no it's on your formula sheet is it not? Yeah. For a wire? How can you tell it's for a wire? Current. Hopefully that's kind of obvious. So example four. Find the magnitude and the direction of the magnetic force on this wire. Let's do the magnitude first. The magnetic force is equal to Bill. It's going to be, how big is the external magnetic field in this very very high-tech diagram that I threw together? Six Teslas, quite large. How big is the current? Five amps. How much wire is inside this magnetic field? 0.7. 30 times 0.7. I don't need a calculator for this. I think the answer is 21 Newtons and Yan, I did it in my head. Yeah, is it 21? That's the magnitude but they also want the direction. Okay, right hand rule. By the way, this is a question they love to do as a multiple choice question where they have the two column chart. So they would have 21 Newtons up, 21 Newtons direction down and you would have to pick the correct one. Let's see. Right hand rule. Try it. I'll talk you through it in about 30 seconds but you need to learn this on your own. So you may as well try it. Which way do you point your thumb? Which one is this one? Okay. I'm getting point my thumb direction of the current, right? So you can point your right thumb in the direction of the current which for me is to my right, to your right. Which way is the magnetic field? Down the page so I can either do for me with my screen here this or I can do this. I don't care which one you do or you can spin your paper. You really need to. Oh, that's way easier but regardless I think my palm ends up pointing. I don't think my palm ends up pointing up. So you ready? I'll do it up here on this screen. Right? Yes? Which way is the magnetic field? Down. Which way is my palm actually pointing? Into the page. Into the page. If the force, example five, if the force on a five cent, is that okay for direction, right? You got to practice these. I'm not going to help as much because you guys haven't worked your way and struggled your way through the right hand rule assignment that I gave you. You really need to. Example five, if the force on a five centimeter piece of wire carrying 12 amps is one times ten to the negative three newtons. What's the magnetic field strength? Okay, they're talking about magnetic force. Is it a moving charge or is it a wire? So magnetic force is going to be built. What does this question want me to find? Magnetic field, that's the B, get the B by itself Pat. And now it's plug and chug. How big is the force? One times ten to the negative three divided by. How big is the current? Twelve. How big is the length? Not five. Point zero. Five because they gave it to me in centimeters, sneaky sneaky. How big is this magnetic field in Teslas? You get one point six seven times ten to negative three. Teslas. Example six. Have any of you seen the movie The Hunt for Red October? Only a few of you. It's Rick Goodflick. It's about 15 years old, 10 years old now. In the movie part of the premise is there is a secret Soviet submarine that basically has engines with no moving parts. It's a jet engine underwater, the magneto hydrodynamic drive. Here's how it works. Ready? We want to use a magnetic field with no moving parts to propel ships or submarines. The idea is to run a current through seawater. Will seawater conduct a current? Yep. While the seawater is passing between large magnets, how will this propel the ship? Okay, let's see. We would have the current coming into the, going into the page. So although you can't see it in my three-dimensional mock-up diagram, Pat, there would be a steel plate right closest to us that was positively charged. Okay, I've deleted that plate because we can't see through it. So current going into the page. Which way is the magnetic field? Magnetic fields always point from what to what. Okay, so magnetic field is pointing this way from north to south. Now what's the current traveling through? What are the charged particles? Water. Water. Which way is the current going? Point your thumb into the page. Which way is the magnetic field? Extend your fingers in the direction of the magnetic, right? Still in current into the page. Which way is the magnetic field downwards? Point your fingers down your paper. By the way, I think you'll find it easier instead of doing, I would find it easier to do this way. Kieran, right now your fingers are pointing up the page. Right now your fingers are still pointing up the page. Keep rotating, keep rotating, other direction, other direction, other direction, other direction. Keep going, keep going, keep going, keep rotating. Oh, he's rotating the paper. Boys and girls, which way does your palm end up pointing? Which way will these water charged molecules experience a force? Out the back. It's a jet engine with no moving parts for ships and subs. No moving parts. Would that be quiet? In particular the US military, but various countries, would they be interested in making their submarines even more quiet? I wouldn't be shocked if they have this and no one knows because it's classified. But certainly the hunt for red October proposed this about 15 years ago. The book actually came out in 81. The book came out in 81. It's a story about a Russian commander who defects with a Soviet submarine and it's so detailed that many people assume that Tom Clancy had actually been told the true story by the CIA, by someone who told it to him over a beer or something like that and written it into a story. In fact, if you watch the movie, the very first frame that appears on screen is, according to the US government, what you are about to see never happened. But there is some suspicion that it actually did occur that way. Or not. But there you go. So, right hand rule, magnetic field dillon into the page. Current into the page, magnetic field down the page. And Kiran for me, my palm is pointing towards the left of the page. Charged water molecules, experience, the force. And again, because the concept here is as far as you can see, no moving parts, it would be very quiet. In fact, you know what it would sound like? Rushing water. Do you think that computers can detect the sound of rushing water in the ocean? Probably not. Indistinguishable from all the other rushing water in the ocean. Alright, so we've been talking about magnetic fields. How do we create them in control? The best way to create a controlled magnetic field is through an electromagnet, a solenoid. So, here is the magnetic field of a solenoid. It depends on several things. It depends on the number of turns of wire. We use a capital letter M. More wire, more turns, stronger field. Because each wire adds a little bit to the overall field. It depends on how long your solenoid is. If the wire is packed closer together, you'll get a stronger magnetic field. If the wire is spread further apart, you'll get a weaker magnetic field. You guys with me back there? That too is over? Or whatever it was? Okay. It depends on the current running through the wire. Stronger current, bigger field. That's what gives you the magnetic field strength. So, ampere determined that the magnetic field inside a solenoid depended on certain variables. The current running through the wire, more current, bigger field. The number of turns of wire, more turns, bigger the field. Length of the solenoid, shorter, bigger. In other words, the magnetic field was directly proportional to the number of turns and the current, but it was inversely or reciprocally proportional to the length. Very similar to, remember the gravitational field was M1, M2 over R squared and the electric field was KQ over R squared. Magnetic field is that. Except for all of these two, we needed a constant. For me to find the gravitational field, I needed the constant big G. For me to find the electric field, I needed the constant big K. For me to find the magnetic field, we get this. The magnetic field in a solenoid is equal to mu0, except I had a British physics teacher, so I learned to call it mu0, and I'll always call it that in his honor. N times I over L, where mu0 is a constant. It's a constant, Jordan, just like big G was 6.67 times 10 to the negative 11. Remember that? Just like K was 9 times 10 to the 9. And I gotta be honest, mu0 has one of the best names ever. If you find mu0 on your formula sheet, what's it called? The permeability of free space. Isn't that a great name for a constant? Dylan, what did you learn today in school? Mummy, mummy, I learned about the permeability of free space. Oh, Dylan, you're so smart. We're so proud of you. You are ever so much smarter than your brothers and sisters. What is mu0? And someone I think over here was asking me about this the other day. How big is mu0? By the way, find it. You need to know where it is on your formula sheet. What? How big is it? Pi? What the heck does pi have to do with the permeability of free space? Your serious pi shows up at it again? And this is again one of the places where my little math nerd heart gets a bit of a shiver or a tingle. Because I go, the universe is weirdly cool. If you ask me for some reason, the universe likes the number pi and it likes the number e. Because those guys show up in some of the most bizarre places where you would swear they have nothing whatsoever to do with what's going on. It's 4 pi times 10 to the what? To the negative 7. That's the permeability of free space. That's the constant we're going to use in this unit. That's our big g. That's our little k. And I just love saying it. The permeability of free space. Way better than gravitational constant or Planck's constant. Permeability of free space. Nerd note, yes, pi rears its head again. Pi shows up all over the place. I can't remember if I told you this one or not. If you take on a map a meandering river like this and you take its length and you divide it by the distance from top to bottom as the crow flies. You know what that ratio starts to approach? Yeah, pi shows up in some of the weirdest places. Now this one I can sort of visualize because I can say, you know, if the river's meandering, that's sort of a half circle. That's sort of a half circle. That's sort of a half circle. Maybe pi should kind of show up, but it shows up in some of the weirdest places. There is a second version of this equation. Okay. Sometimes we don't know, oh, what does the letter N stand for? Read your notes, I included it there. What's the letter N stand for? First of all, let's do the obvious. What does I stand for? Current going through the wires. What does L stand for? Length of the solenoid. What does number N stand for? Okay, then the force? No, that would be an F, my friend. Read. I included there. I gave you a list. What does the letter N stand for? You need to know this, so make me look it up. Okay, the number of turns of wire. Sometimes there's so many turns that they didn't bother counting them. Instead, they gave you the number of turns per meter. They gave you this divided by that as a ratio. In fact, most solenoids don't tell you how many turns grand total. They tell you the ratio. So there is a second version. This is also on your formula sheet where it's mu naught little N times I, where little N is how many coils of wire divided by how long the wire is. It's turns of wire per meter. If you see, they say, a solenoid is rated at 12 turns per meter. They've just given you little N, used this one. It's also on your formula sheet. If they say a solenoid has a total number of coils of a thousand, well, they used the previous one. Let's try a couple. By the way, here's why this is so nice then. We can control Regan exactly how big a magnetic field we want. You want it bigger, add more turns, or beef up the current. You want it smaller, remove some turns, or lower the current. It gives us pinpoint, like to seven or eight decimal places, pinpoint control of how big a magnetic field we want. Very nice. Why we like solenoids. Example seven. A solenoid is carrying a current of 4.2 amps. Okay. If the solenoid is 1.2 centimeters long, and it's made up of 750 turns of wire, what's the magnetic field at its center? What does this question want me to find? Magnetic field. What's the variable for magnetic field? Pardon me. What's the variable we've been using for three days now for magnetic field? B equals, hey, what's the only equation that you have on your formula sheet that has B equals mu naught? And we're going to use N over L times I. Why do I know to use this one? They told me the total number of turns and the length of the solenoid. The magnetic field generated by this particular solenoid is going to be mu naught 4 pi times 10 to the negative 7. N, 750. I, 4.2 amps divided by, oh, not 1.2, because it's not 1.2 meters, it's in centimeters. How many meters? 0.012. How strong a magnetic field will that generate inside the solenoid? By the way, all of you want to try this, because on some of your calculators, on some of your calculators, you won't be able to type 4 pi times 10 to negative 7 without getting an error. So you need to find out if your calculator will let you type that. If not, I'll show you how to get around it. Anybody get an error? Scientific calculators? So you can't type 4 pi scientific notation button, negative 7. You'll have to type pi times 4 scientific notation button. On your calculator, the scientific notation button by default only works next to a number, not a variable. And pi, your calculator treats as a variable. So you'll have to, all the time, go pi 4, e negative 7 times 750 times 4.2 times, divided by 0.012. Okay? And that should fix it, yes? What do you get? I think on the TI, as you can go 4 pi, scientific notation button, negative 7. Anyways, what do you get? 0.33, anybody else? 0.33 Tesla's fairly big. Fairly big. Okay? Example 8. Here we're looking right into the solenoid. So we have an end view. We have an end view. It says, find the field and the direction in the center of the coil. Let's do the direction first. So we're looking right into the solenoid. Which way is the, remember the solenoid rule? The solenoid rule says, imagine holding the solenoid. So for me, I'm gonna have to imagine holding my hand like this or like this, because the solenoid runs into the page. Right? I curl my fingers in the direction of the current. Which way is this question telling me the current? This way, right? My particular diagram, this way. Your thumb points north. Your thumb points in the direction of the magnetic field. Which way is the magnetic field inside the solenoid? I think I'm getting out of the page towards me. So you know what? Let's just do this. Out of the page. Out of the page. Out of the page. Out of the page. Magnetic field is coming out of the page. Remember, that's the symbol for out of the page. That's the symbol for into the page. What was they designed to represent? How do you remember? What's what? Arrow coming towards you. Tail feathers of an arrow going away from you. So there's the direction. Now it wants us to find the magnitude. The magnetic field is equal to... Now here, read carefully. Have they told you the total number of turns and the total length? Or did they divide those and just give you the ratio? Ryan. So we're going to use this one. Mu naught n i. Which is also on your formula sheet. The magnetic field is going to be... 4 pi times 10 to the negative 7. The permeability of free space. Little n is 2,550 coils per meter. Times 10. The strong and magnetic field will be generated inside this solenoid pointing out of the page towards us. 0.028. Oh, I'm seeing controversy. No, yes. 0.032. 0.032. Getting a consensus for 0.032. Tesla's. So, so far, just we've done two things. Force on a wire, build. And then we said, okay, how do they generate that magnetic field that exerts the force on the wire? Best way is from a solenoid and there's two different equations depending on what information they give me. So, we're designing a solenoid. We're an electronics company. We're manufacturing parts. Here's the specs that we've been given. We're going to be making the solenoid 30 centimeters long. About a foot long. They tell us that we need a magnetic field exactly 6.28 times 10 to the negative 3 Tesla's for this particular electric motor, power, door lock, whatever. I don't know what they want the magnet for, but okay. And we've been told that the biggest current that our electronic system that this is going to be installed in can handle is five amps. What's this question wanted me to find? Okay, Sally, let's write down our B for a solenoid equals mu naught and i over little l. By the way, I'll always hand write a lowercase l. If I printed that, what number would it look just like? A one. So, good habit. Whenever you're doing a lowercase l, hand write it. Then it stands out. What did you say this wanted me to find? What variable is how many turns of wire? And the number of turns of wire. Let's give you by itself. So, we're going to set up our assembly line to put how many turns on this solenoid? Well, n equals, I think we're going to have Bl divided by mu naught i. Is that correct? L moves up, mu naught down, i down. It's going to be B6.28 times 10 to the negative 3. L, L, L, 0.3. The permeability of free space. 4 pi times 10 to the negative 7. 5 amps. When we're setting up our factory conveyor belt, how many turns of wire have you better put on this little cardboard solenoid? 300 even? Oh, yeah, Mr. Dewitt cooked this one a little bit because 6.28 is 2 pi. The pi's will sort of cancel. Ah, yeah. It's like 299 points, something, something, but very close to 300, right? Or 3,000 points, something, something, something, yeah. Okay. Turn the page. Number one. Take a look at question number two. Question number two says, this wire is floating in midair due to balanced gravity and magnetic forces. To solve number two, I think what they're saying is FG equals FB, right? If it's floating, this is what's going on on those hover trains, on a much larger level, but those maglev trains where the magnetic, the trains are floating on a magnetic field is what they're doing, except much larger masses. Anyways, two. Apparently number six is the same one that I did with you in your homework, so I guess I'm going to skip number six. Just notice that right now. Wow, that seems very familiar. You know, if I hadn't said anything though, seven, eight, ten, and eleven. Most of these, not all, but most of these, it's set up your equation in straight cross multiplying and the right hand rule stuff.