In this problem, we have point charges that are fixed on the X axis of minus three and plus three. And we want to know what charge Creepers of the origin so that the field vanishes at X equals zero y equals three. So let's go ahead and draw this out. So and also right down that kid Givens Q equals Q two. You think it was for Micro Combs? Okay. And, um, we want it to vanish at X equals zero y equals three. And this was meter is not centimeters. Yes. Um, so here's our mystery charge Q. And then here is our Q one Q three. Let's say it's at a distance. Acts and then let's say that axis equal, Teoh three meters. And then, um, we want the field to vanish. Sure. And this is that. Why schools? I guess why you come up with a new name for it. Also call it X, even though it's in the vertical dimension. Hopefully, that isn't good. Too confusing. So, um, que want you to basically they're gonna create a field like this and like this, um and so what we need from the field charge here is we need to feel that, um, equally that opposes the sound so that some of these two fields let's think about that. First, the horizontal components would cancel, but the vertical components will add. So here is the vertical components, and so the some will look something like this. So we basically want the field from here to be equal. Teoh twice the twice the vertical component from one of these front from the Q one and Q three. So let's write down the electric field from Q one. At least the magnitude or he wanted you to. So we can say e as equal to K Q one over. And then we need this distance. So, um, between here and here, So bye, pat diary. And there, um, that's the square root of two times X. So then that's just gonna be so then if you square that will be two x squared, right? Because, um, it's 1/1 over this distance squared. Say that's distance are are equal, started to X, and, um, and then we want the vertical component. So let's call that you why? And so we need to basically multiply by. Um, we can find this angle, and we just need to multiply by the sign of that angle so we can say its times a sign of data. Um, what's this angle s strongest? The triangle created by this are So here's our This is a side of three. This is a site of three. So it's a 45 45 90 degree triangle. And so, um, this is gonna be the sign of 45 seconds. Uh, quickly. Oops. What? What happened? Oh, but okay, data equals 45 degrees. So then that's gonna be the sign of 45 which is one of a route to And then so that's you y of one of these charges. And remember, like I was saying that these two will sum up the total field from Cuba on a cue to it's just gonna be that double the y component of one right, cause he wanted Oh, and, ah, Q two will cause the same, uh, field actually write. That is cute, too. So then we know that the electric field from this one has to equal twice this. So then we can kind of transform this equation. We can say e from Q. So I'll put a subscript Q to the electric field from this. Q. Has to be double. Um, there's the to the vertical component of Cuba. Nick YouTube. So now we need to figure out um, but now you need to kind of right in the generic format of the electric field due to queue. So that's gonna be equal to que que and then, by the way, que needs to be negative. We'll just kind of pepper that at the end, right? If you're gonna make it an electric field that points down Q Q has to definitely be negative. Um, so I equal to cake you and then we wanted to buy that by the distance. Indeed, crew in this point and in that distance is just simply acts. So it's X word. So now, in a position to software Q. In terms of Q one, um, so let's do a bunch of cancellations so we can say goodbye to this K and say goodbye to this X squared. And then who did this to cancels as well. Eso Then we're left with the really nice, simple equation that Q is equal to Q one over a square to two, so it has to be sort of less than, um que Because, uh, it's only one charge. Um, you are? Well, yeah. I mean, I guess it it's kind of hard to tell on the surface of it needs to be less than or greater than Q. Because on one hand, it's closer to this point. And then, on the other hand, it's only one charge. So, um, but the mouth sort of balances that affect out, So you get this.