 the homework you would like me to go over please. Four C? I was wondering about number four. Four is pretty cool. So here's what we have. We have a mass and this mass is hanging but it's also being repelled I guess by this charge. So if this is a positive charge I'm pretty sure this is a positive charge as well. Otherwise it would be hanging straight down but it's pushed it away. So we should be able to come up with some kind of a set of equations although because I'm seeing angles in four C I think this is going to be like a triangle equilibrium tip to tail kind of a thing. I would say this. Jeez sorry my mouse has updated the driver and I need to slow it down. What are the forces acting? Get the obvious ones. What else? Tension. What else? Electric force and it's getting pushed to the left. So as a diagram it's going to look like this. I always draw the easiest one first mg. I draw the toughest one next tension but I know the electric force is dead horizontal because they place these on the same level with that dotted line there. Okay they gave me the mass so I think if they're talking about the charge q I'm going to use this equation oh and Sally I'm positive that that's 25 degrees when I do my z rule thing and add extra lines and whatnot. You okay with all that? So we're going to get tangent equals electric force divided by mg. Is that okay? We're going to get tan 25 equals fe over mg. I'm going to get the fe by itself. How would I do that? I'm going to move the mg over and I'm going to write over here because I'm running out of room. mg tan 25 but now Sally I'm going to write the equation for electric force equals k q1 q2 over r squared. Let's see. Do I know the mass? 5 milligrams. Millie is 10 to the negative 3 I think if I recall 0.005 grams. G I know tan I know k 9 times 10 to the 9th. That one's going to be showing up a lot this unit. You'll end up memorizing it because it's a nice one. Charge one is 5 micro coulombs. Mystery charge 2 I don't know. Oh radius I need to get this distance here. Oh they gave me a 15 that's 25. I should be able to figure out what the heck the radius is. I think also using trig. Opposite hypotenuse sine 25 equals the radius over 15. I think the radius is 15 times the sine of 25. So let's put everything together here. I have this m you know what before I rewrite it do you mind Sally I'm going to get the second charge the mystery charge by itself. I'll do it algebraically first so we're going to go move the r squared up there and divide by KQ1. I think charge 2 is going to be mg r squared tan 25 all divided by KQ1. Is that okay? Now I like this question in that I love the idea of having something in equilibrium. Well this is you know what this is? This is the magic wand toy I showed you guys last day except instead of having the charge straight up hovering against gravity we've got the charged object a heavier object megan on a rope getting pushed sideways. So with the magic wand I was able to keep it straight up but if you had a heavier object on a rope I would probably be able to push something a little bit sideways at an angle. I kind of like that. I think it's a little overkill not to give you the radius although you know as a nasty multiple choice one I guess I'd be okay. As a written I almost certainly give you the radius. Have we tried crunching the numbers and does it work? I'm running out of room so I'm going to have to try and go straight to my calculator. I kind of find this one a little bit complicated but that's okay. The first thing I'm going to do is I'm going to find the radius which is oh make sure I'm in degrees Mr. Dewick. Are you in degrees by the way? Okay it's 15 sine 25 so there's the radius 6.339 6.34 oh but that's centimeters right? So my radius is not 6.34 centimeters which is 0.0634 meters that's going to make a difference too isn't it? Let's see if this works. m 0.005 there's five milligrams times 9.8 times 0.0634 squared 10 25 closed bracket divided by bracket 9 times 10 to the 9th times what was the charge 5 micrograms 5 micro sorry not micrograms micro coulombs 2 times 10 to the negative 9 I bet you pico is 10 to the negative 9 how much you want to bet that's a guess but that see I got a 2 so I'm pretty sure we're right okay so what I consider this fair game I think with the radius and with uh like I wouldn't give you everything in milli and I give you better units fair enough any others okay so lesson one as far as I'm concerned later on today you can hand in but before you all get up let's go find lesson two because lesson two was electric field that was last day questions from lesson two now is your chance to ask and the homework Ryan was 1 3 6 13 and 17 1 3 6 13 and 17 what did we say last day about electric field Jordan we said that electric field it's sort of like an invisible octopus set of tentacles radiating out in all directions similarly to gravitational field electric field when you have any charge anywhere it's sending out an electric field the problem is because charges come in two types positive and negative electric field is going to have direction what is the direction of the electric field anybody remember how we decided the direction of the electric field we asked which way will a positive want to move that could that's not on your sheet you'll have to memorize that and you better believe I'll have a bunch of direction questions to ask you on your test we also said Dylan it's tough for us to visualize electric field I showed you a few apps that I downloaded that kind of helped but we use electric field diagrams like this where we said the lines the arrows tell you the direction of the electric field the number of lines tells you how charges compare to each other if they both have the same number of lines it's the same magnitude of charge and how far apart the lines are is the relative strength of the electric field if your lines are far apart electric field right here is pretty weak your lines are close together electric field right there pretty strong and I did a couple of uh where are we I think I had a couple of computer drawings if I can slow down enough here we go yeah there's some of the computer sample drawings that I found so questions from that homework any electric field questions go once going twice okay a little worried but we'll move on so what happened to lesson three you may be asking we're suddenly on lesson four I actually last year retype lessons one two and three and I got them done in lessons one and two because we're a little bit behind schedule I'm trying to catch up so I gotta compress some lessons so lesson three was actually electric field lesson two was actually electric force lesson one was actually charge concepts like positive and negatives but you do some of that now in science I think 10 or whatever or science nine so I skipped some sorry electric potential energy what's gravitational potential well first of all what was energy energy was the ability to do work was the ability to exert a force over a distance gravitational potential energy basically if you removed an object from the earth it wanted to fall back down and as long as you were close to the earth here you could just use mgh but we said on the cosmic scale g changed as you moved way out into space but we still said things want to fall back down well we're going to talk about electric potential energy as well let's suppose that Tyler is a big positive charge and I'm a negative charge which way do I want to move if I could then towards Tyler so let's suppose there's an invisible angel and it's moving me further and further away from Tyler what it's having to do it's doing work because I don't want to move this way the further it moves me the more work it has to do because I want to fall down to Tyler but the work gets easier because the further I go away the weaker Tyler's electric field becomes so I can't feel it quite as strong that's what we're talking about though electric potential energy oh except small problem what if Tyler is a positive charge and I'm a positive charge which way do I want to move okay so if I'm doing work it would take work to move me closer to you and that's where my gravity analogy breaks down because in gravity things don't want to fall up they always want to fall down well here depending on the polarity of your charges maybe you actually want to fall up we're going to define electric potential energy in a manner similar to orbital gravity potential energy we say that electric potential energy reflects the work that must be done to move a charge q from a point near charge q out to infinity you may recall that when we did gravity I did a graph like this where this was our and we said the work was the area underneath a graph we're talking about something similar here but not for gravity for electric force so let's suppose that this is a positive charge and this is a negative charge which way does it want to fall which way does it want to move the little tiny charge wants to move to the left so if I want to move it out a very very long way how far away well infinity but we'll just say a very very long way it doesn't want to move to the right I would have to do work I would have to add energy in order to get it to move to the right recall that the force between two charges is not constant so I can't just go force times distance it can't be we can't use that we have to find the area under a force versus distance graph using calculus I'm just going to say trust me on the calculus here is the equation for electric potential energy and if you haven't already you might want your formula sheet out in front of you because you're going to want a lot of the charges and constants and things like that electric potential energy is k q 1 q 2 over r doesn't that look sort of like what we did for gravity in gravity the difference between force and energy was force had r squared energy had r oh and gravity we put a negative in front in electric force the difference between energy and force is force has r squared and energy has r now we don't put a negative in front here and the reason is because there's two types of charge sometimes you will end up with a positive amount of energy out there it depends whether you're dealing with like or unlike charges so we don't simply say oh zero is out at infinity always therefore everything closer is negative but doesn't that look an awful lot like what we did with gravity in terms of the equation okay you want to find out how much potential energy a charge has at any one location that you need to know the big planet you need to know the tiny satellite charge how far away you are oh and then nine times 10 to the ninth is just like g 6.67 times into negative 11 it's the constant that makes the units work by this relationship who's in calculus who wasn't calculus who knows what limits are the limit as our approaches infinity this will work out to zero by this relationship out at infinity you have no potential energy now by this relationship unlike charges if one is positive and one is negative unlike charges have a negative potential energy does that make sense yes because they have negative potential energy they want to be attracted to each other to get them to zero you would have to add energy if you want to add to a number and get to zero you better be starting at negative under this equation like charges have positive potential energy they want to move away from each other to infinity in fact because they have positive energy you have to add energy to move them in closer to each other excuse me for forces and fields you don't put in negative and positive signs write that down this is important forces and fields we don't put in negative and positive signs these are both vectors for potential energy we put in negative and positive signs energy is a scalar one of the things kids get confused with or have trouble remembering is when am i allowed to put pluses and minuses in mr. do it and when don't i forces and fields no signs scalars signs i'll let you come up with your own little acronym but i just remember scalars signs i haven't found a forces and fields i haven't found a phrase that begins with an f for no signs if you come up with something let me know and i'll add it to my little memory trick but forces and fields signs on your formula sheet sorry forces and fields no signs on your formula sheet see the top row don't put positives and negatives in those but you can't write that on your formula sheet sorry the rest of them i think are all scalars but i'll double check that example one find the potential energy of a negative 75 micro coulomb charge that is three centimeters from a positive 120 micro coulomb charge okay potential energy is k q1 q2 over r by the way you want to make sure you know where that equation is on your formula sheet i think it's the first one on the second row yes third row what's on the second row i can't hear you oh voltage okay so first one on the third row it's going to be nine times ten to the ninth the big charge is 120 micro coulombs 120 times ten to the negative six the little charge is negative 75 times ten to the negative six so gordon here we put in the positive and negative for energy we don't for forces and fields why we decided the direction by using like charges repel unlike charges attract or we decided the directions for electric field by saying which way would a positive want to move it could all over point zero three right now how much potential energy does this charge have you get that so it has a negative 2700 joules of energy now what does the negative mean it means that to get it out to infinity you'd have to add energy because out of infinity how much energy does it have zero so you'd have to add 2700 joules you'd have to do 2700 joules of work so b says write a work energy equation if the negative 75 micro coulomb is moved out to infinity okay b work equals change in potential plus change in kinetic oh what does it say to assume starts and ends at rest so what's change in anything potential energy final minus potential energy initial out at infinity what's your final energy it's not meant to be a trick question out of infinity what's your final energy sorry i can't hear zero minus what was our initial energy negative 2700 how much work would it take to move it out to infinity zero minus minus 2700 or what i'm really saying is you'd have to add 2700 joules of energy so the work done by the applied force what would the applied force be i don't know maybe maybe a battery an external source of voltage is moving this charge far away because it wants to fall to the left and we're moving it out to the right maybe invisible angels or maybe it's just a hypothetical math question but you'll notice again justin for energy for a scalar i put the signs in next page okay by this relationship like charges have a positive potential energy and this makes sense because it takes works to overcome the electrical repulsion and push the charges together example two it says find the work required for an external agent angels battery some kind of electric circuit whatever to place a positive 2.5 milli that's 10 to the negative 3 a positive 10 a 2.5 milli coulomb charge five meters away from a positive 1.75 milli coulomb charge note m equals milli equals 0.001 assume we start out an infinite distance away so is this charge here negative or positive positive megan is this charge here negative or positive does it want to move to the left so we're going to have to do work to force it to get closer to this positive charge here's our fixed charge you can imagine it's thumb tacked to the ground or invisible angels are holding it and then invisible angels are pushing it closer and closer and closer and closer and the further they push it the tougher it's getting because the closer it gets the stronger the electric field the stronger the force of repulsion how much work once again gorg we're going to assume we start and end at rest once again we're going to ask what's changing anything what is changing anything so this is going to be potential energy final minus potential energy initial work is going to be k q 1 q 2 all over our final minus where are we starting according to this question infinity what is our initial potential energy if we're starting at infinity zero i'm going to get nine times ten to the ninth big fixed charge is 1.75 times ten to the negative three the moving charge is 2.5 times ten to the negative three and we end up how far away five meters away from each other how much work will it take to move that charge from that charge from a long distance away into within five meters seven eight seven five two or three sig figs seven seven nine hundred joules again just and we got a positive answer because we would have to do work in fact if you asked what if you started out here and then moved out to infinity and if you asked how much work would you have to do you get a negative answer because your initial would be this your final would be zero and what that will be telling you is it wants to fall up and here's where again where my gravity analogy breaks down so for energy a scalar we will include the plus or minus in the equation unlike forces and fields both of which are vectors where we decided the direction ahead of time by looking at the charges polarity now if there is no external agent pushing the charges around around if the charges are moving in the way that they want to then the energy of the system will be conserved example three three so we have an electron here it starts at rest here's a proton which way does this electron want to move if it could to the left or to the right to the left like unlike charges attract here's my question as it's moving it's speeding up find its speed when it's that far from the proton okay is this question talking about speed everybody say yes is there a change in i'm going to say a change in height think like gravity is it falling this is actually a conservation of energy question we're going to start out by going kinetic energy initial and potential energy initial equals kinetic energy final plus potential energy final or any of these zero yeah now the other one that they'll sometimes do ryan is they'll start out and right now where you are this far away from the proton but sometimes they'll start you out at infinity what they're then saying is your initial potential is also zero and they're saying you let it go it's going to fall in how how fast will it be traveling once it falls all the way to the ground all the way to the proton okay so we're going to have this then potential energy initial minus potential energy final equals kinetic energy final and you know what i'm going to need more room i'm going to move that up here potential energy now this is electric potential energy not mga this is electric potential energy that's going to be k q 1 q 2 over initial r initial minus k q 1 q 2 all over r final and apparently that's going to equal 0.5 m v final squared what do they want us to find v final let's see do i know k yeah do i know q 1 yep do i know q 2 yep do i know my initial radius yep do i know yep yep yep oh do i know the mass of what's moving it's an electron yes here it's on your formula sheet what is the mass of an electron it's small so they're going to often give you questions involving electrons and protons if you need the mass it's on your sheet i'm going to crunch the whole left hand side first let's do this this is going to be nine times 10 to the ninth proton 1.6 times 10 to the negative 19 right fundamental elementary charge electron negative 1.6 times 10 to the negative 19 all over jordan i've scrolled down what was my initial distance here minus nine times 10 to the nine proton positive 1.6 times 10 to the negative 19 electron negative 1.6 times 10 to the negative 19 all over one times 10 to the negative 11 i didn't leave you guys enough room i'm noticing i apologize you'll have to kind of write small i'm going to move on to the top of the next page sorry i'm going to crunch oh and that equals 0.5 m v squared i'm going to do the whole left side then i'll divide by 0.5 then dillon i'll divide by m and then square root to get the b by itself is that okay so here we go e nine times 1.6 times 10 to the negative 19 times negative 1.6 times 10 to the negative 19 divided by 2.5 negative 11 so i get negative 9.216 times 10 to the negative 18 minus i notice just in this second expression here it's identical to the first one i just got to change the radius so i'm going to go second function enter and i'm going to put a 1.0 there because that's the new radius negative 2.304 times 10 to negative 17 negative 2.304 times 10 to the negative 17 that equals 0.5 m v squared negative 9.216 times 10 to the negative 18 minus negative 2.304 times 10 to the negative 17 equals i get 1.3824 change colors mr. do it 1.2834 was that right mr. do it 1.3824 gosh 3824 times 10 to the negative 17 and you'll notice i got a positive answer which is good that equals v squared if i divide by 0.5 and here what was the mass of an electron 9.11 i remember that negative 31 and then don't forget to square root oh i like this question i like this question i like this question i like this question i like this question divided by 0.5 times 9.11 negative 31 square root of that and i get v equals 5.5 times 10 to the 1 2 3 4 5 6 yes that's but not faster than light let me re-explain because i see a lot of glazed eyes so because we had unlike charges this wants to move there and they told me this was fixed so this is like my planetary charge megan it can't move this is like dropping an object to the earth but dropping an object from outer space it's going to pick up speed the further it moves to the left it's going to pick up more and more speed it's going to gain kinetic energy how is it gaining kinetic energy it's losing potential energy and then be very very careful with your negatives and your positives and your calculator and your science in the diagram below it says find first of all the potential energy of the system then it says find the force magnitude and direction on the upper 1.5 micro coulomb charge then it says find the electric field magnitude and direction this is far harder than you're going to be asked so i'm going to just talk about this without doing it if i wanted to find the overall potential energy i would find the energy between those two k q 1 q 2 over r i would find the energy between those two k q 1 q 2 over r and i would find the energy between those two i'd have to do some Pythagoras to find what r was and then because energy is a scalar i don't care that they're set up in a triangular pattern or whatever i just add them up energy doesn't care about the shape of the direction of the forces to find the net force on this one here this is pushing sorry this is pulling it in this is pushing it up you would add them together tip to tail by using the force equation to find the electric field right there you would find the electric field electric field electric field add all three together tip to tail too tough i'm not going to worry about it what's your homework number one number two number three four and five so right now it's been one two three four five six is good seven is overkill eight is fine we're going to pause there what have i got here for those of you who are working on the bonus video game there is one solution that a student did a couple of years ago i've seen someone did a lovely solution only using about 12 points now um and it only took them a few tries i thought that was quite clever what we're looking at sorry uh i don't know not yet i haven't got an email from them as far as i know yeah oh apparently you can google your way through it i chose to just do it without cheating so there um we're talking about potential energy and one of the areas that we store potential energy electrically is in chemical batteries how many have a laptop computer okay watch this this is actually pretty impressive demonstration is extremely dangerous do not try this at home but you're about to see is a stage demonstration of a lithium ion battery player in a generic notebook computer to start with we externally force the battery into the runaway state but the actual battery reaction and ongoing chain reaction of each cell is real so how much potential energy is stored in one of these things it's frighteningly impressive the battery cell has just vented the heat from this cell is going to start a chain reaction into the other cells in this multi-cell as you can see by the small smoke trail that first battery cell vented with such force that it blew a hole in the palm rest if this were a real life situation the best strategy would be to move away from the laptop quickly in other words don't try and put out the fire what you saw there was the second cell in a flames shot outside the field of vision of the camera approximately six feet high you just saw the successive venting of the third and fourth cells in this demonstration the fire continues to burn hotter with each reaction and each cell venting becomes worldwide that's my hand temperature is so hot if this were a real situation your natural tendency would be to try to put out this is a very dangerous situation not only is this an electrical fire and a chemical and a metal fire as well going the long components on this fire will only fuel the fire and they get spread you could use a class de fire extinguisher but if you're uncertain stand back and call the fire department there's a battery came from another portable just to the right of the flames in an earlier failed attempt at this demonstration he had struck a portable blunt force causing the battery to puncture smoke but not ignite we took that battery out of the portable and sent it just to the right of the notebook in this demonstration the system used for this demonstration was not a production room it was made of generic parts it did not contain the recall of the battery more of the story is especially those of you that own laptops if you hear about a recall of your battery take it seriously that's a fair bit of energy stored in that tiny little tube that gets attached to the back of your laptop and if that goes or if you drop it and that battery is damaged it is not worth hoping oh maybe I can continue using it buy a new battery okay there is about 25 minutes left this is your chance to get caught up and work on the homework