 Alright guys, let's go ahead and get started here, because I have a little demo I'm going to do today. So today the theme of the class is going to be setting up and solving problems that involve capacitors. And of course you have Homework 3 do right now. So Nush and I have discussed how we're going to manage grading this because she works all day Thursdays and can't come to campus. So what we're going to do is I'm going to make digital copies of the problem that she wants to grade on Homework 3. And then I will put the homework solutions you guys have handed in back in a folder in the physics main office. And I'll send an email where you can pick them up and you can pick them up at your leisure. So it'll be on the very front desk and you walk into the main office which is room 102. Okay, so just at the end of the hall here on the right. There will be a desk to your left. There may be a student worker there. It's staffed usually by a student worker. It will be like a tray labeled Sakura Physics 1308, something like that. And there will be a folder in it. You guys can just go in there and take your stuff. I got so backed up this morning I couldn't record your scores on the previous quizzes or the score from Homework 2. So there's going to be a big pile of stuff including Homework 3 that's going to be in there for you. So look alphabetically by last name through and make sure you've got all the things in your section of the alphabet. Okay? All right, so any questions on that procedure? So again, that's how we're going to get things back to you as quickly as possible. Any? Sorry, I was a bit worried about it. Can I find it? It'll be in an email but physics main office is where it's going to happen. So don't go there yet. There's nothing there yet. But I will announce it to the class when everything's ready to pick up. So I'm going to spend my afternoon getting all the grades reported and then getting all that stuff digitized for NUSH. And then once that's all done it will all go in the main office. So I'm hoping before I have to leave it for today everything will be in the main office for you guys to pick it up. So, all right, so there we go. All right, so a few concepts to keep in mind. Electric charges exert forces on one another via the electric field. That field is always present as long as there's a charge somewhere in the universe. Whether or not a charge is there to be acted upon. Okay, so all you need is one charge and then you get an electric field. There don't have to be any other charges for the field to exist. That electric field just like gravity is a conservative force field but you have to think a little carefully about what the potential energy looks like for different kinds of charges moving in different directions because there are two kinds of charge. There's only one kind of mass that we know about in gravity but there are two kinds of charge you have to deal with when it comes to the electric force. The field comes along with an associated energy per unit charge. This is known as its electric potential and in fact this is really the more fundamental object in nature. So far as we know every force that we've ever discovered can be described very successfully with this concept of a potential. So an energy per unit something. By understanding how charges move in an electric potential we can understand how energy is stored in the field. So again boiling it down to that fundamental concept of energy. Alright so you do have an assignment for next class. All that will happen in next class is that you'll have a quiz on this assignment at the beginning. So you need to keep reading chapter 25. We're going to finish up capacitors and you're going to watch the rest of that video you started for this class. So you're going to go from about the 42nd minute until the end. It's about 12 or 15 more minutes of video by electrics which we'll touch on a little bit today even ahead of having actually had to watch the video. And then there's an additional piece here you should go and watch as well. Homework 4 will be due Thursday October 1st. So it's assigned today, should already be in Wiley Plus and then there's a paper copy, a digital paper copy on the class assignments page. There is a problem that I've written tacked on to the end. That problem was actually inspired by a question from a student in honors physics. So you get to reap the benefits of their curiosity. How's that sound? They were curious what it would take to capture the energy of lightning and store it. So you're going to do that by exploring the concept of a supercapacitor. That is due in two weeks from today. So your primary focus for next week should be preparing for exam 1 which will cover the materials covered on homeworks 1, 2 and 3. That exam will be in class. It will be 80 minutes of allotted time. My goal will be to write an exam that an average student in the class, whatever that means, can finish in about an hour. And that leaves about 20 minutes or so to kind of go back, think about things that weren't clear, maybe you only got partly through a problem and you want to go back and touch it up a little bit. So that will be my goal in writing the exam. It will be a mix of multiple choice questions at the beginning which will be some fraction of the grade and those will test on concepts in the same style as the quizzes and class. And then there will be, you know, two, maybe three, depends on the length of each problem, with two, maybe three problems that you have to solve after that. And we're going to practice this in class on Tuesday with an in class kind of dry run of a part of an exam. Okay? Alright, so as I said, we will have a quiz on Tuesday morning on this stuff. So don't skip this unless you just don't care about the quiz. You know, I drop lowest quiz grades anyway. So if you really don't care about it, that's your business. And I'm not going to tell you what to do, okay? I'm just warning you, there's a quiz at the beginning of class on Tuesday. Alright, so any questions on this stuff? Okay, Shannon, then Sophie, then Israel. Yeah. homework three? I don't remember the exact one. Yeah, but you should be able to go look at the class materials page and kind of figure out what sections were covered on that. So it will cover basically up to the beginning of sort of electric potential energy and electric potential difference. But to find the crystal boundary, you know, take a look at the chapters that were associated with that homework stuff, okay? There we go. Alright, so, moving on. Oh, sorry, Sophie. So we don't care. Sorry. I'm really tired of that. We know we're being quizzed over Tuesday or on Tuesday over the capacitor stuff. It's not going to be on the test solvers. That's right. Okay, so, treat it as you see fit. Okay, Israel runs out. Yeah. So for the following exam covers homework sections, one, two, and three, right? And also see the quizzes that went with that. Quizzes as well. Yeah. Once reviewing for all of those, do you have, like, maybe an extra, like, maybe, like, you could pick out certain questions that might be similar or irrelevant to the exam? Well, the ones that I write myself will be obviously very close to the style of what I give you on the exam. And in fact, sneak preview, the bonus question you had on integral calculus for Coulomb's law was taken straight off of a previous exam from, like, last semester. Okay? So, there you go. Like, there's a softball pitched right at you. So, like, the style of thing you might have to do. Okay? Yes? So, so, the formula should be given the day of the exam? Well, so the formula sheet, I'm actually going to beta test on you guys on Tuesday. You're going to give me feedback on Tuesday if there's other stuff you'd like on it. And then that will show up on Thursday. All right. So, you get to beta test the formula sheet on Tuesday. Okay? Yeah. That was my question. Okay. Great. Yeah. Okay, any more? All right. So, Grant? Yeah? Sorry. Okay. Grant, challenge problem. So, thanks to all the teams that have turned in minutes so far, they've been very helpful. It's good to see people are sort of bubbling up ideas that could be pushed forward as we go through the semester. The first team meetings with me are going to be planned for this range of dates starting next Friday, the Friday after the first exam, going through the following Wednesday. So, lead editors, watch for my emails with sign-ups for meetings. I'll start sending those today or tomorrow. So, you can query your team and find out if there's a time slot that works well for most people or everyone. Okay? It may not be possible in that limited range of dates to get every member of your team in, but our goal should be to try to do that. Okay? And you'll get a dedicated 30 minutes of time to discuss so far like what's been going on. Okay. So, here's what I had so far based on going back through all my emails that I could find. All right? So, Team Alpha, we're now Coulombs. We got the Fig Neutrons. That'll look familiar to some people in honors physics. Law-abiding Physicists, which is the most upstanding team name we've had so far. Team Delta. You guys, I don't have anything from you. So, Weston. Oh, I did. Okay, great. I'm dropping the class. Oh, okay. All right. Now I'm really super sad. Okay, all right. So, yeah. So, let me know what you decide, and we'll have to maybe take a look at your team size and figure out what to do. But I designed these problems to be something that could be accomplished with as few as two people per team. But I think you're down to three after this. So, okay. So, you're fine. You're absolutely fine. Okay? We had a team last semester that went down to two by the end and they did fine in the class. So, okay? So, no big deal. All right. So, Team Echo, the Dolphins. Is that a reference to the video game of the Dolphin? Yeah. Wow, I'm actually pretty impressed by that. That's obscure. Okay. That's, I mean, I don't even know what to do with that. That's so awesome. And then Team Foxtrot, Faraday's for Days, which to me is the most perplexing name of any team that I've seen so far in two semesters of doing this. So, hey, you guys can do what you want. I don't think this is a euphemism. So, I think we're good. All right. And so, everybody has a lead. Editor assigned. I don't have minutes from Faraday's for Days yet. I do. Sorry. That one's wrong. Which one is it then? I think it's... Oh, it's the Dolphins I don't have minutes from. Okay. Sorry. I put this on the wrong thing again. I was very tired this morning. So, all right. So, that goes there. And I do have Faraday's for Days. That's true. I keep screwing Team Faraday's for Days on. I'm like information here. I apologize. I apologize. Apparently, I have something against you guys. I don't know what it is. It's a subtle bias. Okay. So, any, anything here? Okay. Let's do the quiz then. Over the quiz questions. So, question number one. What is capacitance? Is it one, the total amount of charge placed on the capacitor? Is it two, the energy stored in the capacitor? Okay. Is it three, the constant of proportionality relating the charge on either plate of the capacitor to the electric potential difference voltage across the capacitor? Okay. Some takers there as well as on two. The constant of proportionality relating the potential energy to the work required to place all the charges on a capacitor. Okay. So, the answer is three. It's a constant of proportionality. So, basically, if I have a device with one conductive side and another conductive side. If I have conductor, conductor, and then in here we have insulator so that charge is not free to move across this gap. Okay. So, there's a gap here. If charge is not free to move but can be piled up over here and piled up over here with opposite sign, this is, this is a capacitor. Just taking charge and separating it from one another. So, it's like a super dipole. Okay. The capacitance is simply the relationship between the charge I can place on either plate and the voltage that results, that electric potential difference between these two sides as a result of the field that's created in between here between the charges. So, this thing here is capacitance, quote, unquote, and it has a unit which gets a name, Farads, or F, very close to your name. Okay. All right. So, Farads, F, and they are simply coulombs per volt. That is a Farad. So, one Farad is one coulomb displaced across one volt of potential difference. That's it. So, Farads are coulombs per volts and they can be related to other units in meters, kilograms, second to coulombs as well. All right. So, let's go to the next one. So, let's consider a parallel plate capacitance. It looks just like this. With plates of area A and separation D, what is true about the capacitance if I have that is reduced by a factor of two, the separation between the plates? Okay. So, there's a formula for capacitance for this particular geometry, a parallel plate system, this thing right here. All right. So, it is the answer one. The capacitance remains unchanged. Is it two? The capacitance increases by a factor of two. Okay. A few takers. Is it three? The capacitance decreases by a factor of two. Okay. Is it four? The capacitance decreases by a factor of four. Okay. So, the answer is two. All right. So, for those of you that had hands up for that, good instincts. Okay. The formula, which I'll repeat again in a bit, is that the capacitance for a parallel plate capacitor system is a constant of nature, which I'll talk more about in a moment. Epsilon knot. Epsilon knot you may remember from a long time ago is related to this K constant we've been using this whole time. K is equal to one over four pi epsilon knot. So, you can rewrite epsilon knot in terms of K. Okay. So, epsilon knot equals one over four pi K. All right. And it turns out that's the more fundamental constant of nature. I mean, it's only related to K by a bunch of other constants four and pi. So, it's not that much more fundamental. But this is the one that pops up in a bunch of places as one moves further and further along in electricity and magnetism. And there's a very good reason for that. And we're going to begin to see that reason illuminated inside the capacitor. So, you've got this constant times the area of the plates. So, the plates will have area A in meters squared. Three. And there'll be the gap separation D, which is in meters. So, if you double the area, you double the capacitance. If you double the separation, you cut the capacitance in half. If you have the distance between the plates, you double the capacitance. Okay. So, that's why that happens. It's a proportionality issue. So, you know, building some comfort with this equation, which ain't a bad equation I have to deal with, is a good thing to do just to get a feel for what happens to a geometric system that can store charge when you change its geometry. Okay. And finally, what was true about the electric field inside the ideal archetypal parallel plate capacitor discussed in the lecture video? So, basically this, but imagine the plates are super big compared to the gap in between so that you can ignore the weird effects from the electric field fringing that might happen near the edges of the plates. Okay. So, what was true about that field? One, it is strong next to both plates but very weak in between them. All right. So, it's really strong here and here, but it's weak in the middle. Okay. Two, it's uniform in strength between the plates. That is, it has the same direction and magnitude everywhere in between the plates. Any takers for two? Okay. Three, it's stronger next to the plate containing the negative charge. So, if this was plus Q and this was minus Q, it would be stronger next to the minus Q plate. Okay. And then what about stronger next to the plate containing the positive charge? So, this one over here. Okay. Everyone's tired just like me. All right. So, it's uniform in strength between the plates. And in fact, a parallel plate system like this is a great way to make as close as we can in nature a uniform electric field. So, no matter where you are inside this thing, the field strength is the same and it always points in the same direction. Okay. So, capacitors are really the simplest way to make a functional device that lets you do this. Okay. So, we're going to now engage in some problem solving with capacitors. But before we get into the actual problem solving, what I'd like to do is I'd like to review the basic ideas which are kind of sketched up here. Just one more time so that they're fresh in your mind and you can use them. Okay. And then I'm going to demonstrate capacitors because we can actually play around with one in the classroom. Okay. So, the basic idea is, as I said, a capacitor is merely a device. It's the first useful electric device that we encounter in the course. And it can be actually used in all modern electronics. All modern electronics uses capacitors in one form or another. It's simply a device on which you can place charge, net charge. And as a result of having that charge present, it will develop an electric potential difference that is proportional to that charge. So, that's what that equation says. The charge that develops is proportional to the voltage. The voltage generates a charge separation which is proportional to that. Okay. Either way you want to read it. That relationship is this nice equation here, Q equals Cv. Okay. The way I used to remember this, although I'm not sure this is really helpful anymore because I really doubt any of you really watched TV the way I watched TV when I was in college. But there was, and I believe there still is, a channel on cable called QVC. It's a shopping channel. And that's how I used to remember this. QVC. So, Q equals VC. That for me worked. All right. But you may have to have another mnemonic that works for you in the modern world. So, I'll leave it up to you to cook up some poem, rhyme, song, whatever it is that helps you remember these things. Now, a very simple capacitor that we can actually learn a whole lot about capacitance from is this idea of a parallel plate capacitor. One plate, another plate, insulating material in between, separated by a distance, plates of area A. Okay. The simplest thing you can do to put an insulator between two plates is to suck all the material out from between the plates. So, have a perfect vacuum, absolutely empty space so that the charge can't be soaked up by anything and carried across the gap. Okay. That's the most basic archetypal ideal capacitor. Plate, plate, nothing in between. The capacitance then is calculated exactly using this equation. So, the capacitance of this picture right here is this constant, epsilon naught, which always has the same value, times the area of either plate divided by the separation between the plates. So, if you know A and D, you can get C and then you can use that to figure out, well, if I want to store so much charge, what voltage would I have to put on it? Or if I have a battery that supplies a certain amount of voltage to that plate, what charge do I develop on it instead? Yeah, Darson. Is it possible to have two different areas for the plates? You can, but then the capacitance would be dictated largely by the area of the smaller plate because what will happen is, let's imagine that. Let's imagine that you have sort of a big plate and a small plate, all right? And if we were to put a bunch of positive charges down here, this would cause an electric field to lose the gap, okay? And again, we're dealing with situations where the plates are big compared to the gap, all right? So I'm not really drawing this to scale, but imagine that the plates are much bigger than that space between them. I'm just exaggerating the space for effect, okay? Over here, negative charges will develop. They'll be attracted to the positive charges and positive charge will be repelled by the field. And because there's going to be a little bit of leakage of the field out to here, you'll get some charge out here, but most of it will be concentrated above the lower plate. So that's not a very ideal situation. It's far more realistic. I mean, it's tough to engineer things to be exactly the same size. But as long as you do it within this approximation, that the space between the plates is much smaller than the plates size themselves, you can kind of get away with making this approximation all the time, okay? Now, it's a good question. So that's a much more realistic situation. And in fact, you might be able to design some interesting systems by going away from perfect. Going away from these perfect archetypes we use in physics, introductory physics to motivate things is a good way to design new technology, okay? Because all kinds of interesting things will happen. And you can understand all of them. You can computer model them using Coulomb's law and the other laws of electromagnetism that we're going to learn as we get through the course, okay? All right. Now, I should say, and we will do this a little bit later in the class, you don't have to stick nothing in here. You could just stick an insulating material, glass, air, air is an insulating material, ceramic, all kinds of neat things have been made by humankind in the last century or so, all these new cool materials we have and mostly driven by the need to improve electronics more and more and more, make them smaller and smaller and smaller, make them do more for the same voltage, okay? So, the material that you stick in here is known as the dielectric, and a dielectric is an insulator, and an insulator is nothing more than a medium that when exposed to an electric field will suddenly expose its dipole nature. So, think of water, right? So, if you have a block of water, we know that the water molecules are really dipoles, but they're normally oriented randomly, but if you expose the water block to a really strong electric field, the dipoles will do what? What will they do along the electric field lines? Yeah, they'll rotate and maybe translate depending on if the field's uniform or not, but we know that the dipoles will rotate, right? You have that sort of in the last homework. So, if the dipole starts off perpendicular and a field occurs, you'll get a torque that rotates it so that the dipole moment is lined up with the electric field. The negative charge moves away from the electric field arrow, the positive charge moves toward it, and the whole thing kind of rotates. When you do that, if you work through the math, what you'll find out is that the dipole weakens the electric field in the region around it. So, that's why insulators insulate. They weaken external electric fields, and they don't allow charges to move as much as they would if they were just exposed to the raw electric field. So, we can get some super dipole material and shove it in here that really weakens the electric field so we can pack more charge onto these plates. So, that's how you can store more charge, shove a dielectric in here that weakens the electric field in between. Different dialects have different properties, something like graphene. It's really stable, and insolent as all of those are all carbon-based. Yeah. Graphite, for instance, is a cheap version of graphene. You can make graphene from graphite. So, graphene is a literally a one atom thick layer of carbon atoms arranged in a very specific lattice shape. It's a really sweet material. It's discovery, which was largely an accident, won the Nobel Prize a few years ago in physics. Does anyone know how graphene was discovered? I mean, essentially, if we really want to boil the story down. So, what was going on was that the researchers were using scotch tape to lift off carbon from a graphite sample, and they at some point decided to ask, I wonder what we're pulling off when we yank the scotch tape off and throw it in the garbage. So, they studied what was going on on the carbon atoms that were trapped on the scotch tape, and they found out that they were making essentially a perfect monolayer of this new material called graphene, and it has all these really cool, tunable, electronic properties. They've actually they've been working with companies now to develop printers. So, let's imagine you wake up one day and you're like, oh, I woke up today and my mobile phone was broken, okay? So, what I would love is I would love to have a printer in my home, which is just loaded with graphene cartridges, and you could go to the computer and say, look, I want essentially to print a pay for a copy of the latest Nexus 6 or Nexus 5X or the new iPhone or something like that. So, you just go buy the schematics from the company, hit print, and it will print monolayers of electronics including the case, the circuit board, the screen, all entirely out of graphene. That's what they're trying to do, and they printed simple circuits doing this so far. But, you know, imagine in 20, 30 years, given the rate the technology accelerates in its advancement, you should be able to print your own custom electronics at home. So, yeah. So, how can graphene be used in a medical application? Like, can it be used for, like, CAS, or... Oh, well, that's a good question. I mean, you might be able to custom print a pacemaker. Right? But, of course, you're not going to install that yourself. You're still going to want a qualified surgeon that graduated from the pre-med program at SMU to cut you open and put that inside you. Yeah. Also... Come on, I know I'm getting old. I'm going to die, and I need you to cut me open at some point and fix me. So, I'm not stupid. I'm not going to insult you guys. Yeah. Yeah. This is good. Oh, like, based on, like, biological material? Keep that in mind. We're going to talk a little bit more about that in a moment. So, yeah, capacitors actually play an important role in biology. You'll see one in a moment. So, hold that thought. We can talk about it a little bit more later. Okay? Any more questions at this point? Because I'm going to go demonstrate. Okay? So, let me begin by quitting this video camera. Bringing up demo camera. All right. So, everybody, try to behave themselves. So, what I have here is a, well, and I say everybody, I really mean you. Okay? What I have here, like I said, will work. There we go. Is a volt meter. So, it's a, it's actually a, what's called a multimeter. It can measure electric current that is charged per unit time moving through a circuit. It can measure electric potential difference or voltage. It can measure the resistance of a material to the flow of electric charge, which we'll talk a bit more about in a few weeks. Okay? It's an all-purpose electrical tool. And I'm going to use it today to measure electric potential differences. So, electric potential differences we're all pretty familiar with them. Okay? In the sense that there's one in, many of them in every room in a building that you go into these days. Let me switch this to alternating current voltage. And I'm going to do something you were told to never do. And I'm going to shove these plugs straight into the wall. Okay? So, if I do this. Okay? You'll see that we're getting an electric potential difference, as promised. That isn't a magic box that has little fairies in it that go in and power your lamp by paddling bicycles and running into atoms. Okay? And giving off light with flashlights. No, it's an electric potential difference. It makes electrons go. That's it. Those electrons crash into things and when they crash into things, they give off energy. And that's how light works. Okay? You're told that typical voltages in buildings are about 110, 120 volts. You're enough about 120 volts. Okay? So, there's an electric potential difference there. I'm going to take that out. Now, we're going to play with what's called direct current today, where what's going on in here is that every 120th of a second, the direction the current is traveling switches. And there are a lot of reasons why you would want to do this for efficient power transmission over long distances. This device takes alternating current and turns it into direct current. Current only ever flows in one direction in this device. And it has electronics in it that we'll learn about later in the course that take that 120 volts and step this down to about 6 or 7 volts. Okay? So, I can turn on this power supply over here and I can plug in the voltmeter part of this here. All right? And you see, that's what we're getting out of this. So, this is now direct current. DC voltage, DC direct current. AC alternating current. AC DC, an awesome bend from the 1980s. Okay? No? You know, echo the dolphin, but I don't understand. This doesn't make any sense. All right? So, 6.39 volts is what I'm getting out of this power supply. Okay? So, that's what this thing is called. It's a power supply. It's a battery, essentially, that's generated by plugging into wall voltage and it transforms the voltage into something else that could be useful. All right? So, you know, you could use this to, as you, what's the voltage that comes out of USB, micro USB? It's like 5 volts or something like that. So, this could charge your mobile phone. You know, just a couple of hours, your phone could be charged up. This may be less depending on your phone. So, this is perfectly useful for all kinds of household things. Imagine that you wanted to use this to build up charge someplace and store it so that you could use that charge later for some other kind of work. It could be hours from now. It could be microseconds from now. That's where capacitors come in. All right? Capacitors allow you to store up charge for an emergency or for some other purpose that might be useful in time, but not right away. Okay? So, you can stop for a little bit but there may be all kinds of ways you want to slow charge down over time and then use it later. We'll explore one of those in a bit, you will. I'll talk about a useful one and then you'll look at another useful one. It's even more fundamental than the one I'll show you. Okay? So, what I have here is a capacitor. Now, this is like my granddad's capacitor. Okay? Maybe my great-granddad's capacitor at this point. This thing is huge and it really doesn't have a lot of capacitance. Here, let's see if I can get it to focus. That would be freaking cool. There we go. You see, it says 10,000 UF. 10,000 UF. That sounds really big. 10,000 UF. Well, that U is actually micro. Okay? Because they didn't print Greek letters on these things. UF was easier to print than UF. Okay? So, it's 10,000 microfarad or 10 millifarad. All right? So, this is a 10 millifarad capacitor. That doesn't sound so big. Okay? I can hook it up to an electric potential difference like this one and I can store charge. And by storing charge, I can retain the electric potential difference in the capacitor. So, it doesn't really matter which way I hook this up. We'll find out. If this blows up, this will be fun. So, I'm going to let that sit for a moment and I'm going to now hook up my voltmeter to the capacitor. So, ground high voltage. All right, it's 6.26 volts. All right, let's go back over here. Got ground, high voltage. 6.27 volts. These are the same potential difference within the error of this equipment, which is in the last decimal place. Okay? So, I'm going back to this guy. Just check it one more time. Okay? The power supply from the capacitor. All right, so let me see if I can do that in one fell swoop. We'll let that sit a moment. Now, in principle, if this device is capable of storing the charge that is built up on it, when I disconnect the voltage from the capacitor, the charge is still in there. And so, it should still essentially be making that electric potential difference inside the capacitor. Let's see. 6.18, 1.7. We'll let that sit for a moment. 1.5. All right, so it's declining a little bit over time here. But you see, essentially, I've still got 6 volts stored in this thing. Now, I can carry it around. I can kind of walk this thing around the room and throw it in the air. Oh, yeah. You want to touch your tongue to this thing? All right, there are ways we can drain the charge off this if we were to do what's called short. Short. The leads between this. I haven't drank enough coffee today, apparently. I don't know where I'm from. If I shorted the leads, I would give a path for the charge to escape. So the negative charges, for instance, could recombine with the positive charges on the other side. So let's check in on our little capacitor, now that I've been throwing it around the room and threatening people with it. 5.96 volts. All right, so it's leaking away over time. Any speculation as to why that might be happening? Why would the voltage be decreasing over time? There's a lot of charge over here and a bunch of charge over here, and they're separated by a material. But eventually, we're watching this thing. We're watching this in the real world and the voltage is lowering. Yeah, charges are repositioning. If the V is going down, the C isn't changing. Maybe the capacitance is changing. Maybe something's happening inside that chemically. The capacitance is weakening. That's one hypothesis. But maybe an easier hypothesis and more likely one is that as V goes down, are there any such things as a perfect insulator, something that can absolutely and utterly stop all charge from moving ever? Yeah, it's kind of unlikely, right? I mean, we're in the real world. These are imperfect materials. This thing's old. So it's very likely that the dielectric that's present in this capacitor is not great. It's good, but it's not great. And so it's maintaining a voltage over time, but it's leaking charge across the dielectric. Little separated charges are finding their way home to their parent atoms somehow. Okay? We see we settle down to a comfortable 5.65 volts. Yeah. That's the same kind of concept of any kind of battery. Yeah. So it's not like an electronic decay or something. Oh, like radioactive decay or something like that? Well, that probably is happening in there. I mean, radioactivity is all over the place. But it's likely not the major culprit. It's likely just that a negative charge is escaping through the dielectric and recombining with an ion on the other side. And then now you get a little bit more neutrality in the system in another electron leaks across the barrier and then gets in there too. So, you know, materials are not perfect. Some conductivity will happen even in an insulating material. We do have materials called superconductors that will essentially allow current to pass with no resistance to movement whatsoever. We played around with one of these a little bit in honors physics last night. If you make a material superconducting by cooling it down, which we did with liquid nitrogen, you can actually float a magnet over it. It will just levitate above it. And that's because superconductors will not allow changes in magnetic field. So once you place the magnet in the presence of the superconductor, even if gravity is pulling it down, it will hold itself above the superconductor and it will levitate. You can knock it and it will spin almost frictionlessly. It will only have air resistance to deal with. So once the superconductors principle they float above the track, all you need are jet turbines to push the trainer to slow it down in the other direction. Okay. All right, so I can drain the charge off this, of course. So let me check on this one more time. We're at 5.36 volts. Okay. So I will now short the capacitor. I will hook its positive end to its negative end. Ooh, they got a little spark on that one. That was a good one. And now if we check this, a little bit of residual charge left, but not a whole lot. So I didn't drain all of it, but I drained most of it. Okay. And that's not going to explode, which is good. All right, so that's a demonstration of a capacitor. You see it as physically possible to separate charge and store it for a long period of time, maintain a voltage, and you can imagine using these for all kinds of purposes. So let's look at one of those right now. Almost right now. Okay. Portable defibrillator. Portable defibrillator. We explored this last time. We looked at it from the perspective of energy last time, but this time we can look at it as what it actually is, which is a large capacitor. A large portable capacitor. It can be powered by a battery or plugged into a wall. The portable ones are obviously battery powered, so you don't have to plug a cable into the wall. You can use this on public transportation, in airports and bus stations, in public buildings, in private buildings. I'm sure there's at least one or two somewhere around here within one building of us right now. Okay, they're very useful in case somebody goes into cardiac arrest because they can reboot the pacemaker in the heart. The job of a portable defibrillator is to store a very large amount of charge, and we looked at that number last time. It doesn't seem that big, but actually this is a lot of charge. That charge can be released across the heart to restart it. So you generate a current across the heart, reboots the pacemaker, and you can get back to regular rhythmic motions, rhythmic contractions of the heart, hopefully. So the way that you build up that charge is you expose a capacitor system in here to an electric potential difference, and in particular the electric potential difference that you typically would need to place a capacitor in here is about 2.3 kilovolts. That's the number we had last time as well. So, here's the cool thing. This thing has a capacitor in it, and each of these paddles is hooked up to one side of the capacitor, and it has a trigger on it. So you place the paddles across your chest, and your chest now becomes the path for shorting the two sides of the capacitors, just like I shorted the two sides of the capacitors there. So the reason you need as much voltage is that nobody offers resistance to the flow of electricity, so you've got to overcome that resistance and drive enough current through the heart to reboot it. Alright, so when you pull the trigger, you are basically shorting out the capacitor and connecting its two sides again. So the negative charges will move back to where the positive charges are, and boom, your heart will restart. Hopefully, if it's not too damaged already. So, the question is what's the capacitance required to achieve these conditions? A potential difference of 2.3 kilovolts where you have 145 micro-coulombs stored on each plate. So we can start attacking that question right away from the fundamental equation for the capacitor Q equals CV. Okay? So let's go ahead and write that down. Q equals CV. Well, we're given Q and we're given V, and we're asked to find C, the capacitance. So we're trying to find this thing. Capacitance. And it will have units of Farads if you have volts in volts and charge in coulombs. Alright, so if you get your voltage difference into volts, instead of millivolts or microvolts or kilovolts or something like that, and you get your charge into coulombs instead of micro-coulombs or millicoulombs or mega-coulombs or something like that, that what results from this one Farad is one coulomb and that's the definition of a Farad. One coulomb over one volt. Okay, well, let's go ahead and rearrange this. C equals Q over V, and this is going to be 145 times 10 to the minus 6 coulombs divided by 2.3 times 10 to the 3 volts. So just to do some number gymnastics with this, I've got a 10 to the 3 in the denominator. That's equivalent to 145 over 2.3 times 10 to the minus 6 times 10 to the minus 3 coulombs per volts. Okay? So all I did was I took advantage of the fact that this is in the denominator so dividing by a thousand is equivalent to multiplying by 0.001 or 10 to the minus 3. So I get 145 over 2.3 times 10 to the minus 9 coulombs per volts is Farads. Farads. So I'm nearly there and I just have to do that math. And just like on a cooking show, I've done it already. Okay? So you get 6.3 times 10 to the minus 8 Farads. Now it's often convenient to re-express this in terms of you know, some powers of 10 to the 3, right? Micro, Mill, Leapico, Nano, things like that. So this is equivalent to 63 Nano Farads. Not a big capacitance. This doesn't sound like a big capacitance, 63 Nano Farads. That sounds tiny actually to do that kind of amazing work, storing that much charge we dump through your heart to reboot it. Let's explore that a little bit further in part B. So let's assume that the capacitor that's hiding inside that device is just a parallel plate capacitor, right? Two plates separated by some material. We're going to assume that the gap in between the plates is empty of all material. It's a, I'm sorry Darcy I'm ignoring you. I was just asking, why would you want to put in Nano Farads? Just to show that you know, you can do that. Part of the reason for that is that capacitors if you had to buy one are sold in Nano Micro Mill Leapico Farads. So if you needed to go out really quickly and replace the capacitor in here, it might be helpful to rewrite it in like Nano Farads. So you can go to the store and say, yeah, I need one roughly 60 Nano Farad capacitor for a portable defibrillator please and they'll probably look you and go, I'm not selling you that, you shouldn't be fixing that probably unless you're like a licensed technician so but you could, you know, go to fries or Micro Center and you can buy capacitors off the shelf. They have them, okay? And that's really not a very, doesn't sound like a very big one. You know, we used to be able to go to Radio Shack when those were more abundant and get Pico Farad capacitors no problem, so. Alright, so let's assume that there's a parallel plate capacitor lurking inside this nice plastic box here and since it has to fit in the box what we want to do is say, okay look we know that the area of the plates is constrained if it's going to be a parallel plate capacitor. Really can't be much bigger than let's say 50 centimeters by 10 centimeters because you've got to fit a bunch of other stuff in there as well, like a battery or power supply or something like that. More stuff has to fit in there than just the capacitor. So we're going to, you know, take a parallel plate capacitor, so I'm going to simplify the cartoon of this by just drawing two lines like this. So, in fact, this is the symbol for a capacitor. A capacitor in a circuit, and we'll play more with circuit diagrams later, is just looks like a couple of T's that are mirroring each other, okay? Those are the plates and those are the wires that you could connect to something else, like a battery or whatever, resistors, something like that to make up a circuit that does something. Okay, so we have plates that are not square in shape. They are 50 centimeters by 10 centimeters. So I turn the plate to the side. That's what it would look like, roughly, right? Exaggerate it again the sizes here, alright? We want to figure out what gap is needed to make this capacitor do what we want it to do. That is B, 63 nanofarads in capacitance with plate areas of 50 times 10 centimeters squared or 500 centimeters squared, okay? So we know the plate area that's just 50 centimeters times 10 centimeters is 500 centimeters squared, okay? And we can convert that in anticipation of needing things to be in meters, kilograms, and seconds into meters, kilograms into meters. So 500 times 1 times 10 to the minus 2 meters all squared which is 500 times 10 to the minus 4 meters squared, okay? So we get 5 times 10 to the minus 2 meters squared for the area. 5 times 10 to the minus 2 meters squared, alright? So it should be a tiny fraction of a meter squared because that's not that big. Okay? Alright, great. So we have the area. We have the capacitance. We're told there's nothing but air or nothing but empty space inside this thing. And so if we write down the capacitance of a parallel plate capacitor, it's epsilon naught, a constant of nature, times A over D. We want D. We have A. We have C. We can rearrange. So D is going to be equal to epsilon naught A over C. Okay? And we can plug in all the numbers we have and you should get 7 microns. That's the gap that you'd have to have between these plates. So, you know, sort of roughly this scale, 7 microns in between them. So certainly matches our requirement for the archetypal parallel plate capacitor. The area, the length of any side, is certainly far larger than the gap between the two plates. Is this feasible? Do you think you can engineer something like this with a 7 micron gap that's filled with empty space in between, let's say, two copper plates or something like that? Well, does anybody know? Can anyone give me a scale? How do I compare 7 micrometers to something? Okay, yeah, so human hair, right? That's a teeny tiny thickness. Do you know how thick human hair is? I think it's a diamond. I'm undershooting it a little bit. 200 microns is the thickness of a human hair. Okay? Would it be hard to keep two metal plates separated perfectly in a device that has to come off the wall and work like that if you have to separate those plates at less than the thickness, almost 100 times than the thickness of a human hair? Lucy, are you exploring human hair right now? Okay. Yeah, that's tough, right? Maybe we're just lacking imagination. Maybe in fact there are engineers out there that are bright enough to do this. But the good news is that nature has made it possible to engineer something that size that doesn't require sort of crazy engineering feats like this. Just to give you an example, the smallest working electronic device that we can make like state-of-the-art charged particle tracking systems for leading edge particle physics experiments that I work on. They have silicon micro strip sizes that can be read out that are of order a micron or slightly smaller than a micron. And that technology is like one of a kind, really expensive. You're not going to roll this off a factory floor kind of stuff. It's not going to be in the camera and your iPhone yet. I say yet because one day it probably will be. All right. So that's pretty tough to engineer. But the good news is we know from looking at the capacitor equation that it's actually possible here this is the permittivity. This is a constant. It has a name. And it's known as the permittivity of free space. So let me skip ahead here. Empty space has nothing in it. No atoms, no electrons. For all our purposes there's really nothing there at all. No substance, no matter. But it's possible of course to shove a material in between the plates. And when you do that you're shoving dipoles in and that will weaken any electric field that's present between the plates. And it will allow you to store more charge for a different geometry. So by shoving a dielectric into this material we can actually space the plates out a little bit and still get our target to meet as well. I should note, does this look like a parallel plate capacitor to you? Can you conceive of this being the right shape for something that's just two rectangles separated by a gap? Is this how you would design it if you were going to make a capacitor container for two plates separated by a gap? What shape would you make it? A rectangular. It would be rectangular, not round like a cylinder. Actually this kind of is a parallel plate capacitor but it's a cheap. What you do to make I can demonstrate it with these actually. So here are my parallel plates and I don't want to ruin any of your quizzes here. I'll take one of the quizzes. So here's my dielectric. I want one of the quizzes. I've made a parallel plate capacitor so we imagine that the quiz is made of some non-conductive material that's scary. This is big. I have to make a big case for this but I could maintain the parallelness of the plates while saving volume or saving area at least. Any idea how to do that? See? What's that? Roll it. That's no accident but that's cylinder shaped. So it's actually a new conductive plate separated by a dielectric material that's been rolled into a cylinder and that's why this thing is round. That's why this thing is shaped like a cylinder. So that's how you can make a round parallel plate capacitor a circular parallel plate capacitor. At any point if you look at the plates real close there's just a uniform gap between them it's just that gap, the plates, walls bend as you go. So that does introduce extra little realistic effects into the problem that you have to think about advanced physics and engineering is for. Okay? Alright, so let's sit here. Something fundamental. So if I go out into the middle of interstellar space as far as I can possibly get from planets and stars and asteroids and comets and gas and dust and all the stuff that sort of surrounds us in space in a solar system go really far away and just find a square meter space that has absolutely nothing in it. What I know from the laws of physics and also from just doing an experiment is that if I evacuate that space entirely and if I put a bunch of positive charge over to one side of it and a bunch of negative charge over to the other side of it I will make an electric field through that empty space. Electric fields do not require so far as we can tell a medium to propagate. And that will be an important thing later in the course. So in effect this number right here this number right here tells us about how empty space permits electric fields to pass through it. And that is what makes this the fundamental constant that we have to worry about. This epsilon naught. Okay, so epsilon n a u g h t epsilon naught. Okay, epsilon subscript zero. That actually tells us something very deep about the universe and all from just constructing capacitor systems because it tells us how the vacuum of empty space allows electric fields to move through it. Now we can change empty space by making it not empty anymore. We could put some ceramic inside the capacitor and alter that number. So when you shove a dielectric material inside a capacitor you're just scaling that number up by a number bigger than one. That's it. So you're taking epsilon naught and you're turning it into some number epsilon which is equal to epsilon naught times the Greek letter kappa. Okay, try that. There we go. Kappa. Kappa is what's known as the dielectric constant and all it does is it scales up the vacuum to some other material. That's it. It takes vacuum and turns it into ceramic. So to add a material to alter this equation it's just that there's shove a number in known as the dielectric constant. So let's look at a more realistic capacitor system. You have one but you have lots of them inside you right now. Every cell in your body is a capacitor because it has a membrane that does not freely allow charge to penetrate it unless those charges are intentionally pumped into or out of the cell. The pumps can create charge imbalances between the sides of the membrane and that creates a voltage. So this bilipid membrane here is a dielectric medium with charge separated on either side say positive sodium ions over here and then negative 4E anions over here okay. There's an electric field weakened by the dielectric constant of the cell wall but nonetheless this is effectively a capacitor. That's all this is. It's charge separated by a distance that it can't cross. Okay, so that lipid bilayer is clearly not vacuum. It's not empty space. And so one has to modify the vacuum constant epsilon not by some number kappa. And this is a piece of useful information that you're going to need. Okay, kappa for the cell membrane is about 3. It's about 3. And it's a dimensionless number. It just multiplies epsilon not. So epsilon not has units. Kappa just multiplies it to scale it up to be a material instead of empty space. Alright, let's go to the problem. So here's the picture of the cell membrane again. The membrane thickness of a biological cell specifically I believe was blood cells was measured for the very first time in human history using capacitance. It was not observed by the naked eye. There's a reason for that. You'll see in a moment. The first way in which the cell membrane size was determined was using capacitance and electrical properties of media. So let's say that we have an experiment that determines that this electric potential difference between the inside and outside of the cell is 70 millivolts. And that number ought to look familiar to people that have studied cell biology. The experiment also finds that to maintain this potential difference the cell has to move 0.17 picocoulombs of charge specifically sodium from inside to outside. So it pumps sodium out, builds up a charge imbalance inside and outside and gets to about 70 millivolts potential difference. So what's the capacitance of the cell membrane? That's your first question. What's C for the cell membrane? Second, cells themselves can be seen with microscopes. You guys have looked through microscopes and looked at cells before. Plant cells are really easy to see. Our biological cells have a radius of about 5 microns. So just slightly larger than the gap that was needed in between my parallel plate capacitors for the defibrillator. That's crazy small. So cells have a radius of about 5 microns. What's the thickness of the cell membrane? So here's your hint. Treat the cell as a parallel plate capacitor whose area is that of the sphere. So here's a model of a biological cell. It's a sphere with an inner sphere and the thickness in between is the cell membrane. So that's the dielectric and if you zoom in on any little piece of this bent surface you'll see what looks like a parallel plate capacitor. It's just that it bends very slowly on the scale of this picture right here. So this is a very simple grossly oversimplified model of a cell but nonetheless you'll find that this is a very effective model. So you can pretend that we've taken a parallel plate capacitor and instead of rolling it up like this we've kind of turned it into a sphere. So we've kind of rolled this thing up so it's a perfect sphere. So go ahead and treat this thing like a parallel plate capacitor where the area of the plates is equal to the surface area of a sphere with the radius that's given there. So calculate the thickness of the cell membrane. So yeah, Shannon.