this chapter or this video series will start off with uh electric fields and if you've recalled we this is not the first time you stared at electric fields right you have seen it in your as uh we mainly talk about parallel plates instead all the weird shapes in your electric field lines so if you can't don't really remember because it feels that very far away as was a long time ago you might want to refresh a bit but here we're going to focus on what happens when the fields are not uniform because the thing about parallel plate is the electric field is the same everywhere ah if the electric field is the same everywhere there is very easy because then the force is constant the acceleration is constant and the work done is very easy to find but guess what in a2 these two things ain't constant so here is an example of two point charges and uh let's observe how they interact or exert force on each other okay so if you remember right once more time you see point charges they have a whole electric field but what happens when you bring two point charges together this is what i'm looking at so currently if you look at the charge of the first one on the left zero mu coulomb charge two also zero so no charge got any false or not you see the force zero zero zero no charge no force what if we try to increase the charge of one of them okay so positive charge for a still no force for you see up there zero point zero newton zero point zero newton wire so in order to have a electric force you need both particles also to have charge so let's change the other particle's charge to some number maybe positive six ah now you see up there now there is a force on q1 by q2 there's a force on q2 by q1 and notice how the numbers are the same for both of them i push you you push me q1 push q q2 push q1 q1 push q2 this is just a representation there's no tiny mannequin here pushing the charges okay try increase the charge all the way maximum and see it can make the force bigger oh you increase one side also both still same force increase increase ah now you can start to see the force arrow already the white color on top so that's a force on q2 by q1 so something here you can take away is the bigger the touch on i guess either one of them the bigger the force that will act on either one of them that's the first one bigger charge bigger force what they've got negative charge on me can make one of them negative you see what happened no neutral negative oy now you see the false arrow direction has changed one they are pointing towards each other which means this is what we call an attractive electric force i like you you like me we are pulled towards each other okay so you can it's do the same thing okay though you figure the touch magnitude the bigger the force and you can see the arrows are now pointing towards each other yeah attractive it's not was repulsive yeah and then even for repulsive the magnitude is the same 2.67 2.67 okay now another thing we can experiment is these two charges are certain distance away from each other what if we change the distance between them maybe we drag one of them closer notice how the force have changed while the arrow becomes so big let me see what is happening the force is greater right the values are bigger 10 to the power of 3 now so this is one thing to note also when you decrease the distance between charges they will push or attract each other even more so this is the case where one is positive or negative yeah so they attract and it doesn't matter which one you pull we only care about their separation and also the magnitude is always the same because newton's third law equal magnitude opposite direction same type of forces electric force and acting on different bodies okay so with all these observations in mind now we have to put it together into an equation let's go and see what this equation will be and who named it after themselves okay so here's the notes let's look at all the ideas you observe but now i put it in sentences words and equations okay let's go so here you can see two the two point charges q1 and q2 to make our lives easier let's assume they are both positive and they will repel each other likewise so we're going to label the forces first this is f21 and f12 which denotes the force acting on q1 f21 and the force acting on q2f12 all right so if you're a bit lost in your own notes you might actually want to write force of charge two on charge one like the simulation just now but we're going to make our life easy and just stick with f21 and f12 so both of those these forces have equal magnitude and we know this from newton's third law all right so we're gonna write about the two key relationships that we have noticed in the simulation the first one being that this force is proportional to the product of the charges so you notice that whether i increase the charge on the left or the charge on the right the force will increase together right and the second observation is when i bring the charges closer the force will become stronger so there's an inverse relationship here and it is the square of the inverse relationship so now to put it in the sentence we put it together we can say f is proportional to q1 q2 which is the uh product of the point charge over r squared which is the square of that separation but you know all these proportional sign not nice for mathematics so we need to introduce a constant okay so introducing the constant this will be k q 1 q 2 over r square all right but what is this constant k so for electric fields and the derivation for this will remain unknown until university k is one over four pi epsilon naught means y like that university now you just use that right okay so it's 8.99 times the power 9 this is given in your formula in your data sheet so epsilon naught is known as the relative permittivity of free space so free space here means vacuum relative permittivity is how much how much did the surrounding allows the point charge to set up an electric field that is permittivity does the surrounding permit you to set up electric field so the relative permittivity of free space so these are all physical constant that was determined experimentally and you are given this you you can choose to use 8.99 to the power of nine which is the whole thing or you can choose to use one over four pi epsilon naught all right so now we're going to write that proportionality relationship but before i go maybe we need to give force a unit just to remind ourselves okay like a good physics student that force has the unit of newtons and it's a factor so the direction matters sometimes we will add the magnitude sometimes we will subtract the magnitude especially if there's more than two point charges involved right so now we're going to write it the coulomb's law in the sentence which is essentially a formal statement of the equation that we've looked at just now where the force between two point charges is directly proportional to the product of its charges of their charges okay and inversely proportional to the square of their separation okay this definition is normally two marks you might be thinking oh miss i know one sentence is one mark no no no the directly proportional inversely proportional that whole thing is one mark the idea that this is a interactive force between two point charges is the other one so you never mention point charge or you will lose one so actually you measure point charge okay because what do you mean if it's not quite charged well if it's not point charge for example like you have your bendy graph generator remember you know the thing like a big metal dome and then you put that your hair will fly one so if you if you have this one the charge distribution is not really like a point charge so this is only applicable if all the charge let's say 10 nano is all concentrated on one single point but normally a charge distribute across a 3d body so that one will be the next part of our lecture so that's why the condition of point charge is important when you write a statement for coulomb's law okay the second thing about using this equation is because it's a vector even if the polarity of the sign has a negative you do not substitute a negative into the equation okay and this is because you need to draw vector diagrams you need to see the angle and how the forces interact with each other so there's one thing because sometimes students you might have a let's say i put negative q2 there and you might be thinking oh now the force is negative but whenever i see a negative sign in false i will think about direction okay so in this case the direction does not matter you need to don't substitute the sign draw the vector diagram or map out the direction of all the forces we will do some examples all right so i think the last what remains is just to remind you that the inverse square relationship looks like this force will decrease as we travel further and further away so if let's say i fix q1 on the r equal to zero position and i increase the value of r the interactive forces or the repulsion force between q1 and q2 will decrease as shown in the graph okay okay so that is a coulomb's law here we have a pretty familiar simulation if you watch our as video where if i park a point charge in the middle punk look at all the beautiful lines miss ellie what does the line show so you remember very carefully uh these lines are what we call the uh electric field lines so if this is a positive charge it means all the lines are the arrows are pointing away from this charge remember some air stuff okay so that is for a positive charge you can show the direction but if you want to show the electric field strength i guess you could put a test charge also known as so the yellow is like the yellow point charge is a positive test charge and the thing about drawing these lines is because we need to be able to visualize the field right if you cannot visualize the fuel then a bit hard to start here so we know that at certain position if i were to park another positive charge these two charges will repel each other you see this red arrow is repelling or running away from the positive charge but if we move them closer the red arrow will become bigger indicating a stronger feel so you can see the field is stronger closer and the field is weaker but the strength of this film depends on two things right besides the distance it also depends on how strong this yellow charge is if i want to measure this white color lines or my color feel i would like it to be independent of my sensor that is good signs the thing that you use to measure the thing will not affect the thing that you're measuring does the sensor only test touch uh so the test charge cannot catch out or cannot disturb positive charge that's why when we talk about how strong the field is at this point we will take the magnitude of the force which is the red arrow divide by the charge of the yellow charge i mean of the yellow test charge so that's the electric field that you look at just now let's go back to writing it down a reminder of what electric field strength is see e fuel strength so the definition is a old one electric force per unit positive test charge emphasis on the positive test charge okay because we don't want to be bothered by what the test charge is one to know how strong is the fuel strength that so if you remember a little bit how does electric filter and force relate that means your electric field is the force force is the same one f1 2 f2 one so yeah so force over q but which e and which q is this all you have to be very careful because this particle on the left side has a feel let's say this green color field like i draw all the arrow like that though particle on the right side also have a few so whose field are we using who what are we looking at remember we want to study the charge on the left because the charge on the right we want to only use this to measure the fuel strength or we call this e field strength of q1 so remember which e are using i think there was a as question of this so remember that okay so we are using the e fuel strength of one so this will be e1 to show that oh i want to measure the green color field now you are using what charge to test you're using q2 so this one you must label q2 the f doesn't matter f2 one f1 two same thing already so from here you can remember that oh if what is f you can scroll up i will scroll up and you look at this coulomb's law q1 q2 over r2i you can sub that in and we'll see if we can cancel out the q2 so f here will be kq1q2 that's the force between these two charges can be f21 or f12 same law over r squared divide by the whole thing which is q 2 not q square q 2 then you notice very nice you can cancel out some stuff if you notice here q 2 and q 2 will cancel out what's in the numerator above what's the denominator below so if i want to measure the electric field strength i can do this fast last final line where i know the electric fusion of charge number one which is what i want to measure this green color one that will be equal to just k q 1 over r squared now this thing is beautiful you know why because there is no q 2 at all in the equation i don't care what q 2 is i just want to know what is the electric field strength of this one charge q1 so this is the general formula for testing or knowing what is the electric fusion of one charge yes so whenever we look at field strengths right it's always about force per unit something because to know how strong the field is we will divide by the quantity that causes the force to be in the first place you will see more of this in magnetic fields it also be false per unit something else yeah what's the unit for e oh unit for eagle so many then what are our units so one of the first one is space is related to forces so if you scroll down a little bit here we already talked about forces smartphones phosphors you can relate force to electric field by saying that oh we just defined the electric uh force per unit positive test charge so you can look at your own equation f equals to q e or you can say that e is force per unit positive f over q f over q or you can go the other way law you want to find this one also can f equals q e did the same thing now just rearrange a b so if you want to find the unit or you see here f over q so newton per coulomb is the first one and you see negative one it's another one wall that one comes from the understanding of uniform parallel plates kind of kind of so if you remember potential difference divided by plate separation the oh wanna make a two plate you've got a certain potential difference from let's say here zero to v excellent separation distance d what do you do volts per meter so that's a possible other unit for this one yeah later later in somewhere in the middle of this study we will go full cycle and then you will encounter this again volt per meter and one volt per meter is a unit that makes sense for electric field strength last thing to wrap up this whole section is the graph to remind you again of how it would look like if you plot the electric field strength of this particle green color one and how far you are away from it so if your positive test charge is here what is the fuel strength if you're moving what's so it's pretty much the same as your false graph here like that inverse square ir all the inversely proportional all the shapes so roughly like that one okay so that is how you can think of electric field strength all different things yes so please don't use v over d anymore that's only for uniform parallel uniform electric field between two parallel plates so don't use them don't be over the oh i should write a reminder unless you see parallel plate in the picture or they tell you it's parallel plate for some reason missed parallel plate they call us in a2 there was one anomalous year i don't know why they asked but they got us so just keep that in mind this is for point charges the field is not uniform if you remember the simulation we showed you just now where all the arrows pointing out one right the force is not the same you go further away from the arrow closer to the arrow the field strength is all different all right so yellow parallel plate is uniform feel string this one not uniform closer the stronger the field but the definition f equal to q e can be used for both parallel plates and point charges okay okay so that's all for electric field