 Okay, so let's go ahead and get started today. So I have here a video up on the screen, since we're going to be talking about energy and kinetic energy and potential energy today, I thought it would be nice to kind of tie in something that the honors physics students did last night in class. And that was they dropped a slinky and they tried to answer a simple question. If you hold a slinky up in the air and you let it stretch until it settles and stops bouncing, then you let the top go. Does the bottom remain fixed in space? Pull up or go down? Okay, we'll let it cycle again. But they answered the question by stewing slow-mo video on the drop. And then they tried to figure out, well, what is falling like you'd expect an object to do in a gravitational field on Earth? And they dropped a ball as well. So that's what Sophie's doing here. So watch, she lets go of the top. The bottom hangs there for a really weirdly long time. And what's happening is that the stored potential energy in the spring when you release the top, it begins to fall. And the bottom of the spring is accelerating back up toward the top. But it hangs there in space because gravity's pulling it down and it's going up. And finally, the thing compresses and the center of mass is the thing that's falling with an acceleration of 9.8 meters per second squared. And what you can see that is watch when the spring compresses. The ball and the slinky, once it compresses, are falling at the same rate. They maintain the same distance between themselves when they fall. So watch. You can see it's going to happen a little bit fast even in slow motion. But watch when it compresses and now they're falling at the same rate. So it really is the center of mass. So the slinky is falling with an acceleration of 9.8 meters per second squared. But to the eye, it looks like something funny is happening. Like the bottom of the spring has hang time. Okay, like it's defying gravity. And it's not so much that it's defying gravity as it is that the center of mass is not defying gravity, but the bottom is not where the center of mass is and the spring stores energy, which is released when you let it go. And then poor Parker, who was holding the camera, got that nice surprise. So, you know, so good job, guys. All right, enough fun. Let's do some, let's do some physics. Fun time's over. Why not even a triple on that one? Okay, all right, so concepts. So in the reading and in the video, we've started exploring energy. But just to review what we've done up till now, and it still can all be summarized basically on one slide, is we have these things positive and negative electric charges. They're the sources, or in the case of negative charges, the recipients of electric fields. Those fields are vectors and charges can exert forces on one another through this electric field. Charges respond to the influence of an external electric field by changing their state of motion. So electric fields tell charges how to accelerate. The corresponding position and velocity of the particle can thus be modified over time according to the equations of motion that you should have learned in the first semester style physics courses, okay? So like those four or five equations of motion, all relating position and time and velocity and acceleration. And that acceleration comes from f equals ma, and the f in our case is the Coulomb force deep down at the heart of everything. Because everything appears to be made of point charges, okay? So a few announcements in general. Your next assignment is to keep reading chapter 24. So you're going to 24-3, 24-4, and 24-7. Watch an accompanying video that goes with this. Homework three is assigned today. It should be available in Wiley as of 32 minutes ago. And then there are two tacked on problems at the end of the assignment that I've printed copy I make for you guys. So make sure you get that off the course materials webpage. There's an 11th problem that goes along with the theme of this homework assignment. And then because I had a total goof in trying to walk some of you through how to do problem eight on homework two. The one with the half circle of charge. I've decided, you know what, you guys all deserve a second shot at that, whether you listen to my bad advice or not. So to be fair to everybody, what I did was I'm going to give you all 100% on that one problem on homework two in Wiley. So that'll take care of that. And then you get a bonus problem that adds points to homework three if you do it, right? So if you want to do it, you're welcome to do it. If you felt like you were able to do problem eight with no issues on homework two, then don't worry about it and save yourself the time, okay? So there's a bonus problem, problem 12, basically, that's tacked on to the very end of that. And it's a variation on the theme of a circle or semi-circle or part of a circle of charge, okay? All right, grand challenge problem. So I finished shuffling the team, so all the teams should be settled. So Delta and Echo, you guys got emails this morning about the final shuffle. So please finalize that team name. I think some of you have already settled on a team name, the Coulombs or something like that, that I hear one team was going to do this. Or was this just a joke from last night? No, no, it's real. It's real. That wasn't just the lie you were telling me in honors physics? Okay, good, all right, great. So again, email, if you really settled on that, email it to me so I can add it to this list so I can get your real names in place, okay? Choose a lead editor. Remember, that person's job is not to do all the work. That person's job is to make sure everybody does all the work they promise, okay? And then try to coordinate the writing of the document, be a final editor for the document to make sure it's sort of speaking with one voice. All the tenses are correct. All the we's are I's and all the I's are we's or whatever you want to do, okay? Just homogenize the document with the end. So it looks like one person, a very bright person wrote it. Yeah, it's real. That's exactly how long the document's supposed to be. Minimum of ten pages. Single page. I leave it up to you. I should think that's double spaced but check that. So really it's five pages single space, okay? But you know, you gotta put equations in there. You might think there's a figure that's useful for making a point about setting up a problem if there's a drawing you want to put in. And the figures in, sorry. The figures in drawings are excluded from five pages of writing. Well, within reason they count as part of those five pages. Yeah, as long as it's not just like figure, figure, figure, figure, figure, figure, figure, figure, figure, figure, figure, ten pages were done. Yeah. I want you to talk. I want you to tell me what's going on in these figures. Pictures are worth a thousand words, but not in this case. And then source the site from the figures and all that stuff. Yeah, exactly. Yeah, so you're going to do citations if you hold the figure of some biology website, site the website. Or if that website sites a primary source for it, site that one. Okay, so the usual discipline you're supposed to show on writing and acknowledging. Okay, so this really is like a little research paper. You should have a bibliography and so forth. And we'll talk about that at the first team meetings that are coming up. I'll start scheduling those for the end of the month. Okay, you're supposed to be meeting with your team outside of class once a week. I don't care how long, but use that time to talk about how things you're learning in the class might influence a possible solution, a direction for a solution to the problem. Your goal for the end of the month is to have tried to have cooked up as a team one possible avenue of exploration. If you do more than that, that's fine. I mean, I'm not going to discourage you guys. But that's your bar you have to jump over at the end of the month. Okay, it's one possible direction for a solution with some sketch of how you might do the math to try to answer the question. Okay, so what I'd like you to do is to make sure that you guys are meeting and that you're kind of chatting in the direction that's helpful for you. And then I can understand what you're talking about. I would like the lead editor to collect notes and minutes from your team meetings. So if you guys have already had one, go back to your Facebook group or whatever system you're using to communicate with one another. Send each other recollections from the meeting. The lead editor should copy all those down. Look them over and make sure there's no made up crazy bullshit in there. And then email that to me. Okay, so I expect the lead editor to start communicating with me in the next week. I want the minutes from your first meeting or if you've had two, your first and second meeting, sent to me by next Thursday by 5 PM. Okay, so a week from now 5 PM. If I don't hear from your team, I will email you after that to find out what's going on. Don't make me email you, all right? That's already off to a bad start if I have to bother you. With that much notice about meeting for 15 minutes with your team to talk, okay? There's gotta be 15 minutes in your week. You guys can get some ice cream and talk about physics. I mean, that's all I do outside of class. You guys know that, right? You come in office hours and just eat an ice cream. Science and ice cream, that's it. No, nothing, nothing. You're all dead inside. Okay, we'll find the screw you again, a quiz. No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, so let's go over to that quiz question here. Bless you. Or kazoo tight, or whatever. Okay, so what's the relationship between work, W, done by a conservative force field, on a charge in this case? And the change in potential energy of that charge, delta U, so we've got a lot of notation we're gonna start exercising today. That's kinda why I tossed this in, also to see if you have paid attention to the basic definitions, which we'll exercise today. Okay, all right, so what's the relationship between work? done by a conservative force field on a charge and the change in potential energy of that charge. Is it 1? W equals Q times delta U. Is it 2? W equals delta U divided by Q. Is it 3? W equals delta U. The work is the change in potential energy. And then 4, work is the negative of the change in potential energy. Some takers on that. Okay, work is the work done by the field. Okay, and this is where we're really gonna have to exercise freezing today. Work done by the conservative force field is equal to the negative of the change in potential energy. Well, we'll explore that with an example in a moment, okay? All right, two. Which of these is the definition of the electron volt or EV? This is a unit we're gonna see a bunch in the class. I'll even give you guys some extra questions on it today. Okay? Is it 1? The electron volt is the energy of an electron in the ground state of a hydrogen atom. Is it 2? The electron volt is the energy obtained when the electron in a hydrogen atom is released from the atom. Is it 3? The electron volt is the energy gained by an electron moving through a 1 volt electric potential difference. A few takers, okay? And 4, the electron volt is the charge carried by an electron, okay? It's number 3. So if you have an electron, anything with an elementary charge, positive or negative, if it goes through an electric potential difference of 1 volt, it gains 1 electron volt of energy. It's actually not a bad little definition, so, yeah. In the video, there's some reference to hydrogen. What was that? I don't remember. I don't remember. I don't remember. Yeah, yeah. I mean, so I will say this. These actually, these two statements up here are technically identical to one another. If you think of a hydrogen atom, it's a proton with a single electron in orbit around the proton. And it takes 13.6 electron volts of energy to completely rip the electron off hydrogen and move it out to infinity. So this is called ionizing something. That is, moving the electron so far away from its parent atom that it essentially experiences no more Coulomb force from that parent atom. That's what ionization is, okay? So because at the atomic level, all that matters for an atom, for instance, is how much energy does it take that electron in the ground state and kick it out to infinity? That is the definition of the energy of the ground state, that lowest energy state in hydrogen. These two are actually identical statements, okay? So it turns out the number is 13.6 electron volts. That's actually a feature. We can predict that for a hydrogen atom. You can directly predict from the laws of quantum mechanics what the ground state of the hydrogen atom is in terms of energy. It's one of the major successes of quantum physics in its early days. Okay, last one. What's the definition of electric potential difference, delta V? Is it one, electric potential difference is the change in potential energy divided by charge? Is it two, the electric potential difference is the charge times the change in potential energy? Is it three, electric potential difference is the negative of the change in potential energy? And is it four, electric potential difference is the work done by the field, W? Now, no takers in this one? Okay, not at all, it's one. Yeah, this is the one, this is the new one. Okay, this is the new thing. When you do gravity and you talk about gravitational potential energy, we don't really talk too much about gravitational potential itself, although it is in there, okay? There is, just like there is a potential, an ability to store energy associated with mass in the form of gravity, there's a similar potential to store energy associated with the field of charge, okay? The only difference between the gravitational field and the electric field is that the gravitational field has one kind of thing, positive mass, that can emit it. Whereas electric charge has two kinds of things, positive and negative electric charge that can emit or receive it, all right? If there were negative mass, if we, you know, you could look for negative mass, you can look for negative mass, like if we had a slinky made of negative mass and we held it and let it go, it would fall up in the gravitational field because it would be repelled by the Earth, okay? So we wanna move in the other direction other than the one that normally things fall in. So if I let go of this, it falls down. Okay, and that's because it's made of positive mass. You could look for negative mass in nature, in fact, people do this. They use gravitational fields and very sensitive instrumentation and they look to see if it ever falls up. So there are studies of the properties of things called antimatters. Has anyone ever heard of antimatter before, do you people? All right, what happens when matter and antimatter touch one another? Okay, I heard a lot of them. I don't wanna commit, it's Thursday morning, I'm tired. No, come on, louder. They annihilate. They annihilate, what does that mean? They annihilate. I don't know. They destroy each other, right? And energy has to be conserved. So even though there's no more mass left over, you do get like light out of it. So you'll get a gamma rays when matter and antimatter meet, you'll get light emitted from it, normally in the form of gamma or x-rays, nasty stuff. Okay, actually, this seemingly nasty thing has been harnessed to construct something called the PET scan. So the PET scan is when you are injected with a radioactive element. That element follows your blood wherever it goes, or it's just put in the blood stream and it goes where blood goes. And if there's a suspicion that you have a tumor, tumors are often blood-hungry tissue, right? They'll grow extra sets of blood vessels and feed off of your blood system, basically, so that they can continue to live. And so you get lots of excessive blood vessel formation near tumor tissue, in many cases, not always, but in many cases. So you can look for excessive pooling of blood in the body in the form of small capillaries and things like that by putting a radioactive tracer into the body waiting a few minutes so it distributes inside your bloodstream. And then the point of putting in a radioactive tracer is that it will decay. And you pick the right one and it will emit not a matter electron, but an antimatter electron from its nuclear decay. That actually does happen. And so that antimatter electron will fly through your body not very far. It will strike an electron, because you have lots of those in your body, and they will annihilate and you'll get a pair of gamma rays that come out. So just really high energy particles of light. And if you track back the gamma rays to where they came from and do that over and over and over again for 30 minutes or an hour, you could build up a map of where all the blood is on the human body. And you can look for anomalous masses of blood. And this is how you can spot tumor tissue using antimatter. So it's pretty much safe for the person. You get a little dose of radioactive damage from that. Of course, you're knocking electrons out of atoms or literally destroying them. So that's gonna cost you. And you aren't making gamma rays go through your body, but it's not at a high rate. So you're getting gamma rays from outer space right now. Probably at a rate that's similar to that. You're doing fine. Probably what you're doing fine. So antimatter is kind of cool stuff, but there's a big question. Does it have negative mass? Does antimatter have negative mass? And the way you test this is you make a bunch of antimatter and you watch what it does in a gravitational field. And there have been recent experiments with anti-hydrogen. So making anti protons, anti electrons, putting them together into anti hydrogen and then watching what it does in a gravitational field that reveal that it too falls in a gravitational field. So even though it's antimatter, it does still have positive mass. So that's actually a very basic question about antimatter that it took a long time to answer because you needed very sensitive instruments to do it. So we're gonna explore fields and conservative forces and all that stuff today. And by doing that, we're gonna explore how one sets up and solves problems involving energy and electric fields. So before I get into your problem, let's kind of go over the basic things we're gonna need for this. And a lot of these are actually related to gravity from semester one and we're just gonna apply them to electricity in semester two. All right, so there are sort of old concepts in that sense, but they're universal. As long as you have a conservative field of force, one that you can put energy into by moving something in the field to store potential energy and then get the energy back by letting it go and converting it, for instance, into kinetic energy. This is what we can do with my little pointer here. So this pointer is a mass. We are surrounded by a gravitational field from the earth. And the way we can become aware that it's there, we can trip and fall. That's one way to become aware that gravity is gonna yank us down to the center of the earth. That hurts. Let's drop this thing. It doesn't have any nerve endings. So I can do work against the gravitational field. So this is costing me breakfast energy. I had nice breakfast at Long Metal Endless Morning at like 6.30, so much I like you guys to get in really early on Thursdays and Tuesdays to prep for this. You can tell the quality of the demonstration. Dropping my own pointer. This takes preppy, okay? One day when you're all teachers, you'll understand. All right, so I had eggs and a tomato and a little croissant and coffee, all right? So that's digesting in my system and that's being converted eventually into ATP which fuels my cells. And so my cells, some of my cells are muscle cells and they respond to electrical forces. So they will contract and expand according to internal electrical generation in my body. So that's how you can stretch your arms out and pull them back in, okay? So I can relax my muscles. I can compress my muscles. That's just electricity doing all that stuff for me. But that energy has to come from somewhere. It comes from breakfast or copious stored fat cells for my many decades on this planet, okay? So, you know, I gotta be honest with myself, right? So, like I said, I'm as much a rumor as I am a drummer. So, you know, you can tell. So, and if you heard me drum, you know what I mean. All right? So I can use my chemical energy. I can move my arm. Now this is costing me because I'm doing work against the gravitational field. But the good news is, is that according to physics, I have, apart from the little losses from friction and heating of the air when I move and things like that, I've stored most of the energy that I use to get that pointer up to this point in the gravitational field, in the gravitational field. And I can change the energy from gravitational potential energy to kinetic energy simply by letting go. All right, so once I cease to make a counterbalancing force against gravity and I let the field do all the work, the field wants to move this from a region of high potential energy to low potential energy. In fact, if you had to summarize all of nature in one sentence, it is simply that nature is constantly trying to move everything from high potential energy to low potential energy. Nature abhors things that are at a higher energy state than they need to be. This is why when you excite an atom, if you take a hydrogen atom and you bombard it with light and you knock its electron up to its next orbital shell, if you wait, it will spontaneously fall back down to its ground state and then emit some light. That's because of this operating principle of nature. Nature really abhors things being in energy states that are above the lowest state. And if it can move you to the lowest state, it will, all right? And that's why we fall. When we lose control of our body, we hit the ground because nature really wants us to be in the core of the earth. So it's a good thing electromagnetism is pushing back against us from the electrons and the carpet on my feet or I would be down in hot liquid magma, some nickel iron core right now. That would suck. That would be a bad ending in my Thursday. Nature's constantly trying to get you to the lowest energy state. Now thankfully you can ingest food from the environment, process it, convert it into stored energy and use it to kind of fight nature. But of course you've used up energy from the environment to do that. So it is kind of a zero sum game in all of this, right? Eventually you're gonna have to find a way to put energy into growing more food and it's a vicious cycle. Does anybody know what the major source of energy on the earth is by the way? Where do we get all the energy that we're able to take from the environment without having to really worry about giving it back too much? The sun. Yeah, the sun. The sun is the major source of energy in our solar system. The sun wasn't here if it just winked out and went away. The temperature on earth would plummet. It would take a long time. The atmosphere stores energy through trapping of infrared radiation. But eventually you would settle down. There's another form of energy on earth. What's the second most abundant form of energy on earth? That's actually responsible for the temperature of the earth being so high for so long. What's that? Fossil fuels. Well fossil fuels are only useful if you burn them, right? And the earth doesn't really normally burn its store of fossil fuels. They kind of sit there in the ground and have to drill them up and then set them on fire after refining them, all right? But there is something we take from the earth that has this property that generates heat in the earth and keeps it warm for a long time. People are very afraid of it. Lava? Well, I'm pretty terrified of lava. How many lava plants do you know about? Yeah, oh, okay. It's the major source of power in France? Nuclear, yeah, nuclear stuff. Radioactive elements, uranium, thorium, all that stuff, believe it or not, there's a lot of that mixed into the earth. And if it weren't for the presence of those radioactive elements, the earth would be a whole lot cooler than it is now, even with all that sun solar radiation bombarding us all the time. So sun, radioactive elements, and then lots of other little things that contribute as well, but most of our energy comes from those two things. That's why the earth is not as cold and dead as it should be now, thanks to radioactivity. So we've grown up in a radioactive environment. Our bodies know how to handle that. Our genes have error-correcting mechanisms built into them so we don't constantly get cancer and die. Okay, so we've evolved in that situation so we're pretty well adapted to it. But these are things you have to keep in mind when you're kind of thinking about, I'm gonna eat breakfast. It's gotta come from somewhere, right? So it's not a zero-sum game. There's energy coming from somewhere. Mostly the sun, so we're good. Okay, all right, so let's think about gravity now as our model for the electric force. So again, the whole point of gravity, if you wanna just stop and analyze it, is it wants to move things from high potential energy to low potential energy. Okay, so let's think about this in terms of work. All right, so when we say work done by the field, work done by the field, we call that W with no qualifications on that, no subscripts, no superscripts, just W, okay? And work done by the field is positive. It's greater than zero if you move from high U from high U, that's potential energy, okay? So this is potential energy too low, okay? So that is if U final is less than U initial, that is positive work, all right? And again, I can demonstrate that low potential energy, sorry, high potential energy. Field did work, okay? Energy was lost from the field when this moved now. Now you don't notice it, that's good, all right, or gravity would get weaker, but it does happen, I mean we are draining from the gravitational field when we move things, let it kind of move things now, so, perfect. All right, so work done by the field is W. Now work done by an applied force, an external one, like me, okay? If I wanna take this from low potential to high potential, I have to do work. That was exhausting, okay? All right, so that is me applying a force. The gravitational field gained energy, because I took my breakfast and I moved something up, all right, so now I've gained energy in the Earth's gravitational field, but it had to come from somewhere, and it came from me, the applied force. So in a conservative force field, if the only two things that are acting are the conservative force field, in this case gravity, and me, the external actor in the field, okay? What we find is that the applied force must be equal to the negative of the, so the applied work that I do must be the opposite of the work done by the field, so if I give up energy, my W applied is a negative number, but the field gained, okay? So work was done on it, okay? All right, so that's one other handy relationship, and then there's this thing called the work kinetic energy theorem, all right? So if this conservative force field is allowed to do work on an object like this pointer, and there are no other forces present, so I'm gonna remove me, all right? It accelerated and it gained, oh, well, that's fine. We're probably gonna need those batteries anyway, okay? So I'm just trying to get a new pointer, guys. You should know that this is my strategy. Oh, yeah, I broke my pointer, man. I'm gonna need a new pointer, all right? So what happened to the pointer as it was released? The only thing acting on it was the gravitational force field. It accelerated, okay? So it gained kinetic energy, all right? Since everything in nature really boils down to energy, a kinetic energy which is one half MV squared, okay? The change in kinetic energy due to an applied, due to a conservative force field acting on an object is just equal to the work done by the field, okay? So the gravitational field does work. Positive number, W greater than zero, we gain kinetic energy, V goes up, okay? So nice little handy thing to remember. Now let's go into potential energy. I've already kind of hinted at the relationship here between potential energy changes and work done by the field. Let's have a look. If the final potential energy is less than the initial potential energy, then what kind of number, positive or negative, do I get? If I take the difference between the final and the initial potential energy, again, Uf is smaller than Ui. Do I get a positive number or do I get a negative number when I do that subtraction? Negative, yep. So let's call this delta U. Delta U by convention is the final minus the initial, so what you have at the end, minus which is started with, okay? And this will be in the case that this is true, okay? So in the case that this is true, delta U will be a number less than zero. But if the only thing that's moving an object from high potential energy to low potential energy is a conservative force field, then the only thing that's causing this change is the work done by the field. And in the case that this is true, W is greater than zero, okay? When the field does work, W greater than zero, it moves things from high potential energy to low potential energy. But we know the change in potential energy is a negative number, it's less than zero. There are no other sources of energy in the problem. What must be conserved always in a closed system? Energy, right? So whatever is true, we know that the difference between W, so the sum of W and delta U is a constant. All right and since there is no change in energy in the system, the gravitational field does work, this thing gains kinetic energy, there should be a 100% correlation between those things. The only way we can get away with this is if we say that this statement is true, that W is equal to negative U, delta U, okay? Because one of them is a positive number, one of them is a negative number, we gotta introduce a minus sign to relate them somewhere. Okay, that's that statement there. Work done by the field is related to changes in potential energy by that equation. Now, you can always go back to the force and of course the force we've been exploring is the electric force described by, for instance, Coulomb's law when we're talking about point charges. But in general, if any force due to an electric field is simply equal to the charge experiencing the force times the electric field, okay? Doesn't matter what that E is, this is a universal relationship between the force on that charge Q and the electric field that that Q is experiencing, okay? In the case of a uniform electric field, one that is constant in direction and magnitude at all locations in space that matter in the problem you're looking at, you can relate the work to the force and to the electric field through the old work equation that work is just force times distance, all right? So if I have a force and I displace something over some distance, if I know the amount of energy that that thing gained by displacing it and I know the distance, I can calculate the force that acted on it. So energy and force are related to one another through this kind of equation here, okay? And for a uniform electric field, this is a pretty simple thing to have to solve for, okay? Because you just have a constant vector pointing in one direction. Once you figure out what direction delta R points and you can figure out W from that, okay? It's the dot product of two vectors. And then finally we have this concept of electric potential and electric potential difference. So for every point in space that we have a potential energy, let's say here and here. So here's U initial, here's U final. Okay, let's say we have an electric field that points down and we have a positive charge up here at the initial point. The electric field wants to move the positive charge along the direction of the arrow. I've drawn this just like it were a gravitational field, okay? To kind of guide your eye, all right? So we know that the charge wants to move from this one to this one, okay? Because we know that positive charges in electric fields move with these arrows. Okay, this is nice, but one thing that's kind of helpful is that when you just have an electric field and you don't care about what charge you're gonna drop into the field, you just wanna define what's the potential for storing energy at this point in the field. That's where this V comes in, okay? So the relationship between U and potential is just this. Yes, and I have that right, okay? So this is nice because you can define the potential like the potential at point I, the initial point as just the potential energy per unit charge. And this is a handy concept because then just like with the electric field is the force per unit charge exerted by another charge. Here you have the potential energy per unit charge independent of what the charge is in the field. Then you can drop in a charge and figure out how much work is done, okay? And just like there are delta U's, there are delta V's. V final minus V initial. All right, one more thing that's helpful here. All right, so again, like all conservative force fields, again, think of gravity, although remember, gravity only has one kind of charge, positive mass. Electricity has two kinds of charges. Positive charges move with the electric field, negative charges move against the electric field, okay? Like gravity, the electric field wants to move things from regions of higher potential energy to regions of lower potential energy absent any other forces in the system, okay? So for positive charges, this means just like in this picture that the electric field wants to move you from the top of the board to the bottom of the board. But if you're a negative charge, your region of lower potential is actually at the top of the board. So if you start near the bottom, that electric field will move you up. So this is where the analogy with gravity kind of begins to fall apart, right? It's helpful, you can really think, oh, gravitational field points that way, mass is always gonna move down in the gravitational field. But in electric fields, you have to remember what's the sign of the charge? And actually, if you throw in a negative charge there, you'll find out that what I've labeled I and F for a negative charge correspond to the higher potential energy part of the system and then the lower potential energy part of the system for a negative charge, all right? So signs can change everything. Make sure you know what kind of charge you're talking about positive or negative when you attack problems with work, potential energy, and electric potential, and differences in electric potential in physics. Okay, and one more nice thing, just as in gravity, you have the freedom to define where zero potential energy or zero electric potential are located. Okay, so it's often convenient. There is no absolute reference point for energy in the universe. So we just say, okay, well the only thing that matters in nature is changes in energy. Nature just wants you to move lower, okay? So it's convenient to say that, look, the floor is solid and I really don't expect this device to tunnel through the floor and move to the core of the earth on its own. So I'm not gonna define zero potential energy to be the center of the earth where this thing really wants to go. I'm gonna define zero potential energy to be the ground of this room. So if I drop this, now it's zero potential energy by my definition. Now if one of you comes along and jacked hammers a hole in the floor and then kicks this down into the hole, now it's at a lower point. Is that okay? Is that gonna cause a problem? Okay, why not? Can energy, can potential energy be only positive or can it be negative and positive? And then I'll have a commitment here but I'm seeing some commitment here. Yeah, it can be both, I heard both. Yeah, it can be both. So it's okay. It's okay that you have negative potential energy. If I kick that down, let's imagine that this was the original floor and I knock it down here and say, oh man, it's got negative potential energy. Now all the universe is gonna melt, right? No, it's okay. Energy is a relative concept. It's only changes in energy that matter. There's no absolute point in the universe where energy is exactly zero. In fact, in quantum mechanics, you learn that's not possible. You can never have exactly zero energy. So we are free to define zero potential energy and thus zero electric potential anywhere we like as long as it's convenient for the problem. Some choices are better than others. Mostly this just boils down to simplifying a physics problem. You're not gonna change the laws of physics by choosing a different zero point for your energy. You're just, you're gonna get the same answers at the end. It's just how you get there many easier, okay? So be clever if you can. Try to find a convenient place to set zero potential energy and try to simplify your problem as much as possible. All right, so with all those little bits and pieces in mind, let's look at a problem. How many of you have ever touched a nine-volt battery of your tongue? Wow, okay, great. Yeah, what happens? Christo, what happens when you do that? I'm assuming it has any juice left in it. What happens? That feels pretty messed up actually, right? It hurts. We'll talk a little bit more about the biological effects of moving charge or electric current in very well, very shortly in the class, probably in about another week or so. But yeah, it hurts. That little battery doesn't have a whole lot of juice in it, but your tongue is moist and salty. It's a decent conductor on the surface. You've got nerve endings in your tongue. Nerve endings are excited by electric currents, and that's fine when your body's kind of in control of it, but when you introduce an external source of electric charge into your body, you can cause all kinds of terrible things to happen, including stopping your heart and breathing, depending on the amount of charge you dump through your heart and lungs. So we'll explore that a little bit, but nine-volt batteries are fairly safe. You're not probably gonna end your life by touching your tongue to a nine-volt battery, although if you do try this at home, you'd be careful, it's gonna feel weird. It's gonna taste very metallic, and that's not just the metal. The current running through your tongue will affect your sense of taste a little bit. It's sort of sending messages to the brain that aren't real, and it's gonna burn. You won't be able to leave it there for more than maybe half a second or so. It hurts, okay? But it's a great way, absent, and I don't know if this nine-volt battery's any good. That's one way to find out if it's got any juice left in it before you shove it in a smoke detector, and then find out if your smoke detector doesn't work and then have to take it apart again, and so forth. So let's say you decide to test an old nine-volt battery to see if it's any good, all right? Now, when you touch it to your tongue, so let me kind of sketch this up on the board for you guys. Just in case you've never seen a nine-volt battery before, which may be true. Okay, nine-volt batteries have a nice, convenient little engineering design. They're usually shaped like a rectangle, and they have a terminal that kind of looks like this, and they have another terminal that looks like this. And so the reason that this design is nice is because it's very hard to put a nine-volt battery in backward. It's very easy to flip a double-a or triple-a around, put it in the wrong way. If you can't see the tiny little indented plus sign they put on your little plastic device, and you have to get it in the right light when you're my age, your eyes are shot, right? And then you put everything in backward. You can either fry the electronics if it's a bad electronic design, or it just won't work, right? And they have to flip all the batteries around and get it right. Nine-volts are nice, because they're actually designed to only go in one way. So if you try to put this terminal into another receptacle of the same shape, it just won't fit, all right? That's great. So you flip it around, and then it'll just lock together. So that's kind of nice. So here's our nine-volt, and we'll even here, we'll do an homage to the copper top battery by making it look like that with a little design on it so you know which end is up. All right, so there's your nine-volt battery, and you're gonna touch this to your tongue, okay? So you're gonna stick your tongue on it, like that. But when you do this, negative 0.18 coulombs of charge, so the charge transferred from one side of the battery, that is one terminal on the side of the battery, through your tongue, so through tongue, to other side is negative 0.18 coulombs, all right? So can anyone remind me which is the positive and which is the negative terminal on this? I didn't write it in my notes and I'm completely blank. Anyone remember? Do you have battery experts in here? Nothing? No, okay. Well, what's that? Let's just pretend it's the right one, although I know we're guessing wrong, right? We've got a 50-50 chance in the odds or never in our favor. I don't know how that works. All right, so let's call that plus and minus. So batteries are labeled to tell you which side positive electric charge would be emitted from, okay? That's what those little labels mean, plus and minus on a battery. Those are the terminals. A plus side is the emitter of positive charge, but minus side is the emitter of negative charge. Now remember, the convention in discussions of electricity and magnetism is what direction is electric charge going? That's the convention. So if you're talking about the direction that negative charge, the electrons are going and they're the things that are usually moving in a circuit, it's actually the opposite direction of the one that you have to quote at the end, okay? So this item, it's positive charge. This item, it's negative charge. You hook this up to your tongue and current is gonna flow through your tongue while electrons are gonna flow through your tongue over to the positive side, okay? So there is an electric potential difference in here. Okay, between these two terminals, you have an electric potential difference of nine volts. That's what nine volts means, okay? We can parse that a little bit. If you take an electron and you want electron and you move it from this side to this side, it experiences a nine volt electric potential difference and that means the energy it has at the end is nine electron volts. That's convenient, right? And if you know how to convert electron volts to joules, you can get the joules of kinetic energy that that electron has when it makes this journey through this potential difference, okay? So already there's a lot of really low hanging fruit in problems like this that if you're asked what's the kinetic energy of a single electron at the end of this, you can even start an electron volts and then convert using the fact that one electron volt is 1.602 times 10 to the minus 19 joules. That sounds familiar. And that's because it's the elementary charge. Because E is in electron volts is a simple conversion to joules. 1.602 times 10 to the minus 19 joules is one electron volt, tiny little number, okay? But remember, atoms are teeny tiny things and as I said, the ground state of hydrogen, 13.6 electron volts. That's a lot of energy for an electron actually, okay? Because they're not very big, all right? All right, so we're moving a whopping amount of current through your tongue. 0.18 coulombs is actually a whole lot. That's a lot of electrons. It divide by 1.602, 10 to the minus 19 and you'll come up with something that's about, you know, 10 to the minus or 10 to the 18 or so electrons that are moving through your tongue. That's a lot, okay? Not quite Avogadro's number, but it's getting there. All right, so this all happens in about one second. So the time it takes for this transfer is one second. All right, so that's how long you'll leave it on your tongue and that's how much charge is transferred. All right, well we've already kind of answered the first question, right? What's the kinetic energy gained by the electrons in this process? But what I'm gonna do is I'm gonna walk you through the sort of tricky calculation. I've already given you a clue as to what the simple way of doing it would be and that is just do this in electron volts and then convert to joules and you'll have answered the question, okay? But I'm gonna walk you through how to use the basic definitions to set up this problem in case you don't have a convenient way out like that, okay? All right, so we are to find the kinetic energy gain. So we're to find the change in kinetic energy for this amount of charge, okay? All right, well let's start with basic relationships for a conservative field of force. There's an electric field in this battery, it's capable of doing work, it has an associated potential energy and an associated electric potential as a result, okay? So the change in kinetic energy for those electrons will be equal to the work done by the field, okay? Which is equal to the negative of the change in potential energy, which if we take this one step further is the negative of the difference of the final potential energy and the initial potential energy, uf minus ui. Again, there's a minus sign in front of us. Let me make this a little bit more apparent, okay? All I've done is just written down a bunch of definitions, chain them together, okay? So if we can figure out this change in potential energy, we automatically can get the change in kinetic energy from that, all right? So let's attack it that way. All right, so the other thing we know is that this quantity here, delta u divided by the charge that's moving through this potential energy difference is by definition the change in electric potential. And the good news is we know what that is, okay? That is nine volts. So already we can take this one step further and say, okay, delta u is equal to q delta v. I just rearranged this equation. And I know that this is equal to the negative of the change in kinetic energy, right? So kinetic energy change is the negative of the change in potential energy. So I just move that sign over here and I can write this equation. So I have this little gem right here, okay? And we're like dangerously close to an answer at this point, okay? All right, so let's go ahead and solve. So we have kinetic energy equals the negative of q delta v. Well, we know q and we know delta v, right? q is negative point when a coulomb's delta v is nine volts and all we have to do is plug those numbers in and we get an answer in joules. So fun fact, okay? One joule is one coulomb volt, okay? And we're just all working in these meter kilogram second units. Coulombs is also in the MKS system, okay? So once you get everything into coulombs, meters, kilograms, and seconds, you're pretty much good to go. And since the volt is defined in terms of energy per unit charge, right? Volts, energy, joules per unit charge, coulombs. Energy per unit charge times charge is just energy, joules. So you just get joules at the end of this, okay? Now, next question, what power is delivered to your tongue? What's the definition of power? I kind of clued you guys in that maybe we would have to worry about this by giving you that extra question at the end of last class. What's power in physics? Besides, awesome. You guys get the board? You guys get the board? You guys get the board? Yeah, right, rate of work done. So it's work per unit time, okay? So power in physics, power is the, basically the change in energy over some change in time where the work per unit time, okay? And it has units of joules per second, okay? So it just takes our MKS units and takes it one step further, joules per second, okay? All right, well, yeah, so we want the, in this case, the energy change is, well, space here, so we have power. In our case, we've got charges gaining kinetic energy and they're doing so in some amount of time and the amount of time is one second. Okay, so this is the reason I picked this one for the instructor problem. It's got really easy numbers in it, right? Look at me, so clever. This is just 1.62 joules per second or 1.62 watts. A watt is a joule per second. Another, you know, when you're famous and you discover something, you get stuff named after you. Either you do it, which is kind of egotistical or somebody else does it for you, which is kind of a nice present, okay? So watt, of course, was a physicist and has this unit of power named after him, so yeah. I was being a little loosey-goosey with that. So it's whatever the change in energy is, no pun intended. It's just the change in energy over the change in time. So it could be the change in potential energy, it could be the change in kinetic energy. In this case, let's see, so it was the power delivered to your tongue. So that's going to be what these charges do is they smash into your tongue with all their kinetic energy and that's going to be 1.62 joules per second or once, yeah. Okay. All right, so you know, this hurts and if you kind of remember back to chemistry and like heating up water, how many joules of energy does it take to take one gram of water up one degree Celsius in temperature? Anyone roughly remember? Guestimate. Order of magnitude. You have to get it within a factor of 10. Does that make it comfortable for anybody? Israel, you're smart. Smirking, what is it? Don't smirk. Smirking. It's 0.64. Holy crap, you're just going to bust out like two decimal places on this? Yeah, okay, you're in the right order of magnitude and what are the units on that number? Yeah, right, so if we're doing one degree Celsius, it would be like something in just joules. Yeah, is that four something, 4.162 joules, right? Per gram, per degree Celsius, that's what's required for water, something like that. You guys, Wikipedia, I mean, you've got computers open. Come on, Justin. I was about to start. Oh, were you? Yeah, I know, it was like Facebook, and I mean, this class is so boring and now shit, he's on to me. I've got to go look something up on Wikipedia now. I hate my professor. Yeah, so. I'd love to write my professor, just. Yeah, great, yeah, I know, you guys in real time hate me, it's fine, I don't care. It doesn't change my, I'm going to associate professor, screw all of you, I got 10 here. Say what you want, so. So, any, did you get the number? Not yet, 4.162 joules. Stop doing it. Sorry, because I'm blathering on. Don't be distracted, Weston, don't let me fool you. Rookie move. I don't know, I'm so confused right now. Yeah, go ahead, go ahead, go ahead. It's what, the specific heat of water or something like that, I think that's the name. We had to get this exact chemical length. 4.186. 186, okay, it's 4.162, 186, okay. It's joules per gram per degree Celsius or degree Kelvin, it's the same thing, yeah. Okay, yeah, one calorie per gram, that's the easy way to remember it. Yeah, okay, great. So, you're dumping 1.62 joules per second into your tongue. Pretend your tongue is all salt water for a second, right? So, it's probably got a related heat capacity to just pure water, but basically it means you're able to raise your tongue temperature by about a degree Celsius every three to four seconds. What temperature change can the human body detect? Roughly, does anybody know? How do you know when the temperature's changed in a room, when it's changed by how many degrees? In what units? Fahrenheit Celsius? Celsius. Celsius, okay. It's actually even less than that. Yeah, it's about a degree Celsius. Yeah, it's like about a degree Celsius, about two Fahrenheit, so about half that in Fahrenheit? Yeah, so about roughly two degrees Fahrenheit, you can go, man, it's gotten hotter in here, or it's getting colder in here. So, that's why you can change your temperature by a degree in your house, but not by less than a degree. Because you're not really gonna notice less than a degree, but you will notice two of them. And in Celsius, that's roughly one Celsius. All right, so in about three or four seconds, if you left that on there, you'd notice your tongue is starting to heat up too. Okay, because you're dumping a lot of energy into it, and your tongue is a lot of water, so it's gonna heat up roughly at the rate that water does. Okay. All right, now you get a problem. All right, so portable defibrillator. All right, so again, you can group up, work together on this. So, fundamentally, we're gonna come back to this device a little bit more in the class, but a portable defibrillator is basically a device for storing a large amount of charge, and then delivering that charge through the human chest. Okay. With the goal of rebooting the heart. That charge is actually not that big. You notice we went from 0.18 coulombs of charge being moved across your tongue by a nine volt battery to a measly 145 micro coulombs of negative charge being put through an electric potential difference of 2.3 kilovolts, okay? Nine volt battery, 0.18 coulombs, 2.3 kilovolts, 145 micro coulombs of 10 to the minus six coulombs. All right, but that's sufficient to completely reboot your natural pacemaker, all right? So, part A, what's the change in energy of the charge as it moves across this potential difference? And part B, and I've got more when you guys are done with that. If we assume the electric field across the chest is uniform, and this is the new piece that I didn't just demonstrate for you. So imagine, clear, click, okay? That thing's gonna set up an electric field through your heart. Let's pretend, this is a big approximation, that it's a perfectly uniform electric field, okay? No weird wiggles in the field lines or anything like that. They all point in the same direction. They all have the same magnitude. What's the strength of that field if the paddles are 25.4 centimeters apart on your chest? Okay, get to work. And then when you guys run out of these questions I have more on the next slide that you can play around with. So, group up, talk together. Let's see if you know everything.