 Let's take a look at the data we have from the Coulomb's Law Lab and see if we can find from this data a straight line graph and then from the straight line graph the charge on the two spheres. The first thing we need to do is we need to make a new set of data from our separations that are inverse square sets of data. And the reason again we're choosing an inverse square relationship here is because that's the relationship we see in Coulomb's Law. Okay, so this is an inverse square relationship. The other way we know this is when we look at the original set of data when we graph that on our calculator just electric force versus regular old separation we get an inverse square shape which looks kind of like that. So two reasons that we know we're going to need to take our R values and then inverse square them to make our straight line graph. So here's where I'm going to put the data. I'm going to call it R to the negative 2 which is how we inverse square something. You could also put if you wanted to 1 over R squared but R to the negative 2 is a little easier. And I'm going to put the units that this will come out in as meters to the negative 2. Now what I will do on each of my separations is in my calculator go and put them to the power of negative 2. So I'll write out for the first one what I did 0.41 meters to the power of negative 2 will give me a new value that I'm going to graph of 5.9 and that'll be meters to the negative 2 for its unit. Now I'll quickly go through and just do the rest. I'm keeping my sig digs consistent as I go. Your data very likely will look different from mine because we didn't collect the same data and that's totally fine. And I had a couple of quite large R to the negative 2 values at the bottom so I used scientific notation. This one was 400. My bottom one was 10,000 so we got very very close together. Now I'm going to take these values and I'm going to graph them on a new graph on the next page. I am going to make my R to the power of negative 2 values the x of the graph and I'm going to take my electric force values and make them the y. I'm going to graph on the graphing calculator. When we do this x is going to be list one, l1 on your calculator and y is going to be l2 and this is my reminder to you that the steps we're going through in doing this are in your lab manual so although I'm going to go through this pretty quickly you can use the lab manual to help you out with the steps to make a graph in your calculator. So this is l1 that I'm filling in right now and I'm putting in here all of the the values of R to the negative 2 my x values and then I'm going to put in all of my forces. It's important that when I'm putting in for example these forces which are in scientific notation, don't forget to put the scientific notation part. So I'm remembering to put in the power of negative 3 for each of these and a good little thing to check is just that you entered all your data into your calculator properly. So my data is in my calculator. What I'll do now is I'll press the window button and I want to pick a good window setting here so my x values on my graph are going to be all of these x to the negative ones and they're uh pardon me R to the negative two values and they're really quite a big spread so I think my smallest one is 5.9 so if maybe for my x minimum zero is fine but my biggest one is 10,000 so maybe I'll go to like I don't know 11,000 as my maximum maybe I'll go up by thousands because I've got quite a bit of data to fit in there on the x you can have different window settings based on what your data looked like for my y values I think zero is a good starting place my biggest one looks like it's going to be about 4.1 times 10 to the negative 3 so maybe I'll use for my x maximum 5 times 10 to the negative 3 I want something just a little bit bigger than my biggest point and perhaps my scale I'll go up by 1 times 10 to the negative 3. Once I have the data entered into the stat plot menu and I have my window setting set I just press the y equals button and I make sure that plot one is shaded in if it looks like this where it's not shaded in just scroll up to plot one hit enter in your calculator and when plot one is shaded in the data will show up and really other than that one point this is actually some fairly linear data at the start that one point out towards the end is maybe a little more out to lunch that's okay it is a it is a tricky lab to collect data for it I'm going to get the slope of this graph by pressing stat I'm going to go over one to calculate and I'm going to go down to linear regression I hit enter on lin reg I've got an older calculator so once I have that program on the screen I hit enter once and it works out the slope for me you might have to enter it press enter three or four times on a newer calculator and I get a slope of 2.5 times 10 to the negative 7 the advantage of graphing in your calculator is you really don't need to spend quite as much time sketching your graph this is all I'm looking for is a title electric force versus separation to the power of negative 2 here's an x axis pardon me a y-axis label so the y-axis is electric force and newtons here's an x-axis label arc to the negative 2 in meters to the negative 2 maybe we'll put down sort of what our window settings were so I think I went between 0 and 11 000 between 0 and 1.5 times 10 to the negative 3 and then I just sort of sketch out what did my data roughly look like so I had a bunch sort of at the beginning I had one piece way over there and I just draw a very primitive line of best fit and I'll just label it with its slope so from my calculator the slope value was 2.48 so I want two sig digs 2.5 times 10 to the negative 7 your lab manual actually has a spot for you to do your slope calculation but we did on the calculator so there's no need to actually fill in any work there I'll just write the slope down again because it's kind of convenient the units of the slope are newtons over meters to the power of negative 2 because the slope is rise which is measured in newtons over run which is measured in meters to the negative 2 and you can simplify that unit down a newton per meter to the negative 2 is the same as a newton meter squared now we're nearly done I need to take my slope and I'm going to somehow from that slope work out what the charge is on the two spheres that created this data there's two steps to doing that the first step is to think about what the slope actually represents slope is rise over run so the rise of the graph is electric force that's the y value on that graph the run of the graph is r to the negative inverse square of the separations which just like the units can simplify down to electric force times r squared so this is what the slope is actually equivalent to kind of like the slope of a displacement versus time graph gives velocity or the slope of a force versus amplitude graph back in in physics 20 gave spring constant here the slope of a force versus inverse square of separation graph gives force times separation square so that's sort of my first step that i'm doing in this analysis the second step that i'm going to do is i'm going to manipulate the formula which ties all this data together the electric force formula coulomb's law and i'm going to manipulate it so that i can get the same little piece of algebra that i had from my slope and it's actually not too bad to manipulate it's even a little easier than the momentum lab we did i multiply both sides by r squared and what i end up with here on the left hand side is electric force times separation squared equals k q 1 q 2 well q 1 and q 2 are the same in this lab they have the same amount of charge so i can call that q squared now the reason i changed the formula and put electric force and r squared next to each other is because i know that electric force times r squared is the same as the slope so i can put in place of electric force times r squared the slope of my graph which was 2.5 times 10 to the negative 7 newton meters squared that equals k which is coulomb's constant or the electrostatic constant 8.99 times 10 to the 9 newton meters squared per coulomb squared multiplied by the unknown charge that i'm looking for squared out comes the calculator we're going to divide these two to see what we get and then we're going to square root them so i'm getting to two sig gigs 5.3 times 10 to the negative 9 coulomb's for the charge and either one of those pith balls and if you recall when we did our hypothesis in this lab we said that our hypothesis was the charge would be somewhere between a micro coulomb and a nano coulomb so this is 5.3 nano coulombs which is actually a pretty realistic amount of charge for one of those tiny little spheres to be