 Bear with me. I'm still fighting my cold So homework from lesson five number seven Which I like says a proton is accelerated from v equals that many volts to v equals that many volts Miguel what's number seven asking me to find Okay As soon as they start talking about speed in this unit I Start thinking I'm going to solve this using energies. I'm going to solve this by going Kinetic energy initial plus potential energy initial equals kinetic energy final Plus potential energy final I think we're starting from rest so I'm fairly sure I can do that When we're talking about point charges Potential energy is no longer Mgh it's electric potential energy But when they give me the voltage so you have your formula sheet in front of you I hope you do by the way, I hope all of you have your formula sheet in front of you Don't be really handy. Can you find me the equation for EP potential energy? Now that one I would use if I had two charges are there two charges in this question Find another equation that has PE in it or EP in it Not change in velocity Change in what? okay potential energy is Although if you want the potential energy at one location You can just do that in other words. I'm going to take this equation here And I'm going to rewrite it as I'll scroll up a little bit here. Oh too far Qv initial Equal that's potential energy initial A half mv final squared Plus Qv final I Got a problem here and Miguel you actually actually kind of tumbled on to it initially you didn't call it voltage on the formula sheet What did you call it initially? The fact that I have multiple V's here my physics prof when I was in college He said since voltage is capital V But you can't really tell a capital V from the lowercase V when you're writing in a hurry He always put little wings on his capital V's and I'm going to start doing that from now on He put little horizontal bars. That's a capital V for voltage. I'm going to do that for the rest of this unit Okay Do I know the charge? Proton what's the charge on a proton? Do I know my initial voltage? 300 do I know the mass of a proton? Oh? 1.67 that's not that's not the charge on a proton Okay, by the way the number that you read me does isn't there a kilograms next to it? Yeah, let's not do that 1.6 times 10 to the negative 19 is the charge on a proton a Guarantee it does not You're looking at kilograms you're telling me the mass of charge Okay Hey folks first day back five people late come on. I know one person had a legitimate excuse Can I go back to here now? What's the charge on a proton? Sorry? I? Can't hear you speak louder No, no the whole charge you need to find it on your sheet Yes, it's the elementary charge That's what it's called on your sheet and you all need to know that because I will not help you on a test In fact, I will mock you mercilessly if when we get to the test you find that you were unable to get the charge Okay, so 1.6 times 10 to negative 19 additional voltage 300 Where am I 300? Mass of a proton. It's on your sheet. What I have no idea what you're saying. You need to find it and speak louder. I Think it's called mass of a proton Yes V is what I'm trying to find What's the charge on a proton? final voltage is 200 so what I would do first of all is I'm gonna minus this over Q the initial minus Q the final Equals one half m The final squared and I've told you I'll put the wings on the capital V for voltage so I can sell the difference You want me to keep going or can you take it the rest of the way yourself? Okay, and this will be talking about a lot more in the next couple of days as well That all right any others from the homework Yep Yep, so I'm gonna race all this is that okay, Miguel No, sorry Okay What do they want us to find who asked them to add them? What do they want us to find? I like this question. I like this question. What do they want us to find by the way 9a? Okay, remember Potential is another word for voltage and I know it's easy to get potential mixed up with potential energy No, what's the equation for potential from a point charge the equation for potential or for voltage is? K Q over R They want the total. What does the word total imply? What mathematical operation when they say total month? I Think I'm gonna call this charge a I'm gonna call this charge B I'm gonna find the voltage at charge from charge a I'm gonna find the voltage from charge B And then I'm gonna add them up Okay This is gonna be 9 times 10 to the night one oh One whole Coulomb So not one times 10 to the anything one whole Coulomb. That's a huge charge. It'll probably kill you All over the distance is two meters. I think you get 4.5 times 10 to the night that I can do in my head It's gonna be 9 divided by 2 B now voltage is a scaler So it's still gonna be the same equation 9 times 10 to the night But the charge here is negative 2 and we said for scalars you put the signs in all over a distance of 1 I'm gonna get negative 1.8 times 10 to the 10th, I believe volts and volts the total voltage Is going to be 4.5 times 10 to the 9th plus negative 1.8 times 10 to the 10th The net the overall the total voltage there is negative 1.35 times 10 to the 10 There's a negative voltage there. What does B want us to find now? I could go Putting that charge right there, and I could go KQ 1 Q 2 over R KQ 1 Q 2 over R and add them up because I know the total voltage right there the shortcut is going to be why don't I just go? Qb complete with the wings now so that Miguel can tell this is voltage and not velocity You're not the only one someone always does that mistake by the way, and I always bring up the notation right then It's gonna be Q Point two three times ten to the negative six Voltage negative one point three five times ten to the tenth And that should give you negative three point one times ten to negative it is a positive three joules Why negative? Oh, it's telling you if you wanted to move it out to infinity you'd have to do work It wants to stay there Which makes sense because even though this positive charge is repelling it It's closer to this bigger negative charge. It really wants to fall as opposed to fly away Okay Now the fact that these are at angles because voltage and energy are scalars who cares that's the beauty any others Really getting the vibe that people haven't done much of the homework. I I'll warn you one last time you can't cram this unit Nine total so four more and on that note Taylor you've given us a lovely segue into lesson six so far We have been talking about point charges One charge sending out either an electric field or a voltage Miguel the problem with point charges is the electric field is constantly changing because remember the electric field Depended on how far you were away the further you went away the smaller the field and that makes for a yucky math What we would love to find is a situation where we could have a nice Constant electric field Nick so the math was nicer and there is such a situation. It's between parallel metal plates So today we're going to look at parallel plates and some of their properties Another important voltage problem is the parallel plates problem If you have a large flat metal plate and you charge them up using a power supply Circuits, this is the symbol for a battery We'll be doing circuits next unit, but I'm going to Introduce some of the symbolism now The long bar is always the positive bar the short bar is always the negative bar So when we're doing circuit diagrams, that's how you know which one's positive which one's negative So if we hooked a battery up To two parallel plates This would have a net positive charge and this would have a net negative charge electrons would gather over here and protons would gather over here Normally they would repel each other, but this battery is forcing them to be gathering this way and forcing them to be moving this way If the metal plates are very large How large yeah, oh, yeah, not cute like I'm not talking room size, but hand size As it turns out we get a very very nice property We find that the voltage varies directly with the distance from the plates say what when we say that again It turns out that the voltage varies directly as the distance from the plates for example If you knew that this was a 300 volt battery, which means This is 300 volts and this is zero if you were to now Remember there's a bunch of positive charges here each of them is throwing out an electric field There's a bunch of negative charges here Each of them is throwing out an electric field and because we're throwing out an electric field That must mean that if you put a charge right there It would want to move either fall up or fall down Depending on whether it was negative or positive so it has energy and since voltage is energy per cool over there must be a voltage If you measured the voltage exactly halfway You would find that the voltage was exactly 150 volts If you measured the voltage halfway between the plates, so let's add one more measurement or one Let's say that this distance here is Three centimeters if you went one point five centimeters, you know what your voltage would be 150 right there if you measured at that location. Oh if you went one centimeter You know what your voltage would be think about it hundred hundred volts if you go two centimeters You know how many volts you've gone through 200. It's a direct one-to-one linear relationship so Let's imagine that we have plates separated by five millimeters not very far And charge to 500 volts It says make a graph of voltage versus versus distance from the lower plate so if we start at zero volts and We move up one millimeter since this total distance is Five millimeters and the total voltage is 500 Evan it turns out that each millimeter is going to be a hundred volts in other words at One millimeter. I would be at 100 volts At two millimeters, I would be at 200 volts At three millimeters, I would be at 300 at four million liters I would be at 400 at five millimeters. I would be at 500 If I were to graph this We would get that lovely slope right there. What is the slope? Can someone go rise over run? What's my rise? 500 volts What's my run? I'm gonna go point zero zero five meters because it's millimeters. What do you get? Ten thousand or one thousand or a hundred thousand a hundred thousand there we go volts For meter missing a zero Sorry. No, I'm not. Yes. I am Can't remain writing um I? Want to look at these units here I'm gonna do that right here volts we said was Joules For Coulomb so volts per meter is joules for Coulomb per meter so far so good I want to go with this mr. Duke Volts per meter volts or joules per Coulomb per meter. Yeah, okay How do I divide by fraction Okay, when I tidy these up. This is really joules per Coulomb and the meter ends up on the bottom Big deal. Well, I want to tailor look at this What do I measure joules with? What's them? What do I measure in joules? energy What do I measure in? meters Okay I'm gonna say this also Work equals force times distance remember that force equals work over distance What units do I measure work in? Tailor yes, what units do I measure distance in so what is joules per meter actually a measure of in? In fact, this is really Newtons for Coulomb ah Hey Newtons per Coulomb we spent the whole day looking at something that's measured in newtons per Coulomb. What do I measure in newtons per Coulomb? Matt Yes, it turns out the slope of this is gonna be the electric field Kind of a bizarre hey, where the heck did that come from but that's gonna be really really nice We find that for parallel plates There is a constant ratio of voltage drop over distance if you're twice as far you get twice the voltage and This ratio is the electric field even better Ian Was the slope was the slope a nice straight line or was it a curve? Which means the electric field is constant. It's a not changing slope So earlier Miguel I said the problem with electric field with point charges is as soon as you move anywhere The electric field is always changing at least a yucky math It leads to curvy graphs like we had in gravity It leads to stuff that we can't do without calculus However, we can set up a very easy situation where we have nice Uniform constant electric field put two metal plates parallel to each other not very far apart reasonably big metal plates So not little microscopic ones The electric field is thus uniform inside the plates and is given by voltage difference over plate separation Y'all got your formula sheets out. I Think you also I believe have this one Electric field equals that Do you is it written like that or do they have the voltage by itself? Do they have voltage equals ed? Okay, electric field equals change in voltage the difference between the top and the bottom Divided by how far apart the plates are and it's also a vector But this one is a little bit easier to figure out now How do we figure out the direction for electric field? We asked ourselves a question what? Which way would a positive want to move if it could so if I'm a little positive charge right there? Which way do I want to move? Down definitely because the negatives are pulling me down and the protons are repelling me down. I'm really moving down This little gizmo this little gadget here actually was for quite a while the basis behind Most of the technology from the 50s and 60s. This is the idea behind a TV screen Believe it or not a TV screen not the LCD not the LED not the plasmus not the new ones But the old style TV screens the ones that from the side Look like that like and had the big That it's a cathode ray tube. It's an electron gun and the reason they're long is you needed long parallel plates in there You can deflect electrons. We're gonna talk about how that all works. It's actually a very simple technology as it turns out It worked great for 40 years So between parallel plates I have that now How can I keep this one straight from my other electric field equation? So see the other electric field equation on your formula sheet Nick in the top. I think it's the top right one Has that got a little Q in it? Yeah, okay Q is point charge The second electric field equation, which is I think right below it. Yeah Is it I'm going for memory here, but yes, that's also electric fields Got an e do you see a point charge anywhere in this equation here? You see a distance not a radius. That's also our way of saying not a point charge and voltage So you're ready? What kind of questions can we ask you example to find the electric field magnitude and direction inside the plates? So my friend Or I shall yell again so electric field Now I have to ask myself a pre-question before I solve this am I dealing with points or plates Okay, by the way, if you look at your formula sheet top row points point charges Bottom row. I think also point charges. There's Q's and ours. Yes middle row both Some of those can be used for point charges specifically the QB equals energy one can be used But there's also plate ones okay, so electric field is Voltage divided by the distance Can you all look up for a second? It's actually change in voltage and I'll do my wings for Miguel because I forgot to put those there What's the change in voltage here? Yeah, this is almost never the case and what I mean by that is almost always this will be maybe Positive 300 and this would be positive 225 we can never really get stuff down to zero most circuits There's charges on both plates, but the net charge is saying this is more negative than that one What's my change in voltage here still? 225 okay, so often you'll see a diagram like that or what you might see Taylor is a diagram where This is zero and this is negative 225 because I've told you the negative charges the electrons We can move those around really easy can we really move the protons around no We're going to pretend we can't have them, but they're stuck inside the nuclei of atoms They're they're not going anywhere and you've already heard me say Evan Ben Franklin named them wrong You shouldn't name the electrons the positives because they're the ones that are moving. Oh, well, we're stuck with so the electric field is going to be 225 divided by The distance point zero three 7500 units well now I got two options. I can still go Newtons per Coulomb But what's another way that I can apparently measure electric field volts per meter Turns out that's Newton's per Coulomb disguise. By the way, what would the voltage be right there exactly half way? 112.5 half of that What would the voltage be? one centimeter in one third of the way To two-thirds actually I should say I should measure from this way because here's zero one centimeter in which would be right there I'd be 225 divided by three. Whatever the heck that was How does the electric field at the point x compare with the electric field at the point y? So point x is right there point y is right there. How does the electric field compare? This is the beauty of parallel plates the electric field there there there there there there there there there In any of those locations is the same it's the same and I'll convince you of that in just a second but first I need to erase all those little charges that I threw in there for some reason Okay, first of all, what's the total electric field here? 500 is the total voltage divided by what's the total distance? meters please 0.05 right What's the total what's the total voltage? Sorry, what's the total electric field? someone actually do the math please 10,000 10,000 volts per meter or newtons per cool now What would the electric field at location x be well? How many volts have we gone through if we go two centimeters out of five centimeters and it's 500 volts How many volts have we traveled through? 200 so the voltage right there would be 200 Divided by and how far away are we from the plate point zero to two centimeters? When you crunch that you get 10,000 volts per meter the only place E and it's not uniform is right near the ends Which is why televisions never looked perfect? If you ever wondered why they can't do a perfect screen with the old-style TV come close But you could always tell there was some blur Nick really here's what we're saying look up kiddo Let's suppose I put a charge right there a positive charge Which way would it want to move Nick left or right? What's the charge on this bar right here to the right? Okay? Why well? It's really getting pulled by these negatives Now it is getting pushed by these positives, but is it very close to those positives? No However, if I take this charge and I move it right to there These aren't pulling it quite as strong Oh, but these are pushing it a little more stronger because it's moved closer In fact if I move it right to here Well now it's not getting pulled so much but it's getting pushed even more and it's a perfect balance as soon as one of the Pushes or pulls gets smaller the other one gets correspondingly larger and so that electric field that pushing ability Is constant throughout the whole place? What if we compare point charges so example 4 says How does the electric field at the point x compare with the field at point y compare a and b so here? We've already said the electric field is Constant and I could calculate it. It would be whatever v was divided by point zero five What about here and here well here? We said that electric field was not equal to Voltage divided by distance like it was between plates here We said electric field was equal to k q over r squared Will this be constant? Well, let's see if I move from x to y. Does my charge change? Nope Does my radius change yep in fact The electric field at x is going to be bigger than the electric field at y Because as you move further away Taylor, this is going to get smaller As some of you found with electric field hockey a few of you already emailed me your scores or your screen shots still time one student did it with 14 charges which I think is the smallest I've I've had screen sent to me so far. I Don't I think it was 14. I counted it. It's 14. I'll go back and double-check. I got a count on the jpeg, but So most to kids most of the resolutions that I've received so far have been the tunnel solution which works But curious to see if you can figure out how to do it minimal amount of charges Explain your answer using principles of physics. I would then say as r increases e Decreases and I would probably write this over here and maybe find it at the bottom of the page We have a bit of room draw yourself a nice vertical line Well, two of them draw yourself two parallel plates kind of like this Hello line, and we're gonna make this positive Let's say 500 volts And we're gonna make this zero. What would the electric field lines look like? Well, which way would the electric field lines point to the left or to the right? Which way would the arrows point? To the right and remember I said to you how far apart the lines are is How far how strong the field is there? I want to show that the field is the same the whole way through here is what they would look like Uniform lines even the same distance apart Back you know what I'm gonna split the difference here Except at the ends you would find at the ends there would still be some positive charges That would kind of bend like that. You'd probably still get one good one there You probably still get one good one there, but you would also find there was some bending And it's this little bit here that gives TVs blur We'll get more into how TVs work another day. Yep. Oh You can actually with it with the old style cathode ray tube TVs If you put a piece of tin foil across the screen and you clamp two wires on it You can run stuff from it because it's all electrons coming off the screen You can use it as a battery It's all it's also why those old style TVs gathered dust so much because the static dust would get attracted to it Just like balloons being rubbed on your hair to a wall Technical comment we can see why the electric field is constant inside plates and why it varies with distance from a point charge If we graph voltage so this would be the voltage between two parallel plates as distance changes This would be the voltage between two point charges This is a reciprocal graph for those who are in that well. All right, so For all electricity concepts so far force field potential energy I've made a connection to gravity to help us better understand the new idea What's the gravitational analogy for voltage well Voltage also called potential which is energy per charge is kind of like gravity potential Which is energy per mass Because we noticed mass and charge appear in the same spots in our force equation If we restrict our attention close to the earth and ignore orbits, we can use PE equals MGH. You know what? Gravity potential is G times the height Voltage is sort of like the height But it's also affected by how much charge is at that location because the more charge you have the more you want to fall down Gonna make it Dylan anytime you fall asleep Brandon's eyes just naturally stray towards you So it's pretty hard to get away with it even though you're hiding behind Taylor So back to our gravity analogy With this analogy you can think of a parallel plate voltage as a steady sloping mountain a mountain side like that And you can think of point charge voltage as a mountain that's kind of shaped like that In terms of the way the height changes The voltage changes nice and steady The voltage changes rapidly at first and not so rapidly later on thus The field is uniform in parallel plates And it changes around a point charge In terms of direction electric field is away from positive higher voltage and towards negative lower voltage Which is sort of like downhill Kind of I don't know how much that analogy helps for you or whether it hurts you But hear us some questions for you to try and I have a take home quiz for you as well Yeah I decided to give it to you today You didn't get your own time. You need to be quiet. I wouldn't be saying a thing. I'm ready coming after you later number one number two number three Look very carefully at number three. What's your change in voltage not 255 220 okay that most parallel plates are not charged zero and one voltage most of the time there's residual charges in both But the net charges the net voltage is what we're talking about here Four is good five is good Six is good. Oh, that's a wonderful review So so far i've given you one two three four five six and i'm going to give you a take home quiz