 voltage less than five. First of all a little bit of review again I think I've said to you you're gonna find in a lot of the diagrams the micro Coulomb symbol is kind of overlapping but we have it here as well. It says we have a two micro positive two micro Coulomb charge or 75 centimeters east of it it asks what's the electric field there okay. Electric field from a point charge is k q over r squared that's right from your formula sheet. So the electric field is going to be nine times ten to the ninth q oh two micro Coulomb's two times ten to the negative six all over point seven five squared of the glory. What do you get? Remember we said electric fields are usually in the thousands or tens of thousands or even hundreds of thousands so what do you get? 32,000 units. Units less talking more learning units. Now if you can't remember the units for electric field look at your formula sheet seriously. Find the equation for electric field there's two of them. There's two of them that have the e. Find the smaller cleaner tidier one. What is it? Oh what are the units? Look at the look at what the units have to be. Aaron what? It's got not Newton Coulomb's because that means times it's Newton's per isn't it over Coulomb's right? Newton's per Coulomb. In other words the units are there and just got the units are there. The electric field is Newton's per Coulomb. You guys see where I said that where I pointed you there? Okay. Oh direction how do I figure out the direction of the electric field? I ask which way would a positive charge want to move if it could? Which way would a positive charge want to move if it could? It's not meant to be a hard question. Look at this charge imagine a positive sitting right there. Which way would a positive want to move if it could? Northeast, south or west? I would write I'm good with but did they say east in the question as part of the instructions? Then I'll use east west notate. If they say right left I use right left. They say east west I use east west. I'll use east. I wouldn't take marks off. I don't think they went on the provincial but I'm not sure. I've only marked the physics provincial a couple of times and I didn't actually mark an electrostatics one. I don't know how they what their criteria is. B. C. Skip. We're going to do D. The reason I skipped B and C is it's one Coulomb and one Millie Coulomb. The ones don't change anything and I'm worried that when you're studying later on you might think oh it's the same answer. No no it's just because there happened to be a charge of one so I want to get a different answer. Here's what it says for part C. I'm sorry for part D. Charles what's it asking me to find? Now put your pens down. I could do this. I could. Don't write that down. I could do this because I put a second charge right there that's Q2 and I could say oh there's my distance except. Do I know the electric field here already? Yeah it's 32,000 Newtons for Coulomb east. So I have another equation on my formula sheet that has force and electric field in it. Both. What? And if you're hint if you're wondering it's also why I asked you to find that equation for the units. It's the same equation. What equation Aaron? And this is force at that location over charge at that location equals electric field at that location. So if I wanted to find the force, write this down by the way, take your pens. If I wanted to find the force how would I get the F by itself? Cody. As it turns out we could use Coulomb's law but we can just go like this. E Q which is 32,000 times oh this is not micro Coulomb's this is Millie Coulomb's. Millie was I think 10 to the negative 3 on your formula sheet is that right? Yep. Two Millie Coulomb's. I think I do this in my head. 2 times 32 is 64. Is it 64 Newtons even? Someone don't check me. And it's force so Newtons. Direction. If I put a positive right there which way is it going to want to move? And it is a positive they gave me so which way is it going to want to move? East. Now if this shortcut makes you uncomfortable Leslie what is oh I should put a vector there technically what is the equation for electric field? Well if you look up for a second it is KQ over R squared if in my mind I put that there don't actually have KQ Q over R squared I have the force equation in disguise it is the force equation in disguise. If you plug that in for E you'll get Coulomb's law formula number one in your sheet. But if you know the electric field and you know the charge at the same location then you know the force at the same location a little shorter. The electric field tells us the Newtons of force per Coulomb at that location. For energy there's a similar concept an analogous concept that tells us the jewels of energy per Coulomb at that location. So electric field is how many Newtons of force any Coulomb at that location experiences? Voltage tells us how many jewels of energy any Coulomb at that location has. We call it voltage. Well actually we don't. It's commonly called potential. I prefer the term voltage because listen closely to the English here. The potential tells you how much potential energy you have per Coulomb. Did you hear me say potential twice? Those are two totally different concepts. Potential energy is jewels potential is volts they're totally different they're related but they're totally different and I think it's confusing terminology unfortunately it's the standard they're going to call it potential. I'm going to say voltage also because you know what symbol we use for potential? V for voltage which makes it easier to remember. So the units of potential or voltage are jewels per Coulomb but as it turns out one jewel per Coulomb is the definition of one volt. We must be careful not to confuse potential with potential energy. This is where I'm sorry keep your formula sheets out keep looking at them memorize what goes where keep stuff straight because Matt watch. This is the force between two charged objects. This is the electric field between two charged objects. Do they look fairly alike? This is the potential energy between two charged objects. Oh except they don't use PE they use do they look do they look do they look fairly alike? This is going to be the voltage between two charged objects. Do they look do they look do they look do they look fairly alike? Oh it gets better. This is potential energy this is potential not energy but potential how do you keep them straight keep up with the homework I'm erasing this we're going to do this later on in our notes and I just realized I kind of went halfway over the page it won't print properly but this is where we're going to have to really keep things straight. Here is the definition of voltage so voltage is defined as how much energy per charge jewels per Coulomb. Example two says fill in the proof to find the potential or voltage due to a point charge q so if we have to move a test charge q to the field point and then find the ratio of energy per charge potential energy we said yesterday was k big q little q over r not r squared mr duic that's force over r where big q is the planetary fixed charge and little q is the moving satellite charge if I want to find the full voltage it's this divided by q because it's energy per Coulomb it's this energy per Coulomb who's in my math twelves I would never write it like this Kelvin I would write away want whatever one fraction any fractions and then I would say to myself self how do I divide by a fraction this simplifies to k q q over r times 1 over q what do you notice the little q's cancelled the little planetary moving charge cancels sorry not the planetary little satellite moving charge cancelled sorry folks I can't kick this card and I'm not going anywhere warm for spring break rest and this is where we get the voltage near a point charge equation okay big planet over r if you're in orbit around a planetary charge that's your voltage that's how much energy per Coulomb that's why batteries are measured in volts by the way batteries are measured in both but they're really telling you is how much energy each Coulomb of charge has and using that you can figure out then how much work this battery can do if it's a remote control toy how high it can lift the toy or if it's a calculator or an iPod how long because there's also a function of time in there how long it can last before dying and again the bad news is when you look at your formula sheet the first equation the second equation the first one on the third row the first one on the fourth row look at all look a lot of light well keep them straight let's try some example three says find the potential or voltage 75 centimeters east of a two micro Coulomb charge in fact example three is the same as the first example that we did erin except instead of electric field potential and then instead of force potential energy so let's find the potential the voltage is going to be k q over r i believe that's the correct equation yes which is going to be nine times 10 to the ninth two times 10 to the negative six all over 0.75 if you're lucky you might have this in your calculator but with a squared in it you might be able to just go second function enter backspace and delete the square what do you get by the way most voltages in the thousands hundreds of thousands sometimes 24000 volts once again we're going to skip b we're going to skip c and we're going to go to d and once again i'm going to say that you put your bets down now d we magically put a two micro Coulomb charge there and it says find the potential energy lastly i could do this that is uh from your formula sheet that is potential energy but do i know the voltage right here you see we defined voltage as energy per Coulomb for charge get the potential energy by itself the potential energy at that location is going to be the size of the charge at that location times the voltage at that location it's going to be two times 10 to the negative three times 24000 units it's voltage you know what a measure voltage in yeah named after scientists whose last name was no volta italian he built one of the first chemical batteries he was one of the first ones to say oh if i put different types of metals together with some i think he used uh some kind of acid clock clocks sorry what's the answer or 48 sorry and i you know what kim units what did we find not voltage what did we find no we didn't find potential because potential is the same as voltage this is why they pick bad names i know it's not potential it's potential what which is measured in no what's energy measured in joules do you see why like by the way kim the math we've done so far up to lesson five i don't even think we barely cross multiply but do you see the potential for confusion do your preaching to the choir never mind oh no i'm not preaching to the choir do your homework if we know the change in voltage why that sounds like now there is a fancy term for change in voltage what's change in anything final minus initial and you know what a math word for minus is difference so the fancy word that they use for change in voltage is there sometimes say find the potential difference then we can find the work required to move a charge between these two points says find the potential at point x how many charges are there in this picture two so once again less than going to use the principle of superposition if they want me to find the voltage right there i'm going to temporarily ignore that one and just find the voltage from this guy then i'm going to temporarily ignore that one and just find the voltage from this guy oh can we all let's go back to this box here draw a little arrow and write the word scalar because voltage is a scalar and what that means is we're going to put in the signs we're going to put in the negatives and positives it didn't matter so far because all we've had were positive charges but if they give me a negative charge i'll get a negative voltage in fact most often that's what you have when you're dealing with a circuit or a battery it's actually a negative voltage because we can move electrons around way easier than protons so going back to here i'll call this charge oh i don't know a and charge b charge one and charge two charge alpha charge beta i don't care and part a they want me to find the total voltage the voltage right there the total voltage is going to be the voltage of a which is k q a over r a matt what's k yep probably the easiest constant you'll ever come up it's seriously it's one of the only nice ones out there nine times 10 to the ninth q two positives i won't put the plus sign but positive 2.5 i think that's supposed to be micro coulombs again all over what's r this distance here which is oh 0.2 what's the voltage from charge a at location x don't all rush for your calculators at once i think this one if i recall is in the hundreds of thousands i think hundred twelve five hundred it's not my final answer so i won't do sig figs just yet units this time kim yay need after a scientist his last name was no volta now i also want to find the voltage from location b but take a look at location b erin is location b the same charge is location a it is and is the distance the same as distance a in other words i'm going to say you're going to be putting the same number there and the same number there i'm just going to say the total voltage at location x let's make that a v mr do it cannot you the total voltage at location x is two times a hundred and twelve thousand five hundred because both these happen to be identical and greg because voltage is a scalar i don't care about i don't need to know theta i don't care about that's a scalar who cares uh 250 000 volts yes 225 000 volts that's what i said what does b want me to find what does b want me to find the potential another word for voltage well that's going to be nine times 10 to the ninth still 2.5 times 10 to the negative six oh better location why i'm going to use this distance here which is which is what what is this distance here 435 can someone crunch that please my friends i can't hear sorry 64285 anybody else 64286 units volts that's the voltage from a erin does charge b have the same charge as charge a is the distance the same then you know what the voltage from b is going to be identical to the voltage from a so i'm just going to write voltage b equals the same answer the voltage at y then is going to be two times 64286 what do you get you get that 128 500 600 sorry i get 1.29 times 10 to the fifth joules volts did i say joules i wrote volts boy what kind of drugs are you on mr do it oh some good cold ones c justin what does c want me to find that doesn't say voltage is it there's a potential difference change in voltage they want me to find that justin my friend what's changing anything what's my final reading the question what's my final location x or y read the question carefully oh we're ending up starting at y ending up at x so it's going to be right starting at y doesn't say that so there's my initial and my final final minus initial it's going to be 225 000 mixed up 12 let's see 225 000 minus 128 600 boy i'm battling wake up mr good it's not helping my throat at all so whatever i'm working on uh 225 000 minus 96 428 units this is still voltage d here is the whole point if i gave you this i'd probably just give you d and say go to town hannah once you finish yawning can you read d to me please put your pencils down normally up until now we would be going don't write this down hey work equals change in potential plus change in kinetic and uh starting at rest ending at rest and you could go change in potential and you could go change in kinetic we got a better way in moving from here to here it's talent we've just calculated we traveled through 96 400 volts and do you remember how we defined volts we defined volts write this down in just a second not yet as energy per coulomb oh per charge i think that means the change in voltage is going to be the change in energy per coulomb and work is going to be the change in potential plus the change in kinetic can you see a shorter way to write change in potential energy that's change in potential can you see a shorter way to write change in potential energy in other words can you get this by itself no no this is a completely separate equation take this equation here get change in potential energy by itself see this is going to give us a new equation for work as it turns out work is also going to be q v about q change in voltage you want to know how much energy you have to supply to move from y to x all you need to know is how many volts you're traveling through and multiply it by how big the charge is that's how much energy you need in our case how big a charge are we moving what does part d say milli or micro milli how many volts are we moving through nine six four two eight how much work 121 joules this method used in d is a much quicker method given the fact that we have two points that are not at right angles in fact here's the beautiful thing about this this Leslie both energy and work are scalars and that means that if I had chosen to go like this to get to x the answer would still be the same it doesn't care about what happens in between it just cares about before and after or even if I decided to go like this the matter whatever I lost I'd gain back and eventually I'd end up with the same total so next page if the charge is beginning end at rest carly the work will just be the change in potential energy which is the charge times the change in voltage work is going to be that sorry I won't introduce the wings yet that comes later later on we're going to have an equation with two v's in it one capital one lowercase and because my capital v's look an awful lot like my lowercase these because I don't have lined paper I add little wings to my capital v to make it work better so it says prove that if the charge q begins and ends at rest then this equation is true well we said this work is equal to change in potential plus change in kinetic except sophie if you start and end at rest that's zero what's changing anything I'm not going to use that instead what I'm going to say is and I also know this the change in voltage is equal to the change in energy for coulomb that's on your formula sheet I believe is it not I think second row or third row second row which means if I get this by itself Aaron how would I get the p e by itself multiplied by q work equals oh and if you're not beginning at ending at rest you would just drop the change in kinetic down and you can go final minus initial let's summarize we can find voltage by using the definition voltage is energy per coulomb or we can use the point charge equation voltage is k q over r and we can find energy in two ways we can find potential energy by going k q1 q2 over r if we know both charges and how far they are apart we can also find energy by saying the energy at any location is going to be the charge at that location times the voltage at that location a little note a little reminder potential energy and potential are not vectors and they have no let's try that again potential energy and potential are not vectors so they have no direction that means that we're going to include the sign positive the negatives but the other nice thing is that means if we have several charges contributing potential energy or voltage we just add them all up we don't care if they're not a nice street line we don't add them vectorially we don't worry about going winter minus add them up homework what did i assign this morning well i gave out one two missed one no one two four five seven nine one two four five seven nine one two four seven or was soapy saying no no nine i mean yes number nine