 So, Justin, how does a generator work? We said last day that pulling a bar through a magnetic field as long as the bar, the motion of the magnetic field, well, 90 degrees, could separate charges. Faraday then asked, okay, is there a way to do this by spinning something? So, here is a diagram that I found. It's a very, very simple generator. What we have in real life is some kind of an axle, Justin, that goes this way, and this would be attached to your water wheel at the dam, let's say, or it would be attached to your steam engine that was causing something to turn. Over here would be something that was causing this whole thing to turn. So, the rotation is coming from off the page, Sally, but it's there. We have a north pole here and the south pole here. So, which way is the magnetic field? Magnetic fields always point from what to what? South to south. And what we're going to do then is we're going to spin this thing. I want you to draw one tiny little positive charge right there in the middle. Remember, we called this the armature. That was the coil, the armature, that's what you're spinning inside either an electric motor or a generator. Now, most armatures are made up of several thousand loops of wire. This is one single loop of wire. It's our simplest K score. In this snapshot right here with this spinning in this direction, which way is this particular charge moving? Use your imagination. I'm going to argue, Tyler, I think it's going to end up moving downwards on that side as it spins. Is it not? Yes? So, point your thumb down the page. So, point your thumb down. Which way is the magnetic field? Always from north to south. Oh, we actually put the arrows in. So point your fingers, extend your fingers in the direction of the magnetic field. I know you've got to do a little bit of bending here, but I think the force on this charge would be in this direction. The magnetic force would be towards you out of the page kind of in this three-dimensional drawing. Down and right if you're looking at it literally. Is that okay? And Justin, we're going to look at one more positive charge, a little positive charge on the here. As this spins right now, which way is this positive charge moving? Up. So, if you point your thumbs up, magnetic fields to the right. This particular charge right here would experience a force this way. In fact, I think you would get in this particular situation a current like this. So what would happen, Justin, is this? Charges would be forced up on the left, forced down on the right. We've got a current, we've got a generator. Now use your imagination again. Give this a half turn. Once this little positive charge gets to this side, he would be getting, well, let's walk through this. The generator was invented by Michael Faraday. If you're bored sometime, read a biography or read the Wikipedia page on him. Good guy, very interesting fellow. The previous figure shows a simple hand operated generator with a coil consisting of only one turn. So you've all seen hand operated, so a hand cranked flashlight or an emergency radio. Many of you might have those at home in your earthquake kit, earthquake kit or something along those lines. You folks might have one, you never know. When the coil is rotated, the two long sides of the coil cut along across the lines of force and a varying EMF is induced. In fact, let's look at the four situations. We're going to look along the end of this coil. Next page for me. So we're looking down the end of this particular generator. There are four main locations for the coil. The first is the coil could be dead vertical. We're looking down the end, which means if this is spinning in this direction, which way is the top of the coil traveling to the right? Which way is the magnetic field also to the right? Are they parallel? Then you have no force for a split second. You would have no voltage. Then as it continues to rotate, it would reach this position. Well now you have this part traveling down, this part traveling up. If you point your thumb down the page on the right hand side, and which way is the magnetic field to the right? So if I go down the page to the right, I think my palm does end up facing me. That's what this dot signifies, current coming out of the page. And if I go up magnetic field to the right, I end up with my palm pointing away from me, Minsik. That's what the X right there is signifying, current away from me. You would have your maximum voltage right then. Is that okay, Megan? We're going to keep going. Then it rotates a further 90 degrees. That means this is moving to the left parallel to the magnetic field. This is moving to the right parallel to the magnetic field. Your no voltage again, you're back to zero. Continues moving a further 90 degrees. This is moving up the page. This is moving down the page. Now in this arm earlier, Sally, back here, it was coming towards you. Now, because it's the same arm that's rotated all the way around. Now it's going away from you. We would say technically you have a negative voltage. This is why we use alternating current so much. It's so easy to generate. Generating direct current is a pain. Generating alternating current, any device that's based on this idea of a rotating arm automatically generates an alternating current. Then when you reach your original point, again, you're back to zero. Something like this. This is a bit more complicated of a system. We have here a water tap. What we're going to do is we're going to spin a magnet. We're actually going to induce a voltage in a coil over here. You will notice that the current alternates if I start it going a little bit. Look at the electron flow in one direction, then another direction. In one direction, then another direction. When you have a spinning series of magnets, it will give you alternating current. You can see the compasses moving as well. Hey, let's even show the magnetic field lines if you want. Sorry, your picture is darker than my picture. I'm going to try and figure out how to make it brighter, but not right now. These three paragraphs repeat what I just said, that the voltage goes from zero when it's parallel to the magnetic field to maximum when it's perpendicular to the magnetic field to parallel zero to perpendicular maximum, but opposite direction to zero. Turn the page. Here's what Faraday asked. How can we combine the induced voltage in a wire, lesson one, and the induced voltage in a loop of wire, what we just did? Faraday racked his brains and he said, all right, what is it that actually causes a voltage? How can I link moving something to the right, last lesson, Megan, and spinning something, this lesson? Here's the following example. We have a rectangular loop of wire moving to the right perpendicularly to a magnetic field. I think on yours, correct me if I'm wrong, your rectangle is completely closed right there. Does it continue? For some reason my diagram doesn't. We have five situations, Kellen, situation A, B, C, D, E, and F. Where will we get a voltage? Because this is a coil of wires, we'll actually get a current because just like if you're standing in a circle playing ring around the rosy, if you take one step to the left, everyone has to take one step to the left, but you can get a current going, you can get a circle going, all right. Will there be an induced current here? Well is there any magnetic field here at all? Situation A, have we entered the magnetic field yet? So you know what, no. What about situation B, what I'm going to do here Tyler is I'm going to think about this as one, two, three, four separate rods, okay. And I'm interested in this rod and this rod. These two rods here, this guy and this guy are horizontal. What about my velocity? Horizontal or vertical, horizontal. Are these two rods perpendicular to this velocity, perpendicular to this velocity? What are they? They're parallel. Am I going to induce any voltage in those two rods there? Nope. Ah, but put a little positive charge right there and right there. This section of wire right here is inside the magnetic field. Yes Gordon? All right. Which way is this positive charge traveling? Which way is the velocity? Point your thumbs to the right folks. What do these circles mean? Which way is the magnetic field out of the page? Which way is this charge going to get forced? Okay, it's going to feel a force downwards. What about this charge right here? Has it hit the magnetic field yet? So will it feel a force at all? No, but you will get a current flowing because this guy hits this charge, who hits this charge, who bumps into this charge, who bumps into this charge, who bumps into, you know what? Like when you're playing ring around the rosy. If you're all holding hands and one person starts to move, everybody has to move. So we are going to get a current flowing. We will get an induced voltage in situation B. Oh, well if we got a current flowing when only half of the rectangular piece of wire was in the magnetic field, I bet you we get a big current flowing when all of it's in the magnetic field. Let's see. Once again I'm going to look at two positive charges. Which way is this positive charge here moving? The front guy. Which way is he moving, Justin? Which way is this positive charge here moving? What's the velocity of this whole thing? To the right. Point your thumb to the right. Which way is the magnetic field out of the page? Which way will this charge feel a force down? Okay, cool. Justin, what about this charge right here? Which way is this charge moving? Which way will he feel a force? In fact, here we get oppositional canceling currents. We have opposite currents that cancel each other out. In fact, we don't get a voltage there. I thought we would get a big voltage there. We don't. And Justin, the same argument can be made for situation D because really C and D are the same picture. You're still in the magnetic field completely. But in situation E, we have a positive charge right here and a positive charge right here. Pat, the right hand charge, is it in the magnetic field? Will it feel a force? No. What about the left hand charge? Which way is it traveling to the right? Which way will it feel a force? You're going to get a current going, but do you notice this time, the current is counterclockwise where right here the current was clockwise. You are going to get an induced voltage in the opposite direction current. What about for F? Is it in the magnetic field at all? No. So Faraday observed this in experiments and he said, okay, how the heck can I link this picture moving the bar from last day and spinning something? And this is going to bring us to a concept called flux. To explain this, Faraday realized that a voltage and therefore a current in a coil of wire was induced when the area of the coil that was exposed to the magnetic field changed. When the area of the coil that was exposed to the magnetic field changed. And this leads us again to the concept of magnetic flux. What is magnetic flux? It's the number of magnetic field lines passing through an area. Key concept. It's the number of magnetic field lines passing through an area. Say what? I'll show you. Here's my magnetic field lines. Here's the area that we're talking about, a circular coil, okay? Right now, very few magnetic field lines traveling through this area. Small flux. How can I increase the flux? Well, there's two ways. The first way this animation won't let me do, make the area bigger, can't do that. Or second way, strengthen the magnetic field. And to strengthen the magnetic field, it's pretty easy. I'll just move the magnet closer. And now, in relation to the coil, the magnetic field got stronger. Are more lines going through it? Yeah. So smaller magnetic field lines, smaller number of magnetic field lines, smaller flux, bigger flux. How much voltage is being generated right now? Zero. How much voltage is being generated right now? How about now? When is voltage being generated? Do you see? I know you heard that. This was Faraday's leap of inspiration. He said, aha, voltage and current are created when there's a changing flux. Flux does not cause current. Magnetic field does not cause current. It does not cause current. Changing flux, which means either changing magnetic field or changing the area. That's what causes current. Ready? I'll even get the bulb to light. See it there for a split second? I can really change the flux dramatically by going right through this. In fact, and I need to go find it, I have a flashlight and it's a transparent flashlight. You shake it to charge it and you can literally see the magnet moving up and down through the coil. It used to be on this shelf. I put it somewhere or it got swiped. I got to go looking for it. This is how Faraday linked spinning an object and what we did in lesson one where we just moved a bar through a magnetic field. What's the symbol for flux? Technically it's a tie fighter on its side. Technically the symbol for flux is a zero with a vertical line and two horizontal bars and that's what appears if you find it like in a math keyboard. But I'll be honest Justin, most of us just drop the horizontal bars. So there's the typewriter symbol for flux. I did find it in my word processing Microsoft word symbols feature somewhere. But I'm just going to draw a zero with a big vertical line through it. Flux. What are the units for flux? Well, there's all sorts of types of flux. There's electric flux, which is the number of electric field lines that travel through a given area. There's light flux, which is how many photons of light are traveling through a given area. All sorts of flux. So technically the unit for flux is lines. That works for any type of flux, but for magnetic flux, the unit is Webers named after a scientist whose last name was, he's my little compliment, symbol capital W lower case B. I think that's the last new unit you're going to learn this year, Webers. That's it. How do we calculate flux? Flux depends on two things. The strength of the magnetic field times the area that the lines are going through. Gordon's stronger magnetic field gives you stronger flux. What about stronger area? Except we have to add one key idea. These two have to be perpendicular. I'll show you what I mean. It says for each orientation of the spinning loop pictured below, so we're looking at the side of a generator, what can be said about the amount of flux passing through each loop? Here the flux is going to be the maximum. You have the most number of lines passing through the loop because the area is perpendicular to the flux. What about diagram C? Here the area is parallel to the flux. You know how much flux you have here? Zero. This would be in between, in between. Example, giving you a bunch of situations, if you remember, did you all turn the page? How about at the top of the page we write flux, and we'll do the horizontal bars this time, is equal to BA perpendicular. By the way, if they're not perpendicular, you can use components. We won't do that in physics 12, but all you do is you need the angle theta that your coil is at compared to the magnetic field, and you find the perpendicular component, which technically all of you could probably figure out on your own, but it's not in physics 12. In situation A, the coil is like this. We did these diagrams as simple as possible, so you can imagine the rest of the coil back there if you want to, but that just clutters things up. My magnetic field is increasing, so if my magnetic field is increasing, what's happening to my flux increasing, decreasing, or staying the same? Flux increases. What about if my magnetic field is decreasing? Flux decreases. It's exactly what was going on right here, so to decrease my magnetic field, an easy way to do that is just move the magnet further away. You haven't changed the magnet, but over here, the magnetic field now is way weaker. I only have one, two, three lines. To increase the magnetic field, move it closer. What if the area inside the field decreases? Well, if the A gets smaller, what happens to your flux? Decreases. D. And this is where I got to give Faraday credit. He looked at, remember this diagram from last day? And he said, ah, there is an area in this picture. It's the area behind the bar. As I move this bar to the right, what's happening to the area behind the bar? Increasing, decreasing, or staying the same? Flux is increasing. I don't think I ever would have thought that the area in question there was, yeah, the stuff behind you. I don't know if I ever would have come up with that. What about here? Is your area changing? No? Is the magnetic field changing? No? Staying the same. Which means because the flux is staying the same, no voltage or current will be induced. In the previous four examples, you would get a generator. Move the magnet. Well, when you move the magnet closer, what you're really doing is you're making the magnetic field stronger right here. So the flux would increase. And then here is how most generators work. We spin a coil. What's the flux right now, maximum, minimum, or somewhat in between? Maximum, if we spin the coil to, let's say, vertical, what will the flux be? So if the flux is going from maximum to zero, is your flux increasing or decreasing? If it's going from maximum to zero, it's got to be decreasing. What's really happening is the area that's exposed to the flux is getting smaller because as you turn it, the flux can see less and less of the area until it's dead vertical and the flux can't see any of the area. H, what if we squeeze this loop? Oh, that's making the area smaller so the flux will decrease. Okay, our loop is right here and we have a second external circuit. Which way is the current moving in this bottom wire right here? To the left? I'll point your thumbs to the left then, please. Now this is the right-hand rule for a current carrying wire, which was you pointed your thumb in the direction of the wire's current and you curled your fingers and they told you which way the magnetic field was anywhere around the wire. So below this wire, which way is the magnetic field? Up the page, down the page, towards us or away from us. Sorry. I think the magnetic field is like that, right there. Now Regan, if the current gets bigger, what do you think happens to this magnetic field gets bigger and what happens then to the flux inside this coil if the magnetic field is increasing bigger. So previously, Sally, we said an induced voltage was created when we changed the field, the orientation or the area. So Faraday said, ah, let's link that all in one simple rule. Voltage is created, oh, let's highlight this. Voltage is created if the flux changes. If you have a changing flux, voltage, and therefore current if you look it up to the circuit, is the flux changing right now this moment, Jordan? No voltage. Oh. There it was. There's a negative voltage. There's a positive voltage. There's a negative, positive, negative, positive. Or in this diagram here, what we're doing is having a south pole here, then a north pole here, then a south pole here. What we're doing is we're changing the magnetic field direction, which means the magnetic field goes from positive to zero to negative to positive to back to zero to positive to zero to negative because magnetic field was a vector. Heck, let's add more water and you're getting an alternating current. There's a compass over here so you can see that the magnetic field is changing. Same idea. Changing flux, you can see the light bulb light. Everything still, no good. And I can, again, either increase the magnetic field by moving the magnet or by moving the coil, or if it's an electromagnet by increasing the current, that also increases the magnetic field. The easiest by far, though, from all of our mechanical devices is to spin the magnet. That's how every hydroelectric generator is working. It's more complicated, but that's the theory. Faraday found several things. He found that the voltage varied directly with the change in flux, bigger flux change, more voltage, directly with the number of loops of wire, hey, you want twice as much voltage, put twice as many loops. You want 100 volts, add 100 loops. You want 1,000 volts, put 1,000 loops. Oh, and he also found inversely with the time, the faster the flux changed, the shorter the time, the more the voltage. In fact, Faraday's law looks like this. The induced, so here's Faraday's law. The induced voltage, the EMF, thanks Irwin. You put it on top of the folder face down. Created in a coil or coil of wires is given by, put an equal sign, leave a small space, we're going to add something, M delta flux over delta time. And then I said we're going to add something, Justin, in front of everything, put a negative. Gordon, why negative? You remember when I dropped the magnets in the copper tube? It's to let us know the force is always going to be in the opposite direction that you would want it to be. It's always going to resist what you're doing. So remember last lesson when we pulled the bar and we said, oh, there'd be a force in the opposite direction? What if it wasn't? What if it was in the same direction that you were pulling? Well then you could let go and it would go faster, which would create more voltage, which would make it go faster, which would create more voltage, which would make it go faster, which would create more voltage, which would make it go faster. There's your perpetual motion machine, the universe would explode. The universe says, no, you get nothing for free. The negative tells us, we're going to give that negative a name later. I'm going to call it Lenz's law. It says, you know what? If you're not sure what direction the current is, ask yourself which way the current would be if it made things go bigger and faster. It's always in the opposite direction. No free energy, no free lunch. Oh, where N is the number of coils or turns of wire? Flux is, oh, what did we say flux was? Do you remember? BA, bad attitude, perpendicular. This is on your formula sheet as is this. Oh, by the way though, it doesn't say flux here. It says change in flux. What's change in anything? The blast time, I'll be using that this year by the way. And then change in time, T at the time. And in fact, we're going to get kind of sloppy. I'm going to stop writing the delta T because time is always a change in because you're always starting and stopping a stopwatch. It's always a final minus initial. It's the one unique variable that always is that. So we kind of get lazy. So why negative? I'll give you a better explanation tomorrow. Example, a circular loop of wire of radius 2.5 centimeters is in a magnetic field of 0.4 teslas. If the loop is removed from the field in a time of 0.05 seconds, what's the average induced EMF or voltage? Oh, and it says the axis of the loop is parallel with the field, which means the area is perpendicular, which is good. All right, what do they want us to find? What is the average induced what? Here we're going to use Faraday's law because it's not a bar. Negative N change in flux over time. And because this is the first time we're using an equation, let's defec. What's N? Read carefully. It's a bit tricky. How many coils of wire are there? And I'll give you a hint. It's the first word. What does ah-loop mean? Huh? More specific as a number. 1, a little bit tricky to spot because it's so obvious. And the next easiest one to find is the time. How much time elapsed before and after 0.05? And the last thing I need to find, Jordan, is the change in flux. I almost always do that on a separate line. So change in flux. Jordan, what's change in anything? So let's go flux final minus flux initial. Jordan, here is your final. Are we out of the magnetic field completely? What's my final flux then? Ah, they will almost always do that. One of them will almost always be 0. The only time they won't is if instead they flip the direction of the magnetic field, which will give you one of the magnetic fields positive and one of the magnetic fields negative. We'll do that a bit later. Minus flux initial. What was the equation for flux? BA. So the change in flux is going to be 0 minus BA is just negative. B, 0.4. A, what shape? OK, what's the area? They're going to give you three shapes, by the way. It's going to be a circle most often, a rectangle sometimes, and a square occasionally. You do need to know the areas. Although I think the area for a circle is actually on your formula sheet, I don't think a rectangle or a square is. So you're going to need to know that for a rectangle, it's length times width. And for a square, it's one side squared. What's the area of a circle? Pi. What's r in this question? 0.025 squared. Now we can plug everything in. How much voltage will be induced? The induced voltage is going to be negative 1, negative 0.4 pi, 0.0 2. Oh, I'm running out of room, Mr. Duke. I'll do it down here. The induced voltage is going to be negative 1, negative 0.4 pi, 0.0 25 squared. I'll divide it by 0.05. I don't think, if I recall, you get much voltage here. How many volts do you get? You get a positive answer, kind of nice. Negative 1 times negative 0.4 pi, 0.025 squared divided by 0.05. Do you get 0.0157? Sorry? Yeah. 0157 volts. Not very big, but instead of one wire, have your coil be 1,000 wires. And there, 16 volts. There's a battery. 1,000 wires isn't that much to do with a coil. Easily build those. Turn the page. A square coil of wire, 5 centimeters on each side, has 100 turns. It lies perpendicular to a magnetic field of strength 0.02. If it's rotated through 90 degrees in a time of 2 times 10 to the negative 3 seconds, what's the average induced EMF? So initially, we have our magnetic field like this. And the square is perpendicular to the magnetic field. Initially, it's sitting like that. And then we're going to rotate it 90 degrees. When we rotate it 90 degrees, it's going to end up parallel to the magnetic field. Hey, what's my final flux going to be? 0. We'll just keep that in mind. The EMF is equal to negative N change in flux over change in time. And I always have a tough time drawing the flux symbol. That vertical line just seems to not go down the middle very often. Let's do a little defect over here. What's N? Sorry? 100. What's T? 0.002. That is 2 times 10 to the negative 3 plus typing. What's the change in flux? Well, random what's change in anything. And we've already said the final flux is 0. Initial flux is BA. Change in flux is going to be negative B. 0.02. A. Oh, what shape are they talking about this time? A square. So it's going to be 0.05 squared. The EMF is going to be negative 100, negative 0.02, 0.05 squared, all over 0.002. How many volts this time? 2.5? OK, now we're talking a small battery. 2.5 volts. By the way, as usual, Dylan, with 1, 2, 3, 4 variables, I can give you any three of these and say find the fourth one. So be prepared to also go backwards. Oh, how fast would it have to rotate? How much time? Or oh, how many coils of wire would you need to get a voltage of? Well, how many coils of wire would you need to get a voltage of 5 volts? 200. Stuff like that. The best way to change the flux, the most bang for your buck we've learned, is to change the magnetic field. Because magnetic field is a vector, though, we're going to have to call one direction positive and one direction negative. So we're starting out, for example, in this next question, into the page. And we end up out of the page. I'm going to let into the page be positive. I'm going to let out of the page be negative. Because it's a vector, Sally, direction, direction, direction, one way is positive, one way is negative. You could have let out of the page be positive and into the page be negative, same answer. Example, a circular coil with 100 turns of wire is exposed to a changing magnetic field as shown below. If the field takes 0.12 seconds to change, what's the average induced voltage? OK, Gordon, what's n? More specific in this question, what's n? Yes, I caught you. What's n? 100. What's t? 0.12. The tricky one is always, what's the change in flux? So over here, change in flux. Megan, what's change in anything? So this is going to be flux final minus flux initial. And this time, I don't think any of them is 0. This is going to be B final A minus B initial A. Why did I put the final and initial on the magnetic field? That's what's changing, not the area. What's the final magnetic field, not 5.4? What's the final magnetic field? It's not 5.4. Negative. 5.4. A area. What shape have they given us here? Circle? Pi. What's r? Oh, they gave me r in the actual diagram. I didn't see it in the instructions, but there it is. Pi.1 squared minus. What's my initial magnetic field? What's B initial? 7.8 times pi times 0.1 squared. What is my change in flux? That's going to be negative 5.4 times pi times 0.1 squared plus. No, not plus, Mr. Dewey. Minus 7.8 times pi times 0.1 squared. And the 0.1 didn't show up there. There it is. You get negative 0.41469, blah, blah, blah, blah, blah. I'm just going to keep that on my calculator. I'll write down 0.4147, but I'm now going to plug it in over here. E equals negative 100. Negative 0.4147 all over 0.12. Negative 100 times my previous answer all over 0.12. Oh, hey, this is a generator. 346 volts power house. What's the voltage that we get from our plugs? Do you remember? 120. What's the voltage that your stove and your dryer use? So this would be, and then some. This could recharge a car fairly quickly, probably, if we've got electric cars. Faraday's Law. Example 6. Here's a great multiple choice kind of a using principles of physics, right to explain kind of a question. It says, rank the four loops below in order of increasing induced voltage. So from smallest voltage to biggest, are there any of those that would have no voltage induced whatsoever? Tyler, I didn't hear. You say an answer? B, why? Is the area changing? No. Is the magnetic field that it's exposed to changing? No. So B equals 0. Which of these would have the biggest voltage generated? Which of these has the biggest change in flux? I'll leave a space on the fourth line. A equals E max. OK. Now between C and D, which one has a bigger change in flux? D changes the area, but only by about a quarter. D changes the area as well that's exposed by about a half. So I think from smallest to biggest, I think D. And then I think C. Does that make sense? So those are some kinds of multiple choice questions they would like to ask that they would probably simply say, which of these would induce the biggest voltage? A. Or which of these would induce the smallest voltage? B. They probably wouldn't ask about C and D. That's just to give you more to think about. So going a little technical, for moving wires like a bar, a beam, piece of metal, use BLV like last day. But for a coil that's spinning, it's best to use N change in flux divided by change in time. Except there should be a negative right there. What's your homework? You can now do from the review those there. I'll read them out to you if you want to write them down. So homework from review, 5 comma 11 comma 12 comma 15 comma 16 comma 23, 24 comma 32, 34 comma 36, 37 comma 39 comma 40 comma 46.