 do a little introduction here today. So things I think went, I haven't hand back all the homework yet, but things I think on process went really well. Either my TA is a softy or you guys are all following the process for setting up and solving problems fairly well. We'll see how you fare on homework too and we'll go from there. So today what we're going to do is we're going to learn to set up and solve problems involving charges exposed to external electric field. So we're going to start combining electric force with motion from semester one and this actually will allow us to do a lot of really cool things, okay? So you're going to get some problems today that are a bit more fun than you have a line of charge with Alvogadro's number worth of charges on it. You must now add them up using calculus. I'm already bored thinking about it, okay? This will be a bit more interesting today. We've gotten enough basic material now that you can start to actually make predictions about the natural world and test them and in fact that's one of the things that we're going to do at the beginning of the in-class period after the quiz today. So just to review, again, there are two kinds of electric charge, positive and negative. I think I've beat you to death with that at this point. They exert forces on each other. Positive electric charges are the sources of electric fields. Negative electric charges are the recipients of electric fields by convention. That's a convention, okay? Electric fields and forces are vectors to find the total electric field or force. You add as vectors the electric fields or forces due to individual charges. Now I put the calculus version of this down here. So if you have a finite version, finite number of charges, like five, and you just need to get the total electric field, then all you have to do is sum them up. But if you have a huge, almost infinite number of charges, then you have to use rules of calculus and get all the bits and pieces of Coulomb's law for an electric point charge electric field written in terms of your coordinate system, geometric information, if it's a line, get the length in there somehow, et cetera, et cetera, okay? Charge densities. So linear charge density. If it's a surface, it could be charged per unit area, aerial charge density, and so forth, okay? Those are the basic things that we've exercised so far. Okay, your next assignment, it's actually going to feel pretty light, but that's because the video, I really felt like it was important to review a lot of basic things that should have been covered in semester one, because we're going to exercise them heavily going forward, okay? We are now going to turn our attention to the concept of energy, which is really the foundational concept in physics, that all motion, all changes in nature can be simply described by a quantity called energy changing from one form to another. And as far as we can tell based on just using this in experiments all the time and still having it work out, energy is conserved as long as energy can neither leave nor enter the system, however you define the system. So for a closed system, like the whole cosmos as far as we can tell, energy is neither created nor destroyed, it only changes forms, okay? So you're going to read chapter 24 one, which does have a lot of definitions in it, and there's a corresponding video that adds a little extra material to that on top, okay? Homework twos do Thursday by 9.30 a.m., beginning of class just like last week, and then where are we in the grand challenge problem? Well, remember you're supposed to be meeting with your team at least once per week outside of class, so that means between last Friday and this coming Friday, you shall have had at least one meeting, and I think I got my tense right on that, okay? So what are your big things you should be doing right now? You should be picking a team name, you should be choosing a lead editor, so you'll probably get a sense for each other based on your first meeting together. And if somebody's like, I love to write and I love to organize, and I love to tell what other people want to do, and I should be the lead editor, and no one else feels like they need to combat that. I'll leave it up to you and a democratic civilization to go ahead and choose that person if you like as the lead editor. That person's job is to coordinate the rest of you, so you're kind of giving them a little extra responsibility, but then they're going to put the burden back on you. The job of the lead editor is to expect things from their team, okay? You should be discussing how ideas in the course so far might inform a solution to the problem. Just one, you need three, okay, you need three different outcomes for this person going into the MRI. But you should be thinking about what you've learned so far might begin to inform a solution to a very, and wavy, okay? Hopefully we'll have a little time left at the end today. There's a little bonus exercise at the end of the problem solving part of the class. And I'm intending to use that as a way to motivate making approximations. And approximation is simply an assumption, a simplifying assumption about a scenario, okay? So for instance, if I asked you to calculate my weight, or my mass, okay, you could get the weight from the mass. A simple way you could do this without putting me on a scale would be to treat me like a cylinder, okay? So you could probably eyeball the width and the height from a distance, okay? And you can think of me as just a cylinder of material. And I have a lot of water in my body. So you could approximate me as a cylinder of water. And you could look up what's the density of water, what's the volume of his cylinder and then calculate and estimate my mass. That's an approximation, of course, the real thing you should do is get out of scale and weigh me and then knowing that the acceleration due to gravity at sea levels 9.8 meters per second squared, you could get my mass from that, okay? But I'm not going to let you do that, I'm not going to let you weigh me, I'm going to make you play around a little with numbers, okay? So in the world around us, there are very complex phenomena, and we do not always have the ability to make direct measurements of them. And so one trick that you as a problem solver should use is to learn to make assumptions. When you make an assumption, remember there's the old joke when you assume you make an asset of you and me, okay? That's because most people make assumptions without thinking, wait, what are the penalties I will pay if my assumption is wrong? A good scientist, make an assumption and then write down all the things that could go wrong if that assumption is not correct. Make the assumption, do the calculation and come back later and reassess your results in light of all of those caveats that you could attach to the assumption. I'm not primarily made of water, for instance, that was an assumption. It's a simplifying assumption, but it's also probably wrong. Alright, so then you have to fold in things like carbon and oxygen and hydrogen and then kind of guess at the ratios of those things or take a, take data about a cadaver, what's the typical fraction of carbon, hydrogen and oxygen and the cadaver and then apply that to me. Okay, so this, you can make things more complicated, but you can always start with a simplifying assumption and figure out where your assumption will fail. A good scientist makes assumptions, but also recognizes the limits of making assumptions and is honest about them. Okay, so I will show you how you could make simplifying assumptions and a problem later today and you'll use that to solve what could be a very complicated problem. Okay, so team names so far. So we got Team Alpha is now Team Tachyon. I looked it up on Urban Dictionary, seems safe. Team Bravo, Body's Electric. That's fine. I don't have a problem with that. I mean, after all, we are mostly electricity when it comes down to our movements. Okay, so Charlie Delta Echo Golf. Foxtrot just hedged. Well, we'd like to be Team Foxtrot. Very exciting. Alright, so, so congratulations, you're now named after a letter in the NATO Phonetic alphabet. Good for you. No, I'm sorry, you guys are fine. It's fine. This is not the most important decision you're going to make all semester. So, so Charlie Delta Echo Golf. By the, you know, by Friday, I want to know what your team name is. So, you know, you should at least be communicating by email. If you don't know how to do that, please one of you contact me and I'll send you the email addresses, the university email addresses for all the people on your team and you can start organizing. Okay. Alright, any questions at this point? Because otherwise, we've come to quiz time. Happy games and quiz time. Okay. So, no books away. Let me go over the quiz questions with you guys. Everyone handed in their quiz. Yeah. Okay. Okay. First initial, last initial and something else. What's going on? All work and no play makes Sam with El Boy. All work and no play makes Sam with El Boy. Is that what I'm going to be reading? Okay, just curious. Alright, quiz questions. Let's look at these. So, what's the relationship between the force F on a charge Q and the external electric field E causing the force? Anyone to F equals Q E anyone have a different choice that they prefer? And then we'll fight to the death to defend? It's physics. Okay, yeah, it's two. So, force equals Q E and then this is a great way if you're never quite sure oh boy is it Q over E or whatever. Try to remember forces Newton's. Okay, try to remember the units of electric field which are Newton's per Coulomb. So, whatever equation is that relates E and F, it's got to have Coulomb's in the numerator multiplying E or it won't cancel out and give you Newton's. Okay, so yeah, so the correct answer is F equals Q E. Alright, and actually I would hope if even if in a pinch that you could use algebra to find out that these equations are actually the same and there can't be two correct answers there. So, you can eliminate those right away. Okay, so don't forget your algebra, it can save you. Alright, so what happens to an electric dipole immersed in a uniform electric field one whose strength and direction are the same everywhere. The dipole will experience a net zero torque and it will remain still in the field. The dipole will experience a net nonzero linear force that will cause it to accelerate linearly in the field. The dipole will experience a net nonzero torque that will cause it to rotate until it aligns with the electric field. Dipoles are overall electrically neutral so there will be no forces of any kind even once they cancel out when added together. So, who is who? Thurman, what do you think? You think four? Okay, anyone else? Okay, one, three. Okay. Alright, so the correct answer is three. It is true that dipoles are electrically neutral but there's the charges are slightly separated and in fact, you're going to see what a big effect that has today. Okay, it's okay. As I've said in class before, the reason I put these up here is to want to check young concepts. Okay, and if you're doing everything right, the key thing in all of this is that you go back and review these things for the exam because I'll probably draw from these questions on the exam for the multiple choice questions. So you'll probably see these or a variation on them where I change the wording around a little bit. Make sure you've got the concept down so the wording doesn't trip you up. Okay. Alright, so it will experience a net nonzero torque. So a dipole will rotate in an electric field and line up with the field. Okay, and then finally, what prediction about water and electric fields was made in the video lecture? So one, water molecules, dipoles are overall electrically neutral, no net charge. And so nothing will happen to them in an external electric field of any kind. Anyone think one is correct? Okay, two, water molecules carry a net electric charge. And so an external electric field will accelerate them linearly. Anyone think number two is correct? Okay. Number three, water molecules dipoles exposed to a non uniform electric field will both rotate and accelerate linearly in response to the field. Anyone think three is correct? That was a tiny little hand. That was like, I don't want to know. Alright, four, water molecules dipoles exposed to an external electric field will only ever rotate. Okay, well, none of you voted for it like most of the choices. Okay, great. All right. It's okay. Secret ballot, no one has to know. Alright, so the correct answer is the prediction. The prediction that I made at the end of the video was that water molecules dipoles exposed to a non uniform electric field will both rotate and accelerate linearly in response to the field. I guess you're off the game show. Please play again. I don't know. Again, 5% of your grade. Don't freak out. There will be opportunities for extra credit in this course that will compensate for anything funny that's going on in the quizzes. I care more that you then go back and review the mistakes, the misconceptions, the failures, shore those up. Okay, build a strong house so that when you walk into the exam, you're not going to panic. Okay. Alright, so let's look at that prediction. So let's imagine I could make a stream of water. Now, water is composed almost entirely of water molecules, H2O. And the water molecule has a very specific shape, which is often drawn like Mickey Mouse. H, H, O. Okay. So there's a special angle, the bond angle between the two hydrogens. And because of the way the chemical bonding works, the hydrogen shares its electrons with the oxygen, which greedily will soak up two additional electrons into its outermost shell, which is unfilled. Okay. So oxygen single atoms are not very common in the world because they're reactive. So O2 is very common. Ozone, O3 you can make through chemical reactions. That's also somewhat common. CO2, okay, H2O. So O is often bound up with other things because it has empty places where electrons could go and it's more energetically favorable for it to fill that shell to completion than to leave it unfilled. And so that's the basis of chemistry. Okay. So the electrons from the hydrogen atoms are spending a lot of their time in here. And as a consequence the proton in the hydrogen atom is kind of unshielded by its electron. So you get slightly more positive charge up here and slightly more negative charge down here. And you get a dipole. Now in a non-uniform electric field, say I have a dipole. So here's my dipole. Okay. And dipoles are rigidly bound together. Here the rigidity is provided by the chemical bonds. So I have this dipole and I immerse it in a non-uniform electric field, e-vector. Because the field lines are further apart here than they are here, the electric field is weaker here than it is here. It's stronger here. It's weaker here. Now if you go back and watch the video in a uniform field, actually in any kind of electric field, these two charges will feel forces that pull them in opposite directions. The positive charge wants to follow the electric field line. The negative charge wants to move against it. That will cause a net zero, net non-zero torque. And this thing will try to line up with the electric field. But in a non-uniform field, the force on this would be weaker than the force on this. And so this whole thing would also translate. It would move in a line dragged by the stronger force on the negative charge, which just happens to be closer to the stronger part of the field than the weaker part of the field. So if water is a dipole, and that's what happens to dipoles in non-uniform electric fields, I should be able to make a stream of water move in response to a non-uniform electric field of sufficient strength. It turns out to do this. You really don't need any fancy instrumentation. You can use a hair comb at home. If it's a nice dry day, rub your hair with the hair comb, transfer a charge, and put that near a laminar flow of water. So let me make a laminar flow of water. So that's overkill. Laminar flow would just mean smooth and continuous. We don't want this thing to turn into droplets at all. So let me see if I can get this. And it was low as possible. All right, we're going to let that go for a second. Now, great. So you can see, let's see if I can get that to not roll back. All right, so just to show that I can make an electric field, we've seen this demo before. I do the tribal electric effect. I rub the plastic with a dissimilar material, like this is just shopping bag paper. Okay, the pipe comes from low as you can buy it for like 90 cents for two yards of this stuff. And I should be able to make the can move because I can drag the charges. I can drag the charges around inside the conductor because they are essentially free to move. The outermost electrons are not all that strongly bound in aluminum. So I can make all the electrons go to one side of the can or the other and I can roll the can. Okay, so I can make an electric field. So let's see what happens now. I charge this up, see if I can get less mass in the stream. Still laminar we need. We need a laminar flow so that we don't get droplets. Okay, it's tricky with a sink to do that. See it bending? Oh, let's get the water off of it. It's a nice thing about paper too, nice and absorptive. And if I go on this side, I can get it to bend the other way until I hit it of course and then it just goes around. See if I can get a really good charge built up on this. I've got this all wet. That won't help. Water soaks up excessive charge. So you can do this at home. Just take a bathroom sink or something, something that makes only a small flow of water. This is a bit of overkill. And you can drag a stream of water around, make it dance. It's pretty neat. Alright, so it reveals at its heart that this is not a perfectly electrically neutral point object. Water molecules are extended and their extended nature may only be at the level of nanometers or fractions of a nanometer. I mean, water molecules are not that big. We're talking about maybe, you know, a few tens of angstroms, tops and size. An angstrom is about the size of a hydrogen atom radius. Roughly speaking, half an angstrom is roughly the radius of the ground state orbit of a hydrogen atom. 10 to the minus 10 meters. Okay, so it's not that hard though, even though the hydrogen and oxygens are very close to each other, to get the fact that their charges are slightly separated to reveal itself. And in fact, this is an extremely essential phenomenon. Without this, life as we know it would be very different. So this is, you know, part of why you get things like surface tension. So water molecules at the surface of a body of water will form a layer that is very hard to penetrate. And there are insects that take advantage of this, right? The water walkers will walk on the surface of a pond. How do you get the water walkers to fall into the body of water? Does anybody know? Did you ever do this as a kid? If you had a pond or a stream nearby and you had like those little water skitters, things that were running across the surface? What's that? You could push them up. If you put too much weight on them, too much force, of course then the surface tension will break. But how would you break the surface tension chemically? How do the lungs do it? In an infant or in you and me? What's that? Surfactant. Yeah, so you just need something that will basically relax the bonds between the water molecules. Soap does a really good job. So if you ever want to mess with a water bug, just take a little drop of dish soap, right in the water, breaks the surface tension, and then the bug will fall into the water. Nature, harsh, harsh beast. Okay, so let me see here. Let's kill that view and get this terrible one back up here. Great. All right, so we did all that. Okay, so solving charges, solving problems involving electric fields and charges. All right, so this is sort of where the more fun part of the course begins. Because now that we have a basic toolkit that's established for thinking about charge and force and motion and how charges reach out and communicate with one another through fields, we can start doing things with them. We can start looking at devices that do things with them. And so for instance, one very common device in the modern world now is something that I actually have on my wrist. Okay, so I don't have this. Here, this is for the folks at home. Okay, so I have a Pebble smartwatch. It was like $99 and I cheap. Okay, but it's plastic. Nothing fancy. It's got a little computer inside of it. But it's key feature that everybody sees first is the fact that it has something called an E-ink or electrophoretic ink screen. So these are very common now. They're very popular for a good reason. So here's the Kindle DX. I got this to read scientific papers on when I was first a faculty member here. It's great. And you can take it out in the sun and unlike an LCD or an LED display, which needs to be backlit so that you can get contrast in a bright environment like outside, E-ink is naturally already contrasting like, you know, ink on paper. You know, you can take this outside and read it. You get nice contrast. As long as the sun's not too bright, you can read things no problem. Your eyes can adjust. Similarly with E-ink screens. Of course, they're not actually, you know, there's not actually a pen in there writing on the screen. It's done much more slickly than that. And you'll see how in a moment, that's a pebble smartwatch over on the right. They've got other generations of those things now. But basically it's just an E-ink display. And I can, you know, I can push a button. I can change the display so I can show different watch faces. I don't have to buy a new watch to get a new watch face. I have Monty Python Ministry of Silly Walks here, clock. So, you know, you can have all kinds of goofy things that no one would in their right mind ever pay more than $2.99 for. Okay. So at the heart of it, what is this device made from? It's made from tiny capsules. And I'll actually show you a picture of them in just a moment. This is an illustration that comes from the E-ink.com page. There's a company that essentially owns the patent on E-ink. So companies that want to make devices with it at the license to technology from them. They provide some useful information, although I found some spelling mistakes and some of their demonstration material this morning. So somebody ought to review that for them. But the basic idea is the same. You have these very tiny little tens of micron-sized capsules and inside each capsule, there are black pigmented particles and white pigmented particles. And the white pigmented particles are, I think they're all basically titanium oxide or titanium dioxide that's been coated with a polymer. So the polymer helps to give it the color. So white reflects all light, black absorbs all light. So this is all color and this is lack of color to our eyes. Then you can also, on the polymer, you coat these little tiny nanoparticles with. You can put a net electric charge on them as well. The polymer chain can have a net charge on it that can be moved around with an external electric field. So for instance, typically according to the E-ink website, the white pigmented particles carry a net positive charge and the black pigmented particles carry a net negative charge. And so all you have to do is now expose these capsules to an external electric field and you can make the black particles move to the top of the capsule, effectively creating a black pixel. If we go back here, okay, so you can make a little dot in text or you can move the white pigmented particles to the top of the capsule by reversing the direction of the electric field, which modern electronic devices can do quite easily. And then that would create a blank region on the screen. You can also invert the whole color scheme on these devices. If you prefer having black background, white text, you can just have the computer invert all pixels. So you have this fine-grained control that you don't get with this, which is why I like it so much. And they're even developing this stuff so that it's flexible. My dream one day is that I have exactly one of these on which I write everything. And I just carry it around with me, roll it up, right, put it in my pocket, fold it up, put it in my pocket. When I need a writing surface, out it comes, new page, start writing. That would be great. Okay, that would take the iPad to an extreme level. iPad uses a completely separate technology that isn't discussed here. But E-Ink is an example of something that you can begin to study and think about using just the basic things you've learned in 1307 and the basic things you've learned so far in 1308. All right, so let's take a look at this. So if you were to take a really close-up image of one of these E-Ink screens, and this is from a Kindle 3 or Kindle DX model, you see all these little spots here. Let me do this, okay? So these little spots are all those little capsules. So maybe it's easier to see here. You see there's a little gap, and then there's sort of a circular capsule. Those are the little capsule pixels that make up the surface of the screen. The pixel size itself is actually determined by the grid spacing of your little electric field unit. So you grid this thing up very finely. Maybe the capsules are actually more fine than the electric field grid. And then you can control each capsule's ink particles simply by changing the field around that little capsule. And so here you see all the white pigmented particles have been pushed up to the top of the surface, and here they've been pushed to the bottom of the surface, pushing the black pigmented particles up to the surface. So you have a letter and then an absence of a letter. Okay. So zooming way out it would look something like this. Okay. So your eye can't tell where the individual capsules are. They're too small. So you get a fairly crisp text image as a result of that or pictures. You can get gray scale. You have fine grain control. You can actually control just half a cell using electric fields that are gridded more finely than the cell. Okay. So you can, you have this really nice fine grain control over this device. And this technology continues to evolve as people buy it and then demand things from it. Okay. It used to be on the Kindle DX. It took about quarter of a second to half a second to change the page. So turning the page was kind of a slow, painful exercise. It was even worse on the original Kindle models, but the speed with which these electronics move now is greatly improved in the, you know, almost half decade or so that they've really been in existence. So I bought the Kindle DX in 09, 010, something like that. And the Kindle had been around since like 2008, 2007, something like that. So I probably got about the third generation device. All right. We can look at this from a physics perspective. These are just electric charges and an external electric field. And so we can, we can take all the fun out of this device by thinking about the physics of it. Okay. Count it. This makes it more fun because we can understand it now. Understanding the world lets you change the world. Okay. So physics gives you a deep fundamental understanding in the hopes that maybe you can make a better world for yourself in that universe. Okay. So we have an individual cell, which we can just picture as a sphere. And it's a solid capsule. Nothing can come out of it. Nothing can go into it. All right. You've got these pigment particles inside. Again, the black pigmented ones carry a net negative charge. The white pigmented ones carry a net positive charge. And then you can change the polarity of the field, whether the electric field points up or points down. And move these things past each other accordingly to get a dark pixel or a light pixel. Okay. So typically we're talking about titanium dioxide that's been coated with a polymer, as I said before. And so what's the charge of one of these? Well, you can sort of do some homework. I mean, this technology is not exactly open source, but you can sort of guesstimate, and I did some guesstimating, and came up with the fact that the black pigmented particles, and presumably correspondingly the white pigmented particles have the opposite sign charge. The black pigmented particles have a charge of about negative 16 times the elementary charge. And remember again, the elementary charge is 1.6 times 10 to the minus 19 coulombs. And the mass of a titanium dioxide particle, again, I had to sort of approximate this. I don't know what polymer they coated with, but I came up with an estimated mass of something like 6.7 times 10 to the minus 15 kilograms for just one of these little droplets that carries a net charge. Okay? So the time in like the Kindle DX device that's a bit old now, the time taken to turn the page that is move the particles from the top to the bottom of the cell, or from the bottom to the top of the cell to affect the page change. That's a time difference of delta T, which is the later time when the page change has occurred, T minus the initial time when you press the button to initiate the page change. And that turns out to be about, let's say a quarter of a second, so 0.25 seconds. Okay? So the question then is, I mean there's lots of questions you could ask about this, and I'll give you more in a second that you can tackle with a related device. What's the electric field strength required to achieve this? Okay? So this is a problem about force, electric field, time, mass, and charge. The force is caused by the electric field. The force causes an acceleration A, and that acceleration causes motion. That is changes in position, changes in time. Okay, changes in position with respect to changes in time. So those are the basic things that are at the heart of problems like this. What's the force caused by? Well, we only have one thing that can cause it in this problem, electric field. So the net force on these particles, or one particle, will be caused by that electric field, whatever its strength is. That force from that electric field causes a particle to accelerate, experience a change in its state of motion. And we're going to assume that at the beginning, before you press the button, none of the particles are moving. They're just sitting there in the capsule waiting for something to happen. Okay? So the initial velocity will assume to be zero meters per second as a simplifying assumption. We don't really know how fast they're moving, but we'll make a simplifying assumption that they're not moving before you press that button to initiate the page change. Okay? So we have charge. We have mass. We know how long it takes for the page change to complete. We want to find the electric field, and we've assumed that initially the particles are at rest before they begin to move. So let's start relating all the things here to see if we can get an equation for E in terms of things that were given, like q and m and delta t and things we've assumed, like the initial velocity. So we have this bag of stuff, and we'd like to apply the bag of stuff to solve the problem. Okay. Well, the force caused by an electric field yeah, is equal to the charge that's feeling the force due to the electric field times the electric field itself. So q e vector. Now, we've been asked for strength. So I am not going to worry about direction. I can figure it out. I could draw a picture. I can figure out. Okay. Well, if the negatively charged black pigmented particles need to move to the top of the cell, negative charges go opposite the direction of electric field. So the electric field probably has to point down. So I could sketch that and then I could put some vectors like, oh, that's the y direction. So it's going in negative y. I could do that. But I'm only interested in magnitudes for this problem. So let's do the whole problem just with magnitudes. We don't need vectors for this problem. So I will be very explicit. I'm going to change this equation to a magnitude-only equation. So f vector with absolute value signs around it equals the magnitude of q. Remember, q could be positive or negative. So we want to put some absolute value signs around it so that we're only dealing with positive numbers. And then that's multiplied by the magnitude of the electric field. And that is what we want. We want that thing. Okay. Well, the good news is we got q. Check. The bad news is we don't have f. We don't know what f is. So we have one equation, two unknowns. We care about e. We don't know f. But luckily, semester one physics comes to the rescue because force, as always, is related to motion, as always, by Newton's second law. Which is just f. Any force acting on something with mass will cause a corresponding acceleration a. And they are proportional to one another through the mass. So force equals mass times acceleration. F equals ma. Now, again, we're dealing with magnitudes. So I'm going to be explicit about this and say magnitude of f equals, well, m mass. We've never seen negative mass. In fact, we know it's a positive number here. So you don't have to put the absolute value signs around m. m is always a positive number. You can if you want to be really pedantic about it. I'm not going to. m is always a positive number. But a, acceleration, that could be positive or negative. So I will put some absolute value signs around that to remind me we're talking about magnitudes here. Magnitudes. Cool. Well, I got f in terms of m, which I know, and a, which I don't know. But I have more information I haven't used. I know how long the page change takes. And actually, I forgot there's one more piece of information I gave here in the picture, which is that the distance, delta y, that these capsules have to traverse is 40 microns, which is 40 times 10 to the minus 6 meters, which is 4.00 times 10 to the minus 5 meters. Okay. Just doing a little unit transformation and moving the decimal places around. No magic here. Just a little lous of growing powers of 10. Okay. And let me make that 5 look more like a 5 and less like a French letter. There we go. Okay. So, we have delta y, we have delta t, we haven't used those yet. We have v naught, we assumed it was 0 to begin with. We haven't used that yet either. We need an equation of motion. That's what we need. Okay. We need something that relates delta y and delta t and v naught and the magnitude of the acceleration, a. And there were lots of those from semester one. There's a whole section in your book on this stuff where you can just go go on Google and do equations of motion and the Wikipedia article will pop up. And at first it'd be like, what is all this notation? Up there are the equations. They're like a third of the way down the page. You have to kind of scroll a bit to find them. There's all kinds of crap at the beginning that you guys don't recognize. Scroll, scroll, scroll, scroll. You'll see some friendly faces. Okay. So, so you can do either way. You can look in your book or you can look on the web. Just make sure you understand what the equations are on the web. That's all. All right. So we need something that relates displacement and space to changes in time, initial velocity and acceleration. And well, here we go. Here's some equations of motion. All right. So let's see. Displacements in space, initial velocity, which can be zero anyway. So that's convenient. Acceleration and changes in time more time itself. So that one looks like a pretty good candidate. All right. So we'll just do it this way. Y minus Y naught equals, I'll write it exactly as I think Y equals Y naught, Y naught plus V naught t plus one half. And I'll write magnitude of A t squared. Okay. Well, I can get delta Y in here simply by moving Y naught to the other side of the equation. So Y minus Y naught equals delta Y equals all this stuff. Let's use the fact that initial velocity is zero and just get that term gone. So that term is gone just because V naught is zero. Don't have to worry about it. So this is just equal to one half A t squared. Okay. We have to make some more assumptions here. You'll make them implicitly usually, but I'm going to be explicit just so you understand that there's a thought process behind this. That t there is really a delta t, which is t minus t naught. But you're always free to say, I declare that the moment the button is pressed is time zero seconds. So t naught just becomes zero. And now you just relate delta t and t. So delta t and t are interchangeable on this equation. Okay. But be careful if you were given an initial time of five seconds and a final time of 17.3 seconds. You may want to be careful with where you assume time zero is. Okay. So just be cautious about those things. That's all. Okay. Great. So now I have delta t. I have delta y. I can get A. So magnitude of A is going to be equal to two delta y all over delta t squared. So let's bookkeep here. F equals QE. We want E. So we want E equals F over Q. We have Q. We didn't have F. So we turn to Newton's second law. F equals MA. F equals MA. We have M, but we don't have A. So if I want to solve for electric field, I start with E equals F over Q. I substitute in with MA vector over Q. Okay. Just put Newton's second law in that equation. F over Q. So we have MA over Q now. We didn't have A, but thanks to having delta y and delta t, we can get it. So finally, we just have 2M delta y all over delta t all squared. And there's a Q in here. So 2M delta y over Q delta t squared. We have 2. I hope we have the number 2. It's just 2. We have M. We have delta y. We have Q. We have delta t. We have everything we need to plug in shock now. Okay. So let me go back to the picture. All right. So if you do that, if you plug in the numbers to this now, you will come up with an electric field, strength. That is equal to 3.4 Newtons per Coulomb. 3.4 Newtons per Coulomb. Now, we haven't gotten to this yet. You're going to watch a lecture about this for next class. But it's possible to relate this to something a bit more familiar. And that is the units of electrical energy measured in volts. So how many people have heard of a volt before? Raise your hand if you've heard of a volt. How many people have not heard of a volt before? Okay, good. So 9 volt batteries, 1.5 volt, AA and AAA batteries, okay, D cell batteries, C cell batteries, phone batteries. They're all measured. Their ability to do work is measured in something called volts, which you're going to learn about in the next lecture. So that's a much more familiar unit than Newtons per Coulomb. It's a Newton per Coulomb. Okay. So you can ask the question, in volts, if I could figure out the corresponding work done on each charge, which is what volts is, what does this correspond to? I would hope that this thing is in a 25 volt battery that's required for this, because this is an easy, weasy little device. And 25 volts, I mean, you think about 9 volt batteries, or like that thing, okay? You can't fit a 9 volt battery in this thing. So how are you going to fit a 25 or 50 or 100 volt battery in here? And it turns out the work that you need per unit charge to move this thing is a measly 0.1 millivolt, or 0.1 times 10 to the minus 3 volts. Easy, easy. Tiny battery. This thing lasts a week under normal operations, including talking to Bluetooth on my phone, which is a power-hungry exercise, and changing the screen, like making the little watch-hands tick on the screen. Okay? That animation costs power, because you have to move titanium dioxide particles around in the E-ing screen in order to get motion to occur on the screen. So everything, every time something changes on this screen, it eats a little of the battery power to move the titanium dioxide particles around. Mostly, though, I think it's the Bluetooth connection, the wireless connection to my mobile phone that chews up most of the battery in this. I bet if I could switch that off, this thing would last for a month, okay? Wireless communications costs a lot of energy. Okay, so those are the basic ideas, and now you get one of your own. All right? So very similar. So get your notepads out, partner up, okay? You probably have all your usual suspects you sit next to at this point. All right, DNA, gel, electrophoresis. How many of you have ever had to run DNA in a lab before? Yeah, okay. So at its heart is physics. It's the physics of biological systems. So DNA electrophoresis is the process of using a pretty uniform electric field in a medium that's porous, but with finite pore sizes to separate various genes in a strand of deoxyribonucleic acid or DNA, okay? So it turns out the sugar phosphate backbone of DNA is charged, and so, well, at least the nucleic acid chain is charged. And so it can be accelerated with an electric field. If it's charged, you can move it with an electric field. So if you bust up the DNA into its constituent fragments and then want to find out what the sequence of fragments is in the DNA in the first place, fragments of different size will move at different rates due to the porosity of the medium, which in this case is agarose gel, all right? So over on the right, let me boop, boop. This is a fluorescent dye stained sample that has been run. So the electric field, you can actually kind of see which way the field forces things. You see there are these sort of little U-shaped blurs here. So the field probably accelerates things down in this picture and different blobs all put in the same hole in the agarose gel up here at the beginning have accelerated over the same amount of time to different places in the gel. And that's because these are big fragments that haven't gotten very far through the finite pore size of the agarose and these are smaller fragments that have gotten much further, okay? And so, based on an analysis of this, you can figure out, for instance, you can fingerprint DNA, right? So those famous crime photos in courtrooms where they show, this is the suspect's DNA and this is the DNA found in the crime scene and then they try to fingerprint it. It's much better ways of doing this now, but this is the basic idea that you would have for just running DNA in a gel medium, okay? So here's your problem. A certain gene has an electric charge of Q equals negative 3.4 times 10 to the minus 14 coulombs and a mass of 6.0 times 10 to the minus 20 kilograms. The gene must traverse an agarose gel whose porosity results in a drag force, okay? So a drag force is a force that no matter which way you're moving, it opposes the motion. Keep that in mind. So there are two forces at work here, a drag force and a force from an electric field. And the drag force is 2.6 times 10 to the minus 27 Newtons. That seems weak, but you have to think about what the force is being caused by the electric field. So if this gene begins at rest, handed that one to you for free, and is subjected to an external uniform electric field whose strength is E equals 1 times 10 to the minus 13 Newtons per coulomb, how long in minutes does it take the gene to move 1.0 centimeters? That's what I get for justifying text on the slide, okay? So then if you get through that, I want you to calculate the kinetic energy of the gene by the time it reaches the 1 centimeter mark. So we'll dust off some energy stuff from semester one. Okay, so if you need to see equations of motion, you can look them up on your phone. I had that slide I can go back to if anyone just doesn't have a phone or doesn't have a friend with phone or something like that. Okay, if your partner's refusing to let you use their phone to search on the web, let me know. I can get those equations up. All right, so go at it. You've got lots of time. And if you finish this question, I'll put a bonus up. So when your group finishes solving the problem, raise your hand and say, Professor Sikula, I want bonus points. All right, and then I will put the bonus question up, okay? Which is a bonus question on the problem, I just did. All right.