 No, so last day the last thing we looked at what we made loudspeakers really cool and nearly cool But before that we looked at the electric motor and we said this Amrit if you send a current through we called it the armature It was a loop of wire in the magnetic field Then you could actually get the loop to spin current could cause motion And there was a natural question that Faraday in England and Joseph Henry in the US asked They said well if current can cause motion can motion cause current What they were trying to do was to invent the generator, which is how we get almost all of our electricity So we're gonna look at some of the basics today, and then we'll go a bit 3d after that So the obvious question if a current produces magnetism can magnetism produce a current a bit of terminology recall This funky symbol here Hanna we used in the circuitry unit for voltage it stood for EMF It stands for the word Electromotive force and it's terribly named Madison because it's not a force. It's not measured in Newton's it's measured in volts It's an archaic word an old word that refers not to a force But to a voltage in a cell so voltage and EMF mean the same thing and in fact in this unit I'm often going to use the curly E because we're going to have an equation again Lowerly with V voltage and V velocity in the same equation So I'm going to get around that without the wings this time I'm going to say here's actually why we use the EMF symbol because otherwise you got two V's and Hannah. It's confusing Okay Here's what I'd like you to imagine Suppose we have a magnetic field. That's this rectangle. It's an external magnetic field Alex what direction is the magnetic field? What do I type over here? Okay magnetic field is into the page and I don't know your diagram might not a photocopy quite as clean or as neatly but Cody what I'm trying to show here is a metal bar and We're pulling it with a string Down the page or we're have little invisible angels pulling it or something is causing it to move Okay Now because it's metal Charges are free to move in it because it's a conductor So what we're going to do what I'd like you to do is draw one little positive lonely charge right in the middle Even though it's the electrons that technically move we're going to again pretend that the positive move because mathematics is the same thing Which way is this positive charge moving which way is the velocity of this whole bar Hannah? So this is a great right-hand rule review point your right thumb down the page Which way is the magnetic field according to this question? So point your thumb down the page extend your fingers into the page if I'm looking at the board It would be thumb down fingers into the page. Which way is your palm pointing? Palm is pointing to the right This positive will get forced This way all the positives will get forced to the right of this bar and Alex, you know which way the negatives will get forced To the left in fact what you've just done is you separated the charges Technically Madison what you've just done is Exactly the same thing that goes on in a battery except in the battery chemicals separate the charges They do work on the charges. They create a voltage here Movement is creating a voltage Since the charges have been separated which takes work. We have voltage because voltage is defined as Energy per Coulomb or work done on each charge if you really want to think about it The reason Matt you could run stuff from the battery was the chemical reaction Separated the charges it didn't work on the charges So each charge had some extra potential energy which when it went through the circuit it gave that to the electrical device We call this voltage induced by motion induced voltage or Motion voltage because the energy in this case came not from a chemical reaction like in a Duracell but from moving something and Eventually Ailish will build this into a three-dimensional model or instead of moving it will spin it Which is how every hydroelectric generator works and we'll show how spinning something can create a voltage as well and Man yeah, we've solved the energy crisis at least we can create cheap energy cheap electricity in other words Motion can induce an emf and Kim what's emf another word for voltage Here's the equation says find an expression for the amount of voltage induced by motion and it says first of all What's the definition of voltage? I said it was how much work per charge technically potential energy per charge Lorelie, but I'm going to say work per charge because there's somewhat interchangeable And then it says definition of work. What was the definition of work way back when from physics 11 work was what times what? Malcolm you're right Back when you did homework you had some game. Yeah, this is actually force times distance Divided by the charge except Malcolm I'm going to erase the time sign because it looks like an x. I'm really worried Which force? Well as it turns out Malcolm what's separating the charges is magnetic force, so I'm going to put FBD Over Q What was the magnetic force on a moving charge the magnetic force on a moving charge was Q V B? Oh? And I'll drop the D down and I'm still dividing by Q Matt, what do you know this happens with the Q's? They cancel This is going to give us by the way you might want your formula sheet up to you But this is going to give us the equation for induced voltage now Madison They use the emf symbol not the V symbol and I think they write it like this B V and instead of distance they use L for the length of the rod because that is the distance you're separating the charges is a BVL Or is it BLV? BLV oh and we have to add one more thing though all of these need to be perpendicular to each other otherwise You're not going to get much back to your buck Hey, but this is how you can create a voltage by moving a bar through a magnetic field It's a scalar equation because voltage is energy per coulomb, so it's a scalar energy is a scalar and It says here you only get volts when we're perpendicular It's measured in volts Tesla's meters and meters per second If the wire the speed in the field are not perpendicular, we only get a small voltage Example three turn the page. I'll show you so in the first example Cody in the first diagram. I made the bar horizontal and The velocity vertical so they were 90 degrees here I've got the bar vertical and the velocity vertical of this diagram once again Let's look at a single solitary positive right there in the middle It says indicate which end of the wire is negatively charged and discuss why little voltage is created So Madison, which way is this positive charge moving? Well, which way is the whole bar moving? So put your thumbs all of you down the page Which way is the magnetic field? What did I write on the side there? Into the page so extend your fingers into the page which way will that positive charge feel a force to the The problem is it can't go very far to the right before it runs out of room. Oh especially Imagine if instead of a bar. This is a wire a very thin wire I mean yeah, you're gonna have negatives going that way and positives going that way But we said the voltage was separating the charges. You're not really gonna separate the charges Try that again. Mr. Do it. Come on eraser small L so small Classic multiple choice question by the way, they'll give you four diagrams and they'll say in which of these would the largest emf be created I'll bet you three of the diagrams the bar is either parallel to the magnetic field or parallel to the direction of motion It's not that you won't get zero, but it'll be close enough to zero that that's the point So example four Find the induced voltage Created from motion across the ends of the moving wire. Okay is B L V Let's see. Let's look at this diagram is everything perpendicular. Look at the magnetic field Look at the bar and look at the velocity. Are they all 90 degrees to each other? Yep, so we will get a voltage Magnetic field 1.25 length 0.8 velocity Five point two five How many volts will be induced across this bar? What will this bar be the equivalent of as a battery? What do you get Carly? I think it's five point something if I'm doing the math right 5.25 okay 5.25 volts almost a six-volt battery not quite. Oh Which end would be positive which end would be negative once again? Let's put a little positive right in the middle What's the velocity this time? Oh, what's this symbol mean? Which way is the velocity? So point your thumbs into the page Which way is the magnetic field? I think I'm going to go into the page down the page. Oh, I Think this is going to be the positive end. This is going to be the negative end If I was setting this up in a circuit now Victoria right now The charges get separated and then they clump on the end and they're stuck there So the next question we're going to ask ourselves in a little bit is Hey, mr. Do it. What if you clamped wires onto the end? Could you get a full circuit? Yeah? And we'll start running stuff from it for example example five a Plane is sort of like a metal bar Says find the induced voltage across the wings of this plane. Okay The induced voltage the emf is BLV now. Let's double check my length is this way Why don't I use this length because that's parallel to the velocity I want to use the perpendicular length and I think if you're at 40,000 feet or 50,000 feet I think Cody it's reasonable to assume that the Earth's magnetic field is Downwards because it's kind of curvy, but I think when you're that high it's basically heading straight down to the ground probably You know, maybe 85 degrees not quite 90 degrees and pulse it up How many volts would be created across this airplane? With a point zero eight Tesla magnetic field a length of 60 and The velocity of 320 yet fairly big voltage. I Think higher than what comes out of a plug Point zero zero eight. Yes, it is. Thank you, man Otherwise you get a really high voltage Dan what'd you get or Kim? What'd you get? 154 yeah 154 volts more than out of an outlet I have been told that back in the 50s and 60s when they still had smoking on flights that this is what they ran The pop out cigarette lighters from Like they I've been told that they still they actually have a circuit where they bleed this voltage off and into the plane And they use it to power things and why not? It's there It's fairly easy circuit to set up. I gotta confirm that though, but so I've been told how could you set it up? Here's the most basic circuit. I can't just clamp it to something and let it freeze because as soon as it stops moving No more voltage the whole idea here Matt is it's the movement creating the voltage. So what you could do is you could have Maybe a metal strip that was really well greased. So very little friction and just lay the bar across it and Then if you had a piece of string and you started to pull this to the right or invisible angels pulling it to the right or If you put it on an angle gravity pulling it to the right or there's all sorts of different ways to do this Let's see what would happen. Here's our positive charge right here. Which way is it moving? to the right a According to this diagram. So it's all point our thumbs to the right Which way is the magnetic field this time? Out of the page. I'm gonna go thumbs right. I'm gonna fingers out of the page Which way will the positive get forced in the bar up or down? down in fact Kelvin I Think what we're really saying now is we have a current since we're connecting the ends the current Here's your resistor so they don't have a short circuit And now this is acting just like a battery Here's your chairlift not a chemical one this time a motion-induced one Here's your ski hill so that you don't short circuit back to the chairlift of zero and you've got a complete a complete circuit You could think of it as a circuit diagram Like that now not only that as soon as you have current flowing in this case clock wise as soon as you have current flowing Now these charges are moving in two directions Madison. They're moving sideways because they're part of the bar But they're also moving down the bar because they're part of a current so Here's our current Instead of focusing on the sideways motion. Let's focus on the downwards motion point your fingers down the page Which way is the magnetic field still? out of the page Which way will the bar feel a force to the what that means Gary is as you pulled you would feel something resisting you It wouldn't be there, but you would feel it resisting you. This is a magnetic braking system And I got a great demo to show you So I did my lovely demo there and they're talking about building this into also Amusement park rides for example a magnetic braking system, and I think there are some that already have this. Oh and Maybe if we reverse this process instead of a magnetic braking system, maybe we could come up with a magnetic acceleration system that we call a rail gun Well, let's look at that a little bit The final lesson of the year is on transformers not the cartoon, but the actual electric device so Let's suppose we have again a string Angels gravity whatever something is Causing this to move to the right Says the strip below is 12 centimeters long. It's moving at 4.7 meters per second The external magnetic field is 0.08 teslas and the resistance of the rail circuit is 0.025 ohms find a the induced motion voltage, okay induced voltage is BLV Double-check is everything perpendicular velocity is 90 degrees to the bar is 90 degrees to the magnetic. Yep. We will get a voltage The magnetic field is 0.08 The length of the bar is 12 centimeters so point one two and the velocity is 4.7. You're not gonna get a big voltage here This one's quite small When that cool hand it up like it's very like slow it down physics That's as close as all over come to a nice witchcraft kind of a demo with you guys by the way that one there I still remember the first time I saw that and I was just What do you get for a voltage point four five point four five or point zero four five point zero four five. Yeah, I was Saying I don't think it's that big 500ths of a volt. Yeah What does be want us to find Carly? So I'm gonna write down I equals question mark and I do notice they told me the resistance of the circuit This little resistor here assuming this bar is resistance lists which in our magic physics world will be what's the overall resistance of this circuit? point zero two five oh And what's the overall voltage of this circuit point zero four five now I can use Ohm's law V equals I terms are because remember Alex. I said V and this are interchangeable. So I can use Ohm's law The current is going to be The voltage divided by the resistance Even though we have a very very small voltage How many amps of current would this system generate? Kelvin I think higher than that. I think one point eight, isn't it? I think you divided by point two five is at a point zero two five. It's one point eight Which is a pretty good current like that would shock you that you would have felt Hannah see Hannah, what's the last thing it wants me to find on the strip or on an individual charge? Oh That's bill on an individual charge force was QVB a good review for the test on Thursday, but on a magnetic wire It's bill Let's see B equals point zero eight I Equals one point eight L equals point one two by the way this lesson is also some very good review for some of the stuff You'll see on the test What do you need to know on the test three equations F equals QVB? Oh, and if it's moving in a circle Madison FB equals FC and I can ask you to find for the radius or the mass or the Charter whatever F equals bill if it's a wire and then the magnetic field of solar and I'm Malcolm B equals mu naught the permeability of free space and I over L What do you get for magnetic force probably pretty small not Tesla's were Newton's point zero one seven Newton's by the way What if this guy was moving faster if this was bigger What would happen to this number here if the velocity was bigger Bigger and what would happen to the current if your voltage was bigger bigger and what would happen to the force if that number was bigger The reason this is nice for magnetic breaking is the faster you're going the faster It will decelerate you but it will decelerate you in a nice smooth gradual curve the slower You're going the slower the force so you'll come to like if you're going really fast You'll decelerate really fast and then not so and then slowly ease down nice and come to a gentle stop a lot of that idea Did anybody here Drive or parents drive electric car like a Prius or something like that See, I think this is what's going on with that whole regenerative braking. They talk about when you break You actually Gain some of the energy back into the battery. I think they're using this force not friction to help you break Cool Again, it's in three dimensions and spinning so Hannah. It's a bit trickier to visualize but the principle is there Then Faraday and Henry they both asked the next question. They said well What if instead of moving a single piece of metal? What if I move a loop of wire and so Faraday and Henry both they bent a loop of wire into a rectangle So this is a very thin piece of wire and they put it inside a magnetic field They moved it. Which way is the velocity horizontal or vertical? Horizontal which way is this section of wire horizontal or vertical? What about this bottom section of wire? You're not going to get an emf. In fact, just so to satisfy your curiosity if I put a positive there traveling to the right Fingers out of the page. He'd get forced down But he has nowhere to go because of this little thin piece of wire and same with here here and here you're not going to induce an emf Charles what about a positive charge right on the end here? Well, let's see now. That's a vertical stretch of wire So it is perpendicular to the velocity and it is perpendicular to the magnetic field. Which way is it moving to the? Point your fingers to the right, please. Sorry point your thumb to the right Which way is the magnetic field according to this question? So thumb right out of the page. This is going to get forced downwards That way if we're trying to create a current what about a charge at the very front? Well, which way is it moving Leslie to the? Right point your thumbs to the right. Which way is magnetic field out of the page? Which way will the charge at the front get forced? also Downwards and so they found this didn't work because you got opposing currents that cancelled each other out Remember in the circuitry unit we did one day where we had batteries facing each other And if this was six volts and this was two volts, what was my net voltage four volts? Well, if this is three volts and this is three volts if they're both identical, what's your net voltage? Zero what's your net current? Zero so they said okay, that doesn't work very well a loop in a wire No good. Sorry a loop in a magnetic field. No good. You get opposing currents both ease are in opposite directions So they Cancel it was a good thought then they said, okay, let's try something else Up until now Hanna, we've been moving the bar to get power Will power move the bar for us? So instead of putting a resistor and having this be the battery they said Malcolm What if I add a battery to the circuit will the bar start to move on its own? This is going to be the physics behind a rail gun You've heard the term in the news Saddam Hussein was trying to build one about ten years ago And there's there's still a fact. I think the US is pursuing this because in theory you could fire very large objects very fast Very very fast and if you want it to go faster just add more current which we can control very very accurately. Let's look So it says for the circuit below right now Find the induced voltage. Well, how fast is the bar moving right now? Zero so right now the induced voltage, which is B, L, V, Alex If V is zero, what's my induced voltage right now? Zero. Nothing, but we've got a battery here Okay Which way is the current flowing out of this battery up or down? Let's draw the arrow down Stroll the arrow in the resistor to the right Let's draw the arrow in the bar up and let's draw the little arrow on the top to the left And I'm going to call this clockwise or counterclockwise. Which way is the current flowing? Remember our abbreviation for that from the torque unit. Yeah, okay, let's bring that out again counterclockwise What did you say Cody? counterclockwise Now watch I guess that means that a charge starting here goes this way goes this way and Which way is it traveling as it goes through the bar? It is moving It's not moving to the right, but which way is the charge moving because of the battery Which way is the charge moving because of the current because of the battery will point your thumbs up the page then please Which way is the magnetic field according to this question? So thumbs up magnetic field out which way will the bar experience a force? It's going to accelerate. Here's your rail gun Okay, so we said this if you supply the motion amrit you can get a current or if you supply the current you can get motion What happens to the strip? accelerates okay, and Just to help us visualize. Let's put next to this battery. Let's put 120 volts Let's say we plugged it into a plug household outlet. Now. Here's the neat thing example 11 As soon as it starts to accelerate Madison Not only are the charges traveling up the bar because of the battery because of the current But now they're also moving to the to the right as soon as it starts to accelerate The charges now have two components vertical and horizontal they're moving to the right so as it speeds up What happens to the induced voltage? Well if the induced voltage is B? L V V is no longer zero the induced voltage is going to Increase What happens to the current? Well, let's look at a little positive charge sitting right here Now the battery is pushing it upwards. There's an Electromotive force pushing it up, but now it's moving to the right as well point your thumbs to the right Which way is the magnetic field out of the page? Which way will that charge also feel a force? It's feeling a force in the opposite direction of the battery There is an anti-current that we're going to call it a back current in the opposite direction of the source So the overall current I'm going to call that I net decreases By the way, what do you think the biggest this voltage can possibly get is? The max is going to be 120 volts Because that's our source It's sending a voltage in this direction Dan This is sending a voltage in this direction Eventually you're going to reach an equilibrium point where your net voltage is zero because you have 220 volt batteries facing each other sort of Then it'll stop accelerating Kim and just go at a constant speed Okay. Oh magnetic force on the strip Well since magnetic force is bill and We've already said your net current is decreasing What's happening to the force on the strip also? Decreasing it's accelerating less and less and less and less and less fast that eventually it hits constant speed when? When your BL your BLV equals 120 so it's decreasing and what happens to the speed of the strip? eventually Constant when when the net force is zero Hannah when does that happen when the current is zero? When does that happen when the net voltage is zero when does that happen when you're induced voltage exactly cancels out your source voltage oh? And you can solve for V and figure out how fast this rail gun will shoot things Which is probably what they're interested in Does that make sense? Says explain your answer using relevant physics principles. I think we just we just did this is not a kind of a question I would give you as a using principles of physics right to explain a question if I said hey if you double the current What will happen will it go faster or slower that would be a good question, but not the whole details So this setup has several applications the first is on the international space station They've talked about using this to launch the space shuttle from the space station after it's docked Because if the space shuttle is right by the space station like a meter away You probably don't want to fire your rocket engines if your engines are a meter away from the space station fire bad even in space So here is the thought You use the wings of the shuttle itself as your conducting bar You park the shuttle in outer space when you dock it on the space station You have it touching two very well greased metal rods like this or one metal you shape And is there much friction in space all cases probably work, okay? You have a big solenoid creating a magnetic field in this case into the page And then you run a current through this whole system from your solar cells So the current would go this way this way the space shuttle itself acts like the bar So in the space shuttle the current is going down the page point your thumbs down the page Which way is the magnetic field? What are these X's mean into the page extend your fingers into the page which way the space shuttle experience of force There you go. It will speed up and launch Not bad Any moving parts? Nope Fairly no maintenance. Yep, which is especially in outer space if you can build something it doesn't need maintenance So you don't have to do spacewalks to fix it. That's good Spacewalks very dangerous Even if you're doing all the spacewalk correctly those astronauts are taking cosmic rays by the Gatrillion Cancer risk the more spacewalks you do the more cancer risk you do There's a second Replication and it's gonna happen when we look at electric motors Yeah, as it turns out Electric motors do this same phenomenon out. It's gonna be in a 3d spinning situation What you're gonna have to we're gonna have to look at that dance specially because it's too complicated Just to wrap our brain around it right now, but the faster you rev an electric motor The more back voltage it generates until eventually when you're revving full speed The voltage that the motor is creating exactly cancels out the voltage from the plug Which means when an electric motor is running at full speed, you know how much current is actually running through the motor? Zero Which means if your electric motor is heating up, you know how you cool it off You rev it full because if you rev it full you have the least current in it the least electrons the least heat Very unusual for an electric motor if every any of you have ever used a power drill and you feel it getting warm Stop take it off of load and just hold the trigger down and in about 30 seconds if you let it rev with no load You'll holy smokes. It's gotten much cooler. You rev it up to cool it off It's the only motor out there that does that Nice feature we're gonna spend a whole day looking at back EMF or back voltage and some of the uses of it so as As the strip continues to speed up Although it's accelerating slower and slower so it's not speeding up as fast The induced voltage will continue to grow What happens when the induced voltage is equal to the supply voltage? What happens when? that Supply equals That remember what I said what we talked about A B C or D or sorry a B or C you hit a constant speed why your net voltage is zero Because they're two voltages in opposite directions therefore What's your net current zero? Therefore What's your net force remembering that magnetic force is bill if I is zero and there's an I in the force equation? What's your net force? Zero therefore if force is zero. What's your acceleration have to be because f is still in a And if your acceleration is zero, what's another fancy phrase for saying your acceleration is zero Constantly That would be the maximum speed of this rail gun Oh, I don't think I've ever wondered what do they call it a rail gun because there's two railings To rails Now it seems kind of obvious. I thought it was like with a train or something No says find an expression for the maximum speed of this rail gun okay the source Equals the maximum speed is going to be B L no, that's wrong. Mr. Do it get the lowercase B by itself This is why we don't use the two B's of the equation. Let's start getting the wrong B by itself Madison It's going to be your source voltage Divided by That let's try some with numbers example 14 For each instance below find a B C and D I'll draw the line down the middle And we're going to do each one at the same time, so let's do a the induced voltage at the same time now induced voltage Or emf is B L V It's B L V. How fast are we traveling right now? How fast is the bar moving? So what's the voltage just as we start to throw the switch just as we turn this battery on? What's the induced voltage? Zero now I crunched these numbers last class and they were kind of boring So let's crank this up a little bit instead of 8.0 cross that out and cross that out and Make it 80.0. It's moving. Is it even possible? What's my source voltage Is B L V with 80 bigger than 320 can we get it going that fat? Let's find out 0.35 times a length of 4.1 Times 80 how many volts will be inducing across this bar? Working against the initial source battery 115 yeah Anyone else it's Kim. Yeah, okay And Kim all that means is as long as we have a long enough railing And that's why I've ever seen the pictures. I don't remember that in the first Gulf War back in Holy smokes 1990 whatever it was three or four They stopped a ship heading to Iraq that claimed it was carrying oil pipelines and oil parts It had a bunch of long skinny parts and the US military figured It was rail gun parts because you do need a long railing to get it going that fast. It's not instant What's B want us to find the net voltage? What's the net voltage in the first situation? It's meant to be really easy 320 what's the net voltage in the second situation? Well, our source is 320, but we got 115 in the opposite direction 300 oh 205 so still some voltage left if we have a long enough railing this can still go faster see What's the current and direction? Okay The current is going to be V over R good old Ohm's law from last unit two years ago It's going to be 320 divided by 8.5 How many amps will be flowing through this particular bar right now? 38 37.6 we'll go to three sick things Now here it's still going to be V over R But it's going to be your net voltage right now You only have 205 volts in this particular circuit. So how many amps are flowing through here now? 24 three sick things 24.1 D Find the magnetic force and the direction Magnetic force on a wire or a bar is bill Magnetic force on a wire or a metallic bar is bill By the way, I'm pretty sure the direction is to the right isn't it because if it was to the left This would be a pretty stupid rail gun. Hey You mean, you know, right? Although if you had it going towards well Okay, what was the magnetic field I've scrolled down 0.35 Okay 0.35 Current thirty seven point six L four point one What's the magnetic force when we start? 54 Newtons and partway through it's going to be point three five Twenty four point one Times four point one Once we're doing 80 meters per second how much force is on this bar? 35 Newtons is it still accelerating them must be there's an unbalanced force What's the maximum speed of this thing? Well, the maximum voltage is 320 so if I wanted to solve 320 divided by point three five times four point one That's the maximum speed that we can hit over this given distance or with with a bar of that distance rail guns Voltage created by motion induced EMF BLV What's your homework? You'll notice on purpose. I didn't attach questions to this instead your homework is going to be from the great big unit review You can do one six eight 1820 3543 and you can also work on last unit review and right-hand rule assignment Both of which are due Thursday studying and getting ready for your test. I Guess you can also work on amusement park physics if you haven't finished that here's what I would not do I don't think there's anyone here who is completely and totally caught up including the assignment that I just put there So I shouldn't see books closed or people standing and socializing and yacking and all that their stuff You got 15 whole minutes