Lecture 14 What Pushes Electrons Around a Circuit?

welcome back to physics 272 last time last time was a long time ago wasn't it we've had October break and we didn't meet last week during this class so let me remind you what happened two weeks ago in this class we looked at the magnetic field of a straight wire okay and we saw that for the magnetic field of a straight wire if we have current going in one particular direction then we have a right hand rule where we can put a thumb right thumb always use your right thumb to point along the direction of conventional current and then my fingers curl in the direction of the magnetic field which means that the magnetic field makes concentric circles around the wire and then we also saw that if we had a current loop so now let me have current running a particular direction in this wire same thing I could put my thumb along the direction of the wire the magnetic field curls along the direction of my finger okay and then I curl it in a loop and now what happens okay so if current is going this direction clockwise to you then I put my thumb here and magnetic field is always going through the middle of the ring so this is actually how you make an electromagnet you make a loop of wire or actually make several loops of wire to get a nice strong current and then you get a very strong magnetic field coming through and the shape of that magnetic field looks just like a permanent magnet so that's um that's the magnetic field of a current loop and we talked about magnetic dipole moments and also electron spin we'll talk a little bit more about electron spin again so today we'll get into bar magnets and a little bit of physics about how bar magnets work right so we'll get into bar magnets and how bar magnets work and what it is inside of them that's causing those little magnets it turns out that inside of a bar magnet it's like having little electromagnets little nano scale electromagnets are inside there we'll talk about what does equilibrium mean so what's equilibrium versus steady state in a circuit and we'll try to think about what in the world is being used up in a circuit something must be being used up because to make this circuit work I'm very familiar with this you have to put batteries in these things I have small children we have lots of toys with batteries we spend a lot of money per month on batteries or recharging them or whatever so something must get used up because I keep having to buy batteries at the store to make these cute little electronic toys go so something's used up we'll figure out what it is we'll look at Kirchhoff's current node law which is a really long way to say something that's actually very simple so we'll talk about that and we'll look at the electric field inside of a wire but first let's get back to the magnets anybody ever played with magnets yes everyone needs their own set of magnets I never go anywhere without mine I love my magnets my boys ages eight and five also likes to play with magnets so we have that in common so I have a bunch of little bar magnets here and of course they stack up together nicely I'm gonna get the little these guys out of the way who's gonna make a mess alright so a bunch a little bar magnets here the magnetic balls are not part of the demonstration but anyway of course as you know from playing with magnets there's a particular direction that these guys like to go right if I get the direction wrong they don't win up right they don't want to go together right so there's something going on inside these guys that makes them all line up and actually inside of a permanent magnet itself if I look inside it what it is that's causing the magnet it's actually thanks it's actually little electromagnets inside okay so we said that if I take a current loop of wire it makes a little magnet right this is what's going on inside of a real material so when you have a material that's magnetic the electrons inside are making little current loops and as they make the little current loops they make a little nano scale magnet associated with that that's one source of the magnetism inside the material there's another source which is that the electron itself and this is weird quantum mechanic stuff the electron itself seems to be a little electromagnet to itself okay so the the the it's as though it's as though the electron were a ball of charge spinning fight a big spinning ball of charge that's also like a little current loop and it would make a magnetic field okay the electron as far as we can tell has no size so that's not actually what's going on but it is as though the electron is doing that because it's creating its own little magnetic field we call that the electron spin because it looks a little bit like the electron is spinning on its axis so those two sources of magnetism at the atomic scale that happened in real materials what is each electron has its own little spin associated with it the other is that as the electron goes around its atom it makes a current loop and a current loop makes a magnetic moment so the trick is not getting magnetism in the material the trick is to get them to all line up okay in most materials these little magnetic moments are pointing in all sorts of different ways so kind of like if I took my my toy magnets here and just had them kind of crumpled up in points all in different directions you can't quite see that very well but read them crumpled up and points all in different directions the the the sum total of these guys is not producing a very large magnetic field because they're all pointing in different directions so most materials are kind of like this they're all pointing in different directions but when you have a permanent magnet then the atomic-scale magnets actually all line up okay kind of like this and then they line up and reinforce each other and that gives you a net permanent magnet in fact what I think is pretty cool about this is there's an actual phase transition associated with this lining up okay so phase doesn't matter just tell me some phases of matter what do you know what's a phase of matter solid gas I heard liquid anything else plasma okay all right and we don't really make a sharp distinction between gas and plasma but yeah I guess it gets listed anybody have an LCD display somewhere yes you have a knight anybody have an iPhone something like that okay you have an LCD display LC stands for liquid crystal it's something that's liquid in one direction crystal in another there's tons of phases of matter beyond solid liquid gas it turns out that this net lining up of magnetic moments counts as another phase of matter so let me tell you why okay if I take this magnetic material but take take a permanent magnet and let's put it in a really hot oven hotter than your kitchen oven okay so put it in a kiln and if you raise the temperature on your little Ferro magnet at some point you raise the temperature enough the single melt okay and you would recognize that as a phase transition you would look at it and say oh my magnet turned into a puddle it melted from solid into liquid okay but at a much lower temperature than that around 1500 Fahrenheit when I raise the temperature on this magnet all of a sudden BAM the magnetism is gone even though you would look at it by eye and say oh it doesn't look like anything happened looks like it's it's still intact it's still a solid but there's a well-defined temperature which BAM the magnetism goes away and if you cool the material again BAM the magnetism comes back and what's going on in those materials is that at low temperature all the little atomic scale magnets line up BAM they all line up that gives you the net magnetism and then as you raise the temperature on this thing think of my fingers as the little magnetic moments that are inside the solid as you raise temperature what happens to solid does you raise the temperature on them those vibrations there's wiggling they get excited right so everything just kind of jiggles okay according to temperature so so you know we look at these solids and they look like they're not moving to us they're they're moving there's lots of jiggling and wiggling going on inside and if you're if you're thinking about these magnetic moments on the atoms the atoms are jiggling and wiggling due to temperature and the magnetic moments kind of start wiggling around - and there's a well-defined temperature which BAM there's just no order to it anymore they're all pointing in all different directions and wiggling and wiggling and there's no net magnetism then if you lower the temperature again BAM they all come back and line up again so that's an actual phase transition because there's a real temperature which it happens there's a sharp temperature it's called the Curie temperature and it's a phase transition though not of the atoms in the solid it's a phase transition that the electrons go through so the electrons inside the solid go through a real actual phase transition at that magnetic temperature that's my field of physics by the way I study phases of matter and phase transitions but of electrons what electrons do inside materials so again in most materials they're not winding up in ferromagnets at low enough temperature okay below their Curie temperature which is typically a high number like 1500 Fahrenheit they all line up and make magnetic material now there's something you should know though if you go looking for a ferromagnetic it's a permanent magnet is sometimes called a Ferro magnet so you looking for that kind of material out in the wild anybody here geologists go hunting for rocks or did it as a hobby okay something like that all right so if you're a geologist and you're out capturing rocks in the wild wild rocks and you found a hunk of what should have been a permanent magnet probably when you pick it up it's not got a net magnetization to it probably it's much more like this picture where inside the rock there's little pieces that are pointing all together and little pieces that are pointing all together but in a different direction okay there's actually a good physics reason for that which is that if you've ever played at length with one of these little magnets toys all right you can try it out yourself if you start trying to stack these guys up and make long lengths out of them okay so if I try to stack them up next to each other like this all right what you'll find is that there are certain stable configurations okay and then if I go flipping the North South Poles that'll change the stability of it okay and if you start trying to add them up together then what you find okay let me at least get three of these together all right so you see how these are all aligned let me take the three and compare to the three okay North is up okay if I put these guys next to each other like this they actually don't quite like each other can you guys kind of see that in the front row they don't really quite like each other if I just pull it off and align it like this they actually more prefer that way okay so that this guy on the left has north/south this way and this guy has North pointing down did you did you see what happened there okay they didn't like this but they liked that so so as a ferromagnetic material cooling it actually tends to form domains for that reason and if you've played at length with these little magnetic toys you know that so then you have this question of well how do you get how does somebody sell me a permanent magnet then okay even if kind of on small scales the little magnetic moments tend to line up but then they tend to flip their neighbors how how is it that somebody sells me a permanent magnet the way they make those is they take them up to a very high temperature high enough that all the magnetic moments are pointing all over the place due to temperature and then they apply a large magnetic field and that large magnetic field kind of aligns on the magnetic moments and now you cool it down below the phase transition temperature the ferromagnetic phase transition temperature if you get it cold enough now you can take off your external field and now everything's stuck pointing on the same direction so permanent magnets have been trained by what's called field cooling you cool them in whoo I'm gonna move that so it doesn't happen again you cool them in a net magnetic field and then they all point in the same direction do you have any questions about that sort of physics okay all right so this is the this is the graph that goes along with what I was talking about that inside of the material right inside of the material if I have everything all pointing in the same direction like this there's actually a little bit of tendency on on long link scales for this guy to want to flip and point so that it's North is facing down and it's because this guy is making a magnetic field that goes this way right its magnetic moment puts a field that way which tends to cause this guy to not want a line but flip over so to really get a true permanent magnet you have to you have to feel cool them all right so now did you have any other questions about magnetism you can ask me after class too clearly I like magnets a lot so we're gonna move on to chapter 19 chapter 19 is about electric circuits and of course there's a lot to learn here we're gonna learn about surface charges on the circuit that actually help drive the current we'll see how that happens and about some transient effects well we need to learn the difference - between what's called steady-state at equilibrium and today we'll talk about the current node rule which is kind of a fancy way of saying that what comes in must come out so here are some things we'd like to consider inside of a circuit that's working all right some of the questions we want to ask on the very small scale when we say microscopic we mean the very small scale we want to ask what's going on inside the circuit are the charges being used up somehow what is it that's going on exactly how does a current carrying wire maintain the electric field that's necessary to keep the electrons flowing and I'll tell you what we mean by that and we want to understand the role of the battery so let me remind you how we talk about currents okay there's something called conventional current in conventional current the direction of conventional current is as though the current were carried by positively charged particles okay that's what conventional current is all about and we pretend that there are positively charged particles that pop off the positive terminal of a battery and run around the circuit and come back and enter it at the negative terminal what's really going on microscopically is that current is carried by electrons and real materials so in fact electrons which are negatively charged they're popping off the negative terminal going through the circuit and popping back in the positive terminal now we also need to think about equilibrium versus steady state in so far we've discussed a lot about equilibrium okay equilibrium is where inside of a current carrying materials well inside of a material that can conduct so inside of a conductor like a metal the electrons have net zero velocity that's what equilibrium means there's no current flowing and if I on average average the velocity of all the electrons that comes to zero current flow is not equilibrium it's called steady state so what we mean by steady state is that there's a particular current in the system but the current isn't changing okay now think inside of a material and think of the electrons inside of a metal the electrons inside of a metal liquid-like and your book refers to it as the electron seed because it really is like a sea of liquid particles and even in this equilibrium condition in equilibrium when there's no current flowing and there's no net average velocity to the electrons but actually still move their liquid okay so actually moving around it's just that there's no net current associated with that it's kind of like a big mosh pit okay they're there they're doing stuff but there's no net movement to the crowd that's equilibrium okay if there's no average movement to everything current flow is not equilibrium it's where that big mosh pit of electrons just kind of moves all on mass together and you can say ah now there's a crowd going by there's an average number of electrons per second going by and if that average number of electrons per second going by is unchanging then we call that steady state where there's an average drift velocity of the electrons which is constant do you have any questions about the difference between equilibrium and steady state okay equilibrium is just no net flow of electrons steady state is where there is a net flow of the electrons current but the current is not changing here we have a clicker pull a clicker poll is where you just get points for pushing a button and we want to ask this question let's say that we have current flowing in this circuit and I want to ask the question how would you expect the amount of current at location one to compare to the current at location two would you expect that there's no current at two since the light bulb used it up would you expect that there's less current at two than one since some of it gets converted to light and heat given off by the ball or would you expect that the current at two is the same as the current at one all right and this is just an opinion poll so we're just it's it's just for fun but what are you thinking about this problem what how should we think about it do we think that there's no current a - there's less current at - the current is the same in both cases what are some of the things we need to consider what are some of the lines of reasoning we need to go through here yes okay all right so if you've already learned kirchoff's current rule then you know that current n is equal to the current out and then that tells you what okay so that's going to give you that the answer see what else do we need to think about if you haven't learned kirchoff's current rule yet how what's it what's a line of reasoning we need to go through to think about this yeah please okay all right so so he's saying if you if you're familiar with the loop rules of how current works then what comes in comes back out again and so what did I get right okay okay and you'd say that there's a voltage drop across this guy but not necessarily a current are there other things we should think about I mean something's being used up right so you're saying there's voltage what is so if we think let's think let's think microscopically let's pretend that you didn't know yet the current the the Kirchhoff's current rules and if we think microscopically about what's going on something's going on here right my lightbulbs lighting up but if we think about this possibility that well okay let's say you didn't know kirchoff's current laws and you said well there's current coming in something's getting used up what if the electrons are getting used up right so if I'm trying to put things through and I'm thinking well maybe this bulb is somehow converting electrons well we can't destroy electrons we're not we're not allowed to do that we can't destroy net charge that is so we can't do that we could think that well if there's more current coming in than going out what's really going on if I think of these guys as like a crowd of electrons coming by in a crowd of electrons coming out and this is like a store with a sale going on or something okay so electrons coming in electrons are going out but if there's a if there's a difference right if more currents coming in and it's coming out that there's a crowd building up in the light bulb right so then there'd be electrons gathering and electrons gathering and electrons gathering and that's not can't be what's happening because um electrons repel each other right and so if I let that go on long enough and if I thought that the bulb was actually just gathering up electrons and gathering up electrons eventually the sucker will explode okay and actually we have a little experiment here hook up this light bulb over here and it's not exploding okay so it's not gathering electrons another thing you could think about as well as you know if it were eating up electrons somehow or gathering them in order to cause this to happen then eventually it would get negatively charged and repel the electrons trying to come in so so as you guys pointed out look what goes in has to come out and so this means that the current at position has to be the same as the current at position one this was a poll anyway so I'm just gonna close it all right the bulb must be using something up though right and we said it's it's not consuming electrons right the bulb is not an electron eater much much much much okay can the bulb you know consume current as electrons accumulate in the bulb no if it were accumulating electrons not only would it get enough electrons eventually to explode but it'll get negatively charged and it'll repel any electrons trying to come in so that's not what's going on so what the bulb is using up is it's converting energy from one form to another alright so the chemical energy stored in the battery gets converted into light energy and heat energy and it's very much like a waterwheel so I like to think in terms of analogies for electric circuits and if we think of the current flowing as being like water flowing through it's like I have a river going by a mill and I'm using the current of the river to do something inside the mill like grind grains something like that but I'm not using up the water right the water comes by turns the wheel and then goes on through right what I'm doing is I'm siphoning off some of the kinetic energy of the river to drive the mill but I'm not in the business of gathering water right so just like this what goes in must come out so current comes in current goes out we're just converting energy from one form to another and actually what's going on inside of of lightbulbs it depends on which kind of bulb you have of course this is one of the old-school incandescent bulbs that actually takes a lot more energy to produce the same amount of light then they are more energy efficient compact fluorescent bulb up here these guys use about 20% of the electricity these guys need to give the same light but I really wanted to be cutting-edge I would have put an LED bulb up here okay because those use about 5% of the electricity that these guys need but let me at least tell you how these incandescent guys work the incandescent bulbs inside of them have a tiny tungsten filament and the tungsten filament has a little spiral in it and in said the spiral is a little spiral so it's a little spiral of a spiral of a spiral okay it's a very thin wire and there's a lot of it packed together and we're driving current through it and what happens is that you can see that some of the energy is getting converted into light okay in this case though a lot of it's actually getting converted into heat these guys incandescent bulbs glow because of their temperature it's just a temperature thing okay and in fact you may not know this but but I'm blowing can you see it okay I have a temperature too and I glow has anybody ever used night-vision goggles I love night-vision goggles cool all right yeah okay and in the first lecture I asked this question in the entire ROTC section raise your hands yeah we use night-vision goggles all the time it's an argument for joining ROTC anyway when you're using night-vision goggles what you're seeing is this glow okay but it's it's um everything glows based on its temperature things that are lower temperature like I'm a lower temperature than the bulb I glow too you just can't see the light coming off me because your eyes can't detect it but if you put on night-vision goggles now you have a way to detect what's called that infrared light that's coming off of of other warm objects so why why does that happen alright let's remember what we think about when we think about electrons going through a solid right so in the analogy we use before it's like these desks in here are like the atomic cores inside of a metal okay so your desk to the atomic course and if I'm an electron trying to move along a solid in the right way all I have to do is look out over you guys have a regular arrangement of desks right and I could not going to do it everybody's get a little nervous up here but I could get up on top of the dust and tick tick tick tick tick tick tick run across the top of the desks that's how electrons move inside of a material they they look out and they see what periodicity they need and then they just run along at the right periodicity and that's how they move through so easily now let's say let's say we're actually gonna I'm gonna make you guys a little more nervous so let's say I'm running this direction do you mind if I pick on you he's like I'm never sitting here again okay what's what's your name phone oh sit again okay whoo God thank you so let's say I'm gonna do this I'm gonna run around along the dust and I'm gonna get the right rhythm like an electron inside of a solid but then part is gonna be play football he's gonna sack me okay BAM because what's going to happen is that he in a real material right even though the electron could sneak through just by getting the right rhythm right I could pick the right rhythm and run that direction I could pick the right rhythm and run that direction and so forth if there's something out of place then I will smack into it and I'll lose all my kinetic energy and I'd smack into parts I'm sorry I pronouncing it incorrectly but parked and I'd give my kinetic energy to him okay and then I'd have to pick up again and start running again so inside of a real material there's temperature and you already told me that temperature causes everything to wiggle so think of all these desks not as being perfectly still but with a particular temperature they wiggle they wiggle they wiggle so if I'm an electron running along what will happen is that I get the right rhythm that's okay as long as the desks all stay perfectly still I'd be fine but every once in a while encounter a desk out of place okay and I run into park and bam I convert I give him my kinetic energy and then I'd have to pick up again and start running so every time the electron smacks into something out of place it loses its kinetic energy gives it to the atoms all right and then it keeps dumping that energy into the atoms and the atoms wiggle more and wiggle more and that and so they have a higher and higher temperature that's why this guy's lighting up it's because electrons as they go through it are whacking into the atoms that are out of place every time they whack in they dump a bunch of energy into it which raises the temperature and this is actually very hot okay it's glowing so much that it's white has anybody used the kind of of I on a stove that's got that little spiral on it when you turn it on it glows red okay all right it's just glowing because it's hot okay we're all glowing cuz we're hot you just can't see it with your eyes you need night-vision goggles a stovetop glows red it's hotter than us this is glowing white because it's putting off red and orange and yellow and green and blue so it's got a lot higher energy than your stovetop and if I had this even being hotter and hotter and hotter to eventually turn blue because it would start glowing and the ultraviolet things that we can't detect which are even higher energy this actually this actually tells you a little bit about the color of stars but anyway so in here the electron energy is getting convert it into light and heat okay so that's where the energy is going but it's a bit again like this waterwheel it's not like the electrons are used up right we go through the circuit they come back alright so they don't go away it's just that their their kinetic energy is getting converted into light and heat now I like this analogy for electric potential and height so let's think for example which I'm just reminding you of analogy that we've already used before which is that voltage or potential is a bit like height and a positive charge moving in that potential landscape is a bit like a ball so a positive charge will move along the potential landscape much like a ball rolling down a hill and in any given spot the ball wants to roll a particular direction downhill that's the direction that the electric field points right there it's whatever direction the ball would actually want to roll on that landscape now we can take that height analogy even further and think about it in terms of circuits so here's what it looks like for circuits I like this water analogy because it gives you gives you kind of a physical intuition for what's going on so on the left hand side I have what's going on in a circuit on the right hand side I have what would happen in water pipes and we've just compared the two alright so the circuit will compare to a bunch of water pipes rumour has it that this picture here which is a bunch of water pipes is Google's cooling system so anyway blue would be the cold water coming in red would be the hot water coming off positive charges like water flowing okay current conventional current is like the water flowing through the pipes all right and then I need something to drive the water flow well in a system of pipes what's typically driving the water flow is just gravity fed okay so I have water just flowing downstream in the pipes so height is like voltage there and if I want to move water back up I need some sort of pump so the pump is like a battery right the battery's like a pump I guess is what I'm really trying to say no let's think about this let's have a tub of water let's have a gravity-fed water system where I have a big tub of water on the roof of the house I'm gonna have two pipes coming out of it I'm gonna have a skinny pipe and a big pipe which one has more water flowing through it when I open all the valves the skinny pipe or the big pipe big pipe has more water running through it okay so in our analogy resistance is a little bit like one over the pipe diameter so if I have a skinny pipe it's harder to flow the water through it that's like a high resistance element in your circuit so something that's high resistance has less current flowing through it in the same way that a skinny pipe would have less water flowing through it electric potential energy is like gravitational potential energy in that analogy which is the same way of saying voltage is like height there's a current node rule in electrical circuits just like there's a rule in water pipes right if I have water pipes and I think about let's say this Junction here look at these blue pipes have a big pipe up top and then I have two other pipes coming off of it just like water in pipes what water comes in must come out right so when I see a junction like this I know a certain amount of water comes in and it all has to come back out on the other side so that's is the same as the current node rule the voltage loop rule would be that in any circuit as I go around a closed loop in the circuit and come back I must come back to the same voltage in the same way if I trace these water pipes out and I start off up here and I don't see any closed loops on the diagram but if I imagine the the pipe going underground and coming back up here to the blue part when I go around a closed loop in the pipes I come back to the same height right I have to so come back to the same height it's like coming back to the same voltage in the circuit and a high resistance element in your circuit is like a skinny pipe a low resistance element is like a fat pipe so I like this analogy a lot it gives you intuition about how to think about how electrons flow through a circuit one of the reasons this works so well is that the electrons inside of a metal are liquid they're liquid like so they really do flow around much like water flowing through pipes have any questions about the analogy so far okay all right so if we think in terms of that analogy then kirchoff's current law or the current node rule simply becomes what goes in must come out okay so I know it is any junction in your circuit where two or more wires come together so here I have one wire coming in to what I've called a node and one wire coming out it's a very simple Junction and if I put four amps in right let's put four amps in here what do you think is going to come out on the other side if what goes in must come out look what's on the other side yeah four amps for amps on the other side okay what goes in must come out just like water flowing through pipes let's make it a little bit more complicated okay so now I have a circuit where currents gonna come in here there's a node now with three pieces coming out okay and I'll have four EPS coming in just like before but now we have three pieces coming out let's say up top I measure and I find well there's one amp coming out here two amps coming out here what's gonna come out of the other spot yeah there's one amp left so what goes in must come out and what goes in must come out just like water flowing through tributaries in in a river system so that's it that's Kirchhoff's current law or sometimes it's called the current node rule which is a bunch of words for just saying what goes in must come out it really is just that simple okay and your job on the homeworks is just to put math to that idea do you have any questions about the concept okay current comes in current must come out got it all right does does no questions mean we're good good go on okay all right see in thumbs up good now in the inside the material itself there must be something that's driving the current right because if I go back to to scaring people up here if I go back to thinking about well what is it like to be an electron inside of a material right this is what it's like to be an electron inside of a material I'm the electron you guys are the atoms and I look out and I see this regular arrangement okay going to try to run a particular direction by getting the rhythm right and running that direction but I'm gonna have all these collisions because in the real world the atoms have a particular temperature they're moving about and as they're moving about and wiggling I'll be expecting to run at a particular rhythm but one of the desks will wiggle out of the way and bam I'll fall and when I fall I'm gonna give all that kinetic energy to the atoms and so that's this chicka chicka chicka grasp up there that's what that showing is that as the electron runs along okay it's running along it run along bam whacks into something it loses all its kinetic energy and gives it to the lattice and bam it has no speed again then it's got to pick up again and it starts running again the reason it keeps going and keeps picking itself up poor little electron picks itself up dust itself off it starts running again is because there's an electric field kicking it along kick kick kick kick kick so there must be an electric field applied if I take the electric field off all the electrons will run into something and just stop really quickly you know in about ten to the minus twelve seconds all the current will go away I've got to keep pushing and push push push push push otherwise they just fall down and don't get back up again so there has to be an electric field applied constantly continuously to keep this current going and under that constant electric field condition then this is what the the average speed of electrons will look like it'll go up linearly with time right because there's a constant force applied to the electrons who'll accelerate accelerate accelerate BAM run into something accelerate accelerate accelerate BAM run into something so I need something to keep getting those guys to move through the wire okay so here's what's going on inside the wire we've already figured out that what goes in must come out so inside of a wire there's there's current in the steady state situation whatever the current is here is the current here is the current there alright and if I put equations to this so let's put equations to this idea the current in the wire is like Q and a V let me remind you what all those symbols mean Q is the magnitude of the charge on each charged particle that's carrying the current so little n is number of particles per unit volume it's just the density of carriers in their a is the cross-sectional area of the wire notice that like we said with the with the fat pipes and the skinny pipes of fat wire carries more current just like you would expect and then there's this V average velocity of the electrons we derived that equation a few lectures ago the average velocity of the electrons is something called the mobility times the electric field applied and this mobility is just a number associated with the material you look it up or if you're really good you can calculate it but you can look it up what what it is for a particular material so if you have copper you would look up the mobility of copper and then you could tell me okay if I apply a particular electric field you multiply this no numbered velum ability of copper then you can tell me the average drift velocity of the electrons so feeding this into this equation I get that the total current is Q times the density of electrons times the cross-sectional area times mobility times the applied field okay and all of that was just to show you the equations that go along with what we said intuitively which is that if I have a constant current in a material I have to have an electric field driving it okay so many questions so far yeah oh you want to know where the time is in here the time in here is hiding in the velocity the velocity has velocity as meters from yeah I love it this is exactly how you should be thinking is where are all the units so the unit's here there's charge the velocity has the per second to it the area and the velocity have three powers of length in them right area is meters squared velocity has a meters in it this density here is per volume which has three powers of meters in it so the meters all cancel and this becomes charge per second excellent question that's exactly how how we want you to be thinking about these things so altogether when I put the equation together I see that the current is directly proportional to the applied electric field what that means oh I left my circuit on draining the batteries what that means is that in order for this light bulb to be glowing here can you guys see that okay in the back I apologize it's kind of dim can anyone in the back see the light bulb going all right so what what that means is that all right there's current flowing through this circuit okay and if I if I think about well what's what's going on all right let me think in terms of electron current I find that more physical microscopic way so I've got current coming in and current coming out and what that means is that there's a current here it's the same current here it's the same current here it's the same current here doesn't even matter if I bend the wires right it's the same current no matter what I do and yet microscopically inside the material we know based on what it's like to be an electron inside of a material we know there must be some electric field pushing this guy along okay so how is that happening right I mean you know I have to think about what's the source how in the world is this wire have inside of it an electric field pointing this direction all right what's going on there what are the sources of electric field I might have like it think about the battery right the battery has a positive terminal and a negative terminal so the battery itself is like a dipole the battery is putting on a dipole electric field all right but this bulb is not the the electrons over here are not directly responding to that dipole field right you can tell that by just if I try to put the bulb closer to the battery as long as I hold all the connections steady then it's not it's not driven by that electric field directly okay something is local is going on there's a local electric field right here that's driving that current and there's an ax local electric field inside that's driving that current as well so we want to think about us how right so what's the source of electric field what I mean what what generally speaking what do we know in this class if I see an electric field it's caused by what what there's charges somewhere right there must be charges somewhere so we've just figured out that for this guy to really work there must be some point charges all along the wire that are causing this to happen so the next thing we have to figure out is well what's what's the configuration that would cause this kind of picture there's constant current there must be some sort of electric field that's always pointing along the wire and yet has the same magnitude throughout the wire okay and then the thing we have to figure out is well okay that must mean that there are charges along here that are driving that but the electric field points in the same direction and it actually it turns out it's the same throughout the cross section of the wire we want to find this out where are the charges there must be some charge there in order to drive in order to cause this electric field and here's what's going on okay if I look microscopically so this is a chunk of wire all right and if I look microscopically at what's going on in this circuit here red is positive coming off the positive terminal terminals of the battery black is going back into the negative terminals so let's think from the negatively charged side because electrons are a little easier to think about microscopically so from the negative side of the battery there's negative charges there okay some of those negative charges leak out onto the surface of the conductor if I'm not going to do this right now but you know what happens if I cut a wire and look inside right this insulation on the outside and then there's a copper core so basically from the the negative terminal of the battery there's electrons leaking out and they all go on the surface of a copper wire and they distribute themselves such a way so as to maintain a constant electric field along this wire so there's there's negative charge here but there's a little bit less charge here there's a little less charge here and then they move farther and farther from the battery there's a little bit less charge and a little bit less charge okay all the way until I get to here I happened to put this you can't quite see it cuz they're tangled but it's the same length of wire on both of these guys all right so if I think from the positive terminal side the positive terminal side has positive charges there's a little bit of net positive charge as I move out along the wire away from the battery there's a little bit of net positive charge on the surface of the wire okay it's because some of the electrons have moved away and expose the atoms but I have this net positive charge and there's less as I move away from the battery there's less and less and less okay but what's what's going on is this picture all along the wire there's a little bit of surface charge on the outside of the copper and so here for example I have a little bit of net negative charge and I have a little bit more net negative charge over here okay that makes a net electric field inside the wire that's pointing in the directions so as to push the current along okay so it's all driven actually by by surface charges on the wire do you have any questions about that idea that's the that's the the basic idea there okay and so what party yeah okay so let's think about think about what would happen if I have on a tube here this is the wire alright if I have some surface charges on the outside of it here put some electrons in on the outside here put some more electrons on the outside here there's a net electric field pointing to the right it's probably easier if we think pretend these are positive charges okay so it's positive charges it becomes pretty clear so there would be a net electric field inside the wire driven by those rings of charge so what we want to think about is all along the wire on the surface of it there's a ring of charge here and there's a ring a church here and there's a ring of charge here and that char the difference in charge from ring the ring is what tells you what direction the electric field points in anywhere in in and then the ring of charge stays on the wire right so as I bend the wire it's no it's no big deal it's just I'm looking at the change in the surface ring charge from here to here that gives me a net electric field and it's obviously on the on the wire it's smooth right it's just there's just a smooth distribution of charge it's just that towards the positive end of the battery the surface charges are positive and then there's less density of positive charge as I move away from the battery okay and then as I come out from the negative side there's a surface charge there's a surface negative charge near the battery and as I move away from the battery there's less density of surface negative charge as I come away but all those surface charges are the thing that locally caused there to be an electric field inside the wire driving the current did that kind of help okay do you have any other other questions about what that is that's going on okay you even without talking microscopically though right that was the that was the microscopic idea for all this stuff but even without talking microscopically we know that if the currents constant inside the wire there must be a electric field that always points parallel to the wire inside of it and is always the same magnitude everywhere okay so that's that's the thing that you know for sure it's that it turns out that it's these surface charges on the wire that locally are setting up that electric field I mean how does the wire know to get well how does it have an electric field right there its surface charges on the wire that are causing that electric field okay do you have any more questions about that so here for example this is a battery okay with a circuit around it and this is a diagram of what I was talking about there's surface charges here less surface charge here less surface charge and so on that's what's setting up the electric field okay all right we're done for today I'll see you on Wednesday the hwachun why does that happen all right let's remember think about electrons going through it's all right so the analogy was used before it's like these deficits care are like the atomic cores inside of the metal okay so you're just to the exotic course and if I'm the electron trying to move along a solid in the right way all they have to do is look out over that's a regular arrangement of desks right and I could not gonna do it person will nervous up here but I could get up on top of the desk and tick tick tick tick run across the top of the net that's how electrons move inside of a material they look out and they see what periodicity they need and then run one at the right periodicity and that's when they move immediately now let's say let's say we're actually gonna make so what's that brother this direction to be 150 I'm never sitting here again thank you so let's say I'm gonna do this I'm gonna run around along the nest and I'm going to get the right rhythm like an electron inside the solid but then part is gonna say well he's exactly because what's gonna happen is that yes in a real material right even though the electrons would sneak through just by getting the right rhythm right it picked it right rather than run that direction they can pick the right rhythm and run that direction and so forth and I'd smack into hard I'm sorry jump in for the clock and I give my kinetic energy to him okay and then I have to pick up again running again so inside of a little material there it's temperature and you already told me that summers are causes everything's widdle so think of all these deaths not as being perfectly still but with a particular temperature that wiggle II wiggle II wiggle so on the left are running along what will happen is that I get the right rhythm that's okay as long as the deaths all stay perfectly still I'd be fine but every once in a while encounter a desk out of place I run in the park and bam I can I give him my kinetic energy and that I have to think up again and start funny so every time the electron snacks into something out of place it moves as a tunic energy gives it to the atoms all right and then it keeps filtering that energy into the atoms the atoms little bored with the war in it and so they have a higher temperature that's why the Stars lighting up it's because electrons as they go through it or whacking it in the atoms are out of place every time they walk in they double ones of energy into it which raises the temperature and this is actually very hot okay it is blowing so much the difference right can I go back to the staring people up there now go back to thinking about what kids that like to be an electron inside of a material right this is what it's like to be a lot kind of type of material I'm the electron you guys with the atoms and I look up and see this regular arrangement okay I'm going to try to run a particular direction by getting the rhythm and running that practice but I'm gonna hop will be pleased because the real world atoms have a particular temperature they're moving about and as they're moving about and wiggling I'll be expecting in front of a particular rhythm but wasn't that's will move out of the way and family Paul and when I call I'm going to give on kinetic energy to the atoms that wrap up there the lawn

Channel: Prof. Carlson

Views: 3,970

Rating: 5 out of 5

Keywords: iMovie, Physics, Electricity and Magnetism, Matter and Interactions, Electric and Magnetic Interactions, Electric Field, Circuit, Phys272, Purdue

Id: XNytX9ZYkJ0

Length: 49min 10sec (2950 seconds)

Published: Fri Oct 07 2016