Lecture 21 Relativity and Electromagnetic Fields; Motors and Generators

all right welcome back everybody all right last class we got into possibly some of the wig iasts stuff in physics okay so in my opinion some of the wig is stuff in physics is special relativity Einstein's theory of special relativity and quantum mechanics so anytime we get a chance to touch on those in class to get very excited so special relativity here's my advertisement for special relativity we saw last time the strange conundrum that if we had two charged particles and they were moving relative to you so we saw that you would observe not only that these particles behaved as though there were an electric field between them because they're charged particles but because they're moving you would observe a magnetic field and you would observe that these particles also respond to that magnetic field that you observe remember that right and then we sent quarry running really fast and he was supposed to catch up with them and so when he ran and caught up with these particles that were moving fast he no longer observed a magnetic field he only observed an electric field and yet the motion needed to be the same in some sense so so both observers both the observers sitting here in the classroom when you saw the two particles go by at a particular speed and Cory who ran to catch up with the particles and had no relative speed with respect to them we all needed to observe that the same physics was operating that the same physical equations applied okay so as long as we did our measurements carefully we got reasonable answers as long as Cory did measurements correctly he got reasonable answers and yet we observed a magnetic field that he observed no magnetic field because he was running alongside the particles and since the particles weren't moving with respect to him there was no velocity if there was no velocity of this charged particle it was not putting out a magnetic field you remember this conundrum we had at the end of class okay it's all due to this guy right there Albert Einstein you probably haven't seen this picture yet of him it's kind of a rare photo so this is Einsteins relativistic fitness program okay I call it get ripped with Einstein I hope that doesn't have a meaning that I didn't know about but anyway get physically fit okay so here's the deal if you run near the speed of light Einstein is told by running near the speed of light you can slim up your physique yes yes it's true and as you run faster near the speed of light your muscle mass will increase okay and you will live longer all by running near the speed of light you ready observe me carefully I used to run in college and here's what it looks like okay so you see that I got skinnier right and I got muscle mass increased and I just extended my life by point zero zero zero zero something something mumble seconds okay because I ran and Einstein says that'll make me live longer so here's the physics words we put to that the slimmer physique idea is that there's a linked contraction that happens when you observe things that are moving to the speed of light there's a mass increase that you observe as a particle moves near the speed of light and you observe a time dilation I'll tell you what all of that means but the crux of it is that when you when you observe something that's moving faster than the speed of light you'll observe a links contraction that the lengths you observe for this this object contracts get smaller contraction means gets smaller in the direction along the motion you'll observe the mass of the object increases because it's moving faster we call that mass increase and you'll observe what's called a time dilation that is that if you could read my watch as it goes by okay if I ran really fast and you watched what my watch was doing and I'm watching you watching my watch do something okay you would see my watch slowed down according to you according to me it's fine but according to you you would say hey her watch is running a little bit slowly okay so that's what you would observe so I mean why is this going on why did why was this einstein's great relativistic fitness program alright it's because essentially the speed of light is this inviolable constant okay so the speed of light what we mean by the speed of light see is what we call it is the speed of light in vacuum all right light by the way if light travels through materials light can have a different speed inside of materials the reason being light interacts with materials it can get absorbed and re-emitted absorbed and be emitted absorbed and readmitted all that absorption readmission re-emission takes time so you might observe the photon moving through a material slows down a little bit that's why what we're really talking about here C is the speed of light in vacuum the speed of light where it's not going to be bothered by anything okay that number turns out to be an inviolable constant nothing can go faster than the speed of light and it has to do with this this Lorentz factor and I'll show you how to use that but essentially what we're gonna see is that space and time warp kid you not space and time warp so as to keep the speed of light this inviolable constant so last class we sent Corey running along to catch up with those two positively charged particles if we had sent Corey chasing a photon he would never catch up space and time would warp okay so that he could just never catch up and no matter how fast he ran with respect to us he would always measure that the photon was moving at the speed of light we would measure the photons moving at the speed of light and even Cory running as fast as he runs would still measure that the photons moving at the speed of light there are things that get warped by this constant called the Lorentz factor or gamma we use the Greek letter gamma for it but let me at least let you get to know this gamma factor so this is this is called the Lorentz factor it's 1 over square root of 1 minus V squared over C squared and it'll turn out that things you measure get get changed by this factor okay so there'll be some things that increase by a factor of gamma some things that decrease by a factor of gamma so let me tell you what the gamma is and then I'll show you where it goes in the equations so here's what that plot looks like basically V is the speed of something that you're measuring with respect to u all right and you need to be in what's called an inertial reference frame an inertial reference frame is just that you are moving at constant velocity you're not changing your speed and you're not changing your direction so if you're moving at constant velocity then you get to be called an inertial reference frame you are authorized to make measurements on behalf of the physics world and then the velocities that you measure for other objects relative to you go into this equation okay as speed okay and then you'll measure these speed of objects and as these objects that are being measured relative to you have some velocity that approaches the speed of light gamma blows up let's just look at the mathematics of this thing so if I go back to V equals zero okay let's just say I'm measuring something that's in my reference frame it's not moving with respect to me and then I would say that well the speed of it is zero 1 minus 0 is 1 and then this thing turns into 1 over square root of 1 all right what is 1 over square root of 1 right what is 1 over square root of 1 1 okay so way back here when the velocity 0 gammas 1 as the velocity gets near the speed of light this constant blows up so let's just think about what would happen if V approached C so if V is approaching see this thing gets very close to 1 V squared over C squared approaches 1 I get 1 minus 1 is 0 okay square root of 0 is 0 so what's 1 over 0 infinite ok or the math majors are saying it's really undefined but what we mean is that the thing is tending towards infinity as velocity gets near the speed of light so this thing blows up alright and it's always no matter what it's always greater than 1 ok so it's either at 1 or greater than 1 your whole life by the way where are you on this graph so this thing is blowing up as the speed gets near the speed of light the speed of light in vacuum is about 3 times 10 to the 8 meters per second I don't know if you've noticed this but that's not on your car right your your car's speedometer does not have that on it so this is really really fast your whole life and not just here where it's flat your whole life is way back here ok I'm not I'm not trying to say that you're a zero I'm just saying that you're here somewhere I better use the laser pointer you're there ok your whole life is lived right here in a tinier spot than that pixel ok so you you're used to gamma being 1 ok in your everyday life but if you could run fast enough or observe things that are moving fast enough this gamma starts to become appreciably different than 1 and then things get well kind of Wiggy ok you'll start to notice then that space and time warp to preserve the speed of light so here it is space and time warping to preserve the speed of light see we we use this Lorentz factor gamma gamma we saw from the plot is always greater than one so if I remind you then of Einstein's relativistic fitness program where if something's moving near the speed of light you know you get a length contraction all right there's a mass increase in a time dilation so here so so the way the way we can then work this out is what's on the left hand side is what you observe so the left hand side is what you observe for the object as it's moving quickly the right hand side this L would be the length of that object that you observe when it wasn't moving quickly when it moves quickly the length you observe for it is down by a factor of gamma so now I just need to think okay length contraction and I look at gamma I know that gamma is greater than one so to make this equation work out so that I observe a smaller length I need to divide by gamma right gamma is greater than one I divide by gamma that gave me something smaller so the observed length is smaller I know that the mass is going to increase the VAS that I observe will increase how do I get the original mass this is the mass I would observe for this particle we're not moving relative to me how do I get the mass to increase I need to multiply by gamma then the observed mass has increased time dilation is a little bit trickier to work out but what you're trying to get that to do is so that the time you observe going by on somebody's watch as they're running by really quickly that slows down so time slows down so here all right so what does this look like so I'm gonna try it real quick ready Einstein's relativistic fitness program so as I run really fast me the speed light and turn it to knock off all those mics and things like that did you see it I got I got skinnier okay yeah watch again ready see ya okay so you get a slimmer physique because get that length contraction in the direction you're running also as I ran faster my muscles got denser right everything got Dunster actually okay so you gain mass everywhere but hey if I were writing this as an advertisement I would say hey your muscle mass goes up and I just extended my life by running quickly because I don't know if you can notice here but as I'm running by quickly my watch is moving slow or so I just gained point zero zero zero zero zero something or other zero one seconds on my total lifespan so I'm gonna live that much longer so space and time warp so as to preserve the speed of light see this is what it means for observations it also means that if I took a stopwatch so if I or just have to be a stopwatch but any kind of watch let me take any kind of clock and move it relative to you you'll notice that the clock gets skinnier it gets heavier and it runs more slowly so that's what all you observed here's kind of an interesting thing philosophically speaking okay so you've heard of the theory of relativity before I'm sure have you also heard of relativism it's a philosophical idea okay relativism is a it's a kind of philosophical idea that well things depend on your frame of reference so different people observe different things and and so you know there's one thing that I observe is not the saying that you observe two things are relative so this idea kind of made its way into philosophy and then into pop culture as relativism which is kind of interesting to me because the the original physics is actually not about how things are relative the original physics here is about how the speed of light is a constant so really this shouldn't have been called the theory of relativity as if things are all relative it should have been called the theory of the absolute constant of the speed of light in vacuum it means that every observer observes the exact same thing the speed of light is always the speed of light so it's kind of interesting to me that that physics theory kind of got percolated out and ended up as an idea of relativism all right so these are the consequences for length mass and time as we already saw there's also consequences for electric and magnetic fields so electric and magnetic fields also adjust so that the speed of light is a constant to any observer so it's a little bit like this okay we saw that those two charged particles moving by if the two charged particles were not moving with respect to us we only observed an electric field but if they moved relative to us now they have a velocity I now the vapor they are producing from our frame of reference we see a magnetic field and it depended on the velocity of the particles relative to us it here's an analogy for that okay when the two particles when the two charged particles were not moving with respect to us we just observed II said look they're two charged particles they're not moving with respect to us I observe an electric field and yet as those two charged particles start to move will will measure an electric field and will also measure just a little bit of magnetic field and the faster they move the more magnetic field will see and the faster they move the more magnetic field will see and so on so I can make an analogy between rotating this cube between why are you seeing magnetic field or are you seeing electric field okay and as this object moves faster you're gonna see more and more magnetic field in more and more magnetic field so it's a bit like rotating this cube moving at different speeds is like looking at this cube from different angles you'll see different pieces of the electric field different pieces of the magnetic field depending on how fast you're moving and so really it means that I shouldn't think of the electric field as a completely separate object from the magnetic field I should think of them as a unified electromagnetic field and as I move at different velocities relative to what I'm observing I will see different pieces so if I move faster I start to see more magnetic field if I move faster I start to see more magnetic field so we now call this thing a unified field the electromagnetic field and by moving at different velocities you see different pieces of it this is just an analogy but it's now it's an analogy I happen to like so electric and magnetic fields look different for different observers in different reference frames reference frame means you're moving at a constant velocity with respect to what you're observing everybody can correctly predict what they observe using the exact same laws though okay so the laws of physics are the same in every reference frame it's just that the detail is about well exactly what velocity did you measure those are different in different reference systems do you have any questions about that basic idea okay all right so let me show you what the equations look like for the electric and magnetic fields so here's a positively charged particle moving with a particular velocity with respect to us okay so when the thing was sitting still we might have observed a particular electric magnetic sho magnetic field so on the right hand side you've got the components of the electric field and the magnetic field that you were observing before this system started to move with respect to you once the system starts to move with respect to you now I get a gamma factor okay and gamma is going to then rotate this cube around so whereas you were seeing one side of things as the system gets boosted relative to you this is going to shift a little bit okay so the primed the things over here that have a prime the primed fields are the new observation based on when this thing is actually moving and things get scaled by factors of gamma coming up and also you'll see that magnetic fields convert into electric fields pieces of electric fields convert into magnetic fields because it's all one electromagnetic field and you're just doing seeing different sides of it you have any questions about that basic idea yeah oh you're asking a fantastic question so he wants to he want he's saying okay I've got this moving on the x-axis why are these things not changing on the x-axis think you can think of it and if you I think if you go back to charge particle and what's the magnetic field that I observe so let's let's think about that let's go back to thinking of a single charged particle going by okay and then it's going to have a magnetic field coming out of it so I can think of terms of the right-hand rule again of boosting this charged particle it makes a magnetic field that is in circles around it no matter how fast it goes I will never observe a magnetic field parallel to its direction of motion the magnetic field is always yeah excellent question okay so he's pointing out that this guy didn't change that's because along the direction of motion the the charged particle you would observe the charged particle is creating magnetic fields that circle around it but nothing heading towards or away its motion yeah good question okay alright so that's some fun relativity now back to nonrelativistic there would you I suggest I should ask you have any other questions about the relativistic side of things right okay so now let's get back to using this stuff for useful things okay relativity is also useful by the way we have to use those kind of Corrections to make your GPS systems work so we do actually make use of these things but most of your experience in everyday life things are not moving at relativistic speeds so here's an example of what can happen if I have a current carrying loop of wire in a magnetic field I can actually use it to build up a motor so let's think of how that might happen so I want to think about the magnetic force that a current carrying wire feels in a magnetic field so here the arrows pointing up represent magnetic field I have a current carrying wire okay currents moving along this direction and I have an axial I've made the wire rectangle shaped so that get easy pieces of the wire to calculate so here this is all one particular direction and this is all one particular direction you know and in real applications people don't tend to use square shaped wires they tend to just have them whatever configuration is is easiest so if I look at this guy from the side alright so what I'd like to do is look at this guy from the side and think about there's an axle coming out of the board over here I've got current coming out towards you and over here I've got current going in but I understand that the current comes out of the board runs along a wire that I have not written down right and then goes back into the board and then runs along the wire that's behind the board that I'm not drawing okay current comes out towards you runs back over here goes back into the board now how can you remember the dots and the X's here's a let me give you a couple of mnemonic devices for remembering dots and X's so here I have a pen that's got a point on it okay when the point is pointing towards you that's like current coming towards you yeah let me try it again okay so if the currents pointing towards you okay represented by the direction this pen is pointing you see a point right so that's that's this guy that's a point coming out at you or if I want to think of the other side where the currents reversed and the pen essentially I can think about the pen going through the page okay and poking out you kind of see how it's left is an X this is how I remember which way it goes okay so the X is like the pen already poked through another analogy you can use for this is to think about an arrow so when the arrow is pointing towards you you see the tip of the arrow okay currents coming out when the arrow is pointing away from you let's get those little tail feathers in the back that are kind of a cross configuration you're seeing the end of the arrow going away from you it's just a mnemonic device to help you remember that point means it's coming toward you X means it's going away from you so we're seeing it from the side all right so now if I think about well what happens if I kind of tilt this thing on its axle okay so I have this this current loop I'm going to tilt it on its axle the magnetic field is an applied magnetic field so we have some net large apply magnetic field that's going to be constant throughout all of this and I want to think of how does the current carrying wire respond to that magnetic field so the current loop can rotate on on its axle maybe it's going to rotate this way okay maybe it can rotate the other direction okay okay so let me set up the problem for you so thinking in terms of magnetic force where the magnetic forces I Delta L cross B so this would be the force on a current carrying wire due to an external magnetic field so an applied magnetic field B and then a current carrying wire tell me if this is the situation so same same loop of wire with an axial so have the axial oriented so that's coming out towards you the magnetic field is up and here at the top current is coming towards you then it goes down and back into the page at the bottom and then back and around in this configuration which of those diagrams represents the forces on the wire okay you'll have to use the right hand rule all right this is a tricky problem okay so tell me tell me what you're thinking does anybody want to walk us through using the right hand rule to get to one of these answers because it's not immediately obvious you have to walk through all the steps anybody want to volunteer their neighbor - yes all right oh man he's like I am not sitting next to you anymore yeah exactly that's what I begin okay all right so tell me if I'm getting this right he's saying top in the top the top case here that current coming out toward you okay I'm gonna to use I Delta L cross be I point my fingers in the direction of the current which is out towards you on the top rotates that I can curl my fingers towards the magnetic field and then my thumb points to the right sorry that's my right your left thumb points this direction so one of these two must be right and then on the bottom the currents going back into the board so I point my fingers in the direction of the current curl my fingers up towards the field and I get a force to the rug to yes this is your right as well so I get the force to in this direction now some people like to use the three fingers and and in fact I'm not familiar with the three fingers so I'm learning it because the 8:30 people make me use the three finger rule because they always like that so let me try since a lot of people like that let's do it with a three finger rule so here I've got current coming towards you so index finger along current second finger along field and then some points long force okay and then for the other side you'll just reverse it right it goes in the other direction okay other things may I do it right okay all right yeah this three yeah it must be that ECE must teach the three finger rule because overwhelming that the 8:30 section is all using using this so I had to learn it because this is what they kept telling me to use so I learned it like this okay questions alright this is worth going over again if you if you found this one tricky and a lot of people did definitely go over this tonight okay later so this is the right one it's gonna be D in this configuration that current carrying loop is gonna tend to spin okay so there are some orientations then that we can put this current carrying wire in in the magnetic field where it will tend to rotate okay this is a good thing this means that we can do useful stuff in fact so you remember we had a couple of lectures ago we talked about a bar of metal that we were going to drag through a magnetic field right we had the magnetic field pointing in a direction that was perpendicular to the bar and then we moved the bar perpendicular to the magnetic field we saw we could drive current with it okay so week that means we have a way to convert electrical energy into mechanical energy this is a way to do that right if this loop of wire feels forces tending to rotate it then we're converting electrical energy into mechanical energy or alternatively I also have a way to take a bar right and move it through a magnetic field it'll generate a current all right we said if we kept moving that bar forever hooked up to really long rails we could drive a current as long as we wanted or the other easy thing to do is to just move that bar back and forth now I've got current running one way and then the other way one way in the other way and that's oscillating current or or alternating current and so you can use either of these ideas to convert electrical energy into mechanical energy and back and forth so we should expect then that we have ways to make a motor so here we're going to convert electrical energy into mechanical energy okay we have coils of wire here that are making magnetic fields and then these guys in the middle or responding to the outer magnetic field okay all right it's got a pretty nice axle so that'll keep spinning for a while even when I unhook it so there's a way to convert the electrical energy into mechanical energy you can do the opposite you can you can convert mechanical energy into electrical energy so let's see which of these which bulb is lighting up oh yeah there you go okay so here I'm I'm using that same principle of moving wires through magnetic fields okay I'm supplying the energy but moving wires through magnetic fields in such a way that that generates currents and then can drive the bulb all right and what's kind of fun about this demonstration is that there's different bulbs we can try that's an incandescent bulb all right we can flip this over to the big green guy okay which is pretty bright and this there's something up here that I need to have one of you guys come up here and try this you can tell the class otherwise I don't think you're gonna believe me so I need I need a volunteer to come up here and try this fair's fair man you volunteered him for the I clicker question all right give a round of applause is this this hearts up okay all right all right thank you thank you thank you so all I want you to do is just turn that thing and run the bulb okay so what's what's your observation then about trying to run the two different bulbs by this method okay okay so this is this bulb and they're they giving you no similar output actually this probably is giving out more light this one's LED this one's incandescent and the end caddesi one's harder to run according to you yes all right yeah give her a round of applause that's all we needed thank you very much okay so this is it I wanted a Sudha to try that because it was surprising to me how different it was okay how much harder it was to run that incandescent bulb so if you have incandescent bulbs in your apartment or home or whatever and you flip on a light switch think how hard those little squirrels are working for you okay whereas if you would just convert to LEDs they could take a break once in a while okay so poor little squirrels convert to LEDs so what's going on here is that we've talked about this before that incandescent bulbs are not very energy efficient as far as producing light so these these these incandescent bulbs invented by dear old Edison they just work by getting hot that's all they do you you're dumping energy into heat the filament heats up enough to where it glows right we've talked about this before that everything that has a temperature glows all right we're all glowing in the infrared you can't see it unless you put on IR goggles all right but things that get hotter glow brighter and glow it at higher frequencies this bulb gets so hot that it starts to glow in the visible but that's its main mechanism it's just getting hot so this dumps tons of energy into heat which if all you wanted was a light bulb is not an energy efficient thing to do this guy for the same light output uses 5% of the energy you knew felt it okay so uses about 5% of the energy for the same light output and LEDs are light emitting diodes so that's sometimes call that you'll hear that called solid-state lighting that's my field of physics and my field of physics is is basically about materials we call it condensed matter physics now used to call it solid-state then we decided to modernize and call it cañon s'matter and now nobody knows what it means anymore but it basically means stuff you can touch it means materials okay so this is my field of physics producing cool things like that alright so we can convert electrical energy to mechanical we can do it the other way around we can convert mechanical to electrical it's all basically based on this principle of you need to have some wires that are in a magnetic field you're either going to supply the current okay and then the the loop of wire will turn on its own right and that's a motor or you're going to supply the turning and then you'll cause currents to run in the wire right and that's a generator so let's think in this case what what that looks like so here we've got our loop of wire the axle is coming out of the board at the top here I've got current coming towards you it goes back down again and then into the board at the bottom and then back up and in all these graphs the magnetic field is up let's think about the forces here so you already solved this case you said okay in this case the forces are such that the axe is going to turn that direction let me have it in a slightly different configuration I've still got the current coming out on the top so currents coming out towards you on the top and you do the same right-hand rule the current comes out towards you cross into the magnetic field going up gives you a force to the right so this one tends to turn that direction way over here in case this is later in time it's rotated and way over here it's still got the forces in the same direction basically right so currents coming out magnetic field goes up forces to the right now one of these configurations though is a little bit more stable than than the other and we'll we'll get to that in in just a second okay so you can you can think about how all right this guy's coming around when it gets to this case though forces are pulling it out all right so this guy once it goes horizontal it's really just gonna tend to stick right where it is all right unless I can reverse the current so here all right let me show you again and going from this slide see how currents coming out towards you all right the next slide I've reversed the current okay so reversing the current reverse the forces so now think about this original configuration currents coming towards you this this tends to rotate too over to here alright and now in this case now when you get to this instant in time if this went back down it would tend to just just come back to a stable equilibrium but if when this gets down to the bottom I can reverse the current I'll kick it the other direction okay alright and that has to do with the idea of stable and unstable equilibrium so here think of this configuration and think of this configuration both of these configurations have a net force in a net torque on that on the on the loop of wire that's zero so in this case electric fields go I'm sorry magnetic fields pointing up here currents coming out of the board towards you on this side okay I cross B gives me a force that direction over here the forces in the other direction so it's pulling the wires in opposite directions there's no net motion in this case and this is stable okay so if I were to tilt this thing just a little bit it would tend to come right back to where it was this guy on the other hand is also in equilibrium in the sense of there's no net force on it but it's what's called an unstable equilibrium because in this case the currents going the opposite direction and if I tilt this guy just a little bit out of the plane then that force and this force are such that it's going to rotate the guy okay so in this case it's unstable in the other case it's stable this is very similar to thinking about a ball on hilly terrain so think about a mountain followed by a valley and mountain followed by a valley and so forth and let me put a ball in that landscape where does the ball tend to want to be the top of mountain at the bottom of a valley where's your where's your ball gonna end up roll somewhere and it lands somewhere and it stops yeah I tend to end up at the bottom of Valley okay so at the bottom of the valley it's in equilibrium all right it doesn't have a force on it one way or the other it'll come to rest there it's also an equilibrium at the top of a mountain right there's no force one way or the other if I just place it exactly right at the top of the mountain okay it's balanced but on the other hand it's an unstable equilibrium so if somebody comes by and sneezes or stomps their feet or there's a little thermal fluctuation of an atom kicks it one way or the other the ball will roll off all right so unstable equilibrium yes it has no net force but if there's any slight fluctuation the thing turns here stable equilibrium if there's any slight fluctuation it just comes back to rest so think in terms of energy for a second so remember this hilly landscape that the ball was rolling in okay which one of those is the higher potential energy configuration with a ball at the top of the mountain or the ball at the bottom of the valley which one has higher potential energy okay the top guy right has high potential energy and then if I let the ball go it tends to roll down the mountain decreasing its potential energy and it comes to rest at a stable equilibrium so when we see a stable equilibrium we should think of that as lower potential energy just like that ball in the hilly landscape or if I see an unstable equilibrium I should think of that as high potential energy okay so this guy has high potential energy this guy has low potential energy a slight deviation here it's not going to return right so something happens to knock this a little bit off-center and now the forces are such that it's just going to flip alright but in this case a slight deviation well the forces were already out and so a slight deviation the forces stay out and write it again back to where it had started from okay do you have any questions about that so far okay all right so if we think of of a kind of situation here if I could get this guy so let's say that I have this guy going in both cases the magnetic fields pointing up okay so let's say I have this loop of wire and it's spinning such that it's going to get to this position all right and then if I could if I had a little bit of kinetic energy to this thing so that it passed that point so let it have just a little bit of kinetic energy so that it passes that point okay and then if I suddenly switch the current if I could just go BAM flip a switch current flips direction all of a sudden it's gonna flip over right and then it'll try to get to its other stable equilibrium but if it's moving fast enough it'll pass that equilibrium and if I could at that instant reverse the current it would be another kick and then it comes back to here and then if it as its passing that point if I could switch the courage it would get another kick so Motors motors rely on this principle okay so basically you run the current one direction and you get a torque going one way and then as the system passes through that equilibrium point right basically you you switch the current to us the turn would have been a stable equilibrium into an unstable equilibrium okay so here just as that thing goes passing the midwife's we're going to reverse the current such that it get to kicked and then when it's passing its midpoint again we're gonna reverse the current to a kitchen kick so similar idea would be thinking of this ball and the hill in the landscape okay I get the ball up on top of the hill I let it roll down the hill and just as it hits the bottom at the right time when it's hitting the bottom and ain't going to have a little kinetic energy to to go past the equilibrium I'm gonna flip the world upside down convert mountains in the valleys and so forth put that guy back up at the top of an unstable equilibrium let it fall down and then just as it gets past it again and then I flip the roll upside down and so forth and I'll be able to get that ball to keep going same light gets here energetically we're going to keep flipping the cart so basically all motors are set up wait so as to as Lee currently gets to that's to that spot that is going to be a stable equilibrium you automatically set things up with the current reverses direction here's any way to do that you can think of a lot of configurations but here's anyway so here in this case I have the battery coming up and there's a reading here that splits okay and then screen the split ring is connected to the axle so that as the ring rotates at this rotates a little bit more this tape here is going to hit the other sign of what's called the commutator so the other side of the split ring which will cause current to go in the opposite direction so you just set things up so that ad you thing rotates you put the current and you put the current and it's looking current and that's what's happening here you can't see it from your point of view but there it's um there's brushes out here okay that's these brushes and then there's a split ring in the middle okay so that as the pass of a particular point it changes which side is making find that good system automatically so it's always getting a kick and always getting a kick and well alright so here is switching current source current source which strips which shirt and it's just set up automatically with the geometry done sighs okay so the basic principle for how motors work Joey questions about okay all right so one of the ways that we can think about that idea we can make in terms of potential energy as we sat right there is there's hills and their valleys and so forth and at the top of the hill I want to think of something that's having high potential energy and at the bottom of the hello and I think of it as having low potential energy so the way to think about this in terms of potential energy is here this is the potential energy equation that we can use to describe that okay a current carrying wire has a particular orientation that wants to be in the magnetic does encapsulate in this equation right here in the potential energy so think about for example we have this current carrying loop that were in the magnetic field and they had a particular stable equilibrium if I have a current carrying loop there's something called a magnetic moment associated with that right that a current carrying loop it generates a magnetic field says currents going this direction this is generating magnetic field that comes up and back and around and it looks very much like a match right the current carries water is an electromagnet it generates a magnetic field so it's acting like a magnet old magnets have something called a magnetic moment which gives you a sense of how strong that dipole moment is it's being produced so I can describe any ring of current by its dipole moment okay and what we saw before is that these if I think if I think it is in this case all right that it's like if I think of that dipole moment there's a particular orientation that that dipole moment wants to have with respect to the field okay so this is a current-carrying wire then magnetic fields coming out towards you I would align my thumb with the magnetic field in the middle to tell you the direction of the magnetic moment okay and it sucks that the direction of that magnetic moment then is such that I you tend to either want to align the motivic moment or flip over the magnetic moment depending on the orientation of the magnetic field so here we cap like that in the potential energy equation here the potential energy of a current carrying loop in a bag that I feel is mu not beat okay so that in fact you can see you can see from that that you tend to to lower this energy I'm going to want those guys to line so if I get the situation where the magnetic moment has the lines and I get a field that's the lower energy configuration okay so this is just to kind of help you see the connection here that there are forces between so here I have a drought of a current carrying wire and I'm thinking about the portions of the current wire has with respect to the the magnet here so there's a magnet tears North and South Pole and it's going to interrupt with this coil of wire which is carrying current as though they were both magnets right and so we can think that in terms of the forces and that sports on this current carrying wire if I think of reaching in and grabbing the front trim wire and trying to pull the coil to the right the magnet tends to pull the coil to the left and I'm going to feel that difference so here's a way to to see all that if I have a start carrying direction going going this direction then the net magnetic field that the wire is producing okay you can use the right hand will for that to follow the current and that will tell you the the direction of the magnetic field inside the magnetic moment coming out in the center here the magnetic moment have a circular to the wire and is the current tons of cross-sectional area that could be the strength of it okay and the magnetic moment points in the direction of the magnetic field produced by the wire and then there's a particular energy associated with how this magnetic moment is dotted in tonight all right and though not before that before that this should be a dot product because there were configurations here where this car tickets wannabes concurring turn lieutenant wanted to be perpendicular to magnetic field okay so it had its lowest energy configuration with a magnetic moment of the current red wire in the lines of the magnetic field or if you flip it upside down so those magnetic moment was an two lines without you would feel that there's a high energy situation what's the dot product then okay can I finish equation and think about why this makes sense and the current carrying wire is in a plane that's parallel to the magnetic field okay so keep that magnetic field pointing up magnetic motors this way what's the dot product between two vectors that are considered riding on zero right much pain so you saw that you saw it before okay and that with these guys gets to be sideways in this configuration they're at a place where the energy is actually gone to zero in that case so it'll be one case that's lower anyone cases high energy in the middle goes back to the touring so they credited something point to a stop here

Channel: Prof. Carlson

Views: 1,733

Rating: 5 out of 5

Keywords: iMovie, Physics, Electricity, Magnetism, Motor, Generator, Relativity, Einstein

Id: 82TYIjuSi-U

Length: 45min 20sec (2720 seconds)

Published: Thu Nov 10 2016