 Before we get into solving the worksheet, I want to go over something that I would have talked a little bit more about in class. See, when we've got these electric field lines and you look at something like the link to the textbook, we see all sorts of little diagrams showing arrows for electric field lines or maybe showing these sort of flat images where we've got vector fields, but it's a little bit hard to see what's going on here. So in addition to the textbook sections and the videos, and there's some good videos that show you some visualization, I've got some tools here. So I want to walk you through a little bit about what these tools do. And I'm actually going to show you the second one first, which is this PHET simulations. So this brings up a window here, takes just a minute to load, and we're going to go ahead and play this one. And it allows us to take a charge and put it into a region in space. And it gives us this vector field. So at every point in space, it shows us which direction the electric field points, but also some information about how strong it is. Now this particular one uses shading. So where it's white, that's where the field is strongest and where it fades out to gray, that's where the electric field is weaker. And you can go ahead and put all sorts of different things in here to start building up a view for what's happening. But it's a very flat representation. So I do want you to see this one and we'll take a look at it in one of our other videos on answering some questions on the worksheet so that you can get a sense for what's happening here. The other tool is a little bit more powerful but a little bit harder to understand. Now when it first comes up, it's not actually using the type of settings that we want to use. So rather than using this particle's velocity, we want to go ahead and we can show the vectors. Now this is a three-dimensional representation. So you can actually grab this and rotate it around to realize that vector field doesn't just exist on a flat plane. It's everywhere in space. There's a little arrow in there. Now this one uses coloration so that the white again is the strongest but then it sort of fades out into a green and a darker green in there. In this particular case, the arrows are all pointing towards the charge so it's a negative charge. I can also reverse it and show you a positive charge. Now sometimes when you get all those arrows in there, it can be a little hard to see what's going on. And so here we can put a slicing in. Now give me a minute here because I don't always put the right slice in. Here it's slicing along the x-axis and depending on how I rotate it, you can then see what those fields look like if I rotate it in different directions. And I can actually grab this and see what it's like a little further away from the charge or maybe in front of the charge or right where the charge is. I could also look at slices in other directions and see what's happening there. Now in addition to the field vectors, I can put it in as field lines. Now this program doesn't show you the arrow heads on there so you might have to go back and forth a little bit to see, oh, these ones are pointing out, but that's the lines. And if again I don't show the slicing, I get a better view here that these electric field lines actually point away from that charge in all directions, not just in a flat plane, but it's more like a porcupine ball. If I start getting some other charge distributions, this becomes more interesting. So like a double point charge, we've got a variety of these points and what's happening at the electric field is much easier to visualize in three dimensions if I can actually turn this thing around. And I could again adjust it back to the vector field so I can see, oh, it's sort of pointing towards those, but then I can also turn on my slicing and see what's happening in different directions. Or again I can switch it back over to the field lines. One of the diagrams that you're going to see a lot is the die pole. And again in full three dimensions without any slicing, you're able to see much better the kind of pattern that's happening here in terms of I've got field lines going from one charge but bending out in space around to the other charge. So this is a tool that you can play with a little bit and it takes a little bit of getting used to and you can see how things rotate through space so you can get a better idea of what's really happening. As we move through into the next unit and we start looking at more different distributions of charge we'll be able to see what's happening with the electric field in a full three-dimensional picture for each one of these situations.