24. Electric Force & Field; Gauss' Law

Electric Field

# Electric Field Above Two Charges (Triangle)

Patrick Ford

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Hey, guys, let's go ahead and work this one out together. We have these two charges right here, once positive ones negative. And we're supposed to find out what the electric field is at this point of interest over here. All right, so let's go ahead and do that. We've got a positive charge over here. A negative charge over here. So at this point of interest, we just need to figure out without any just calculations where the electric fields going to point. So we know from this, uh, charge right here. We know the electric field is gonna point off in this direction because it's going outwards, right? It wants to point away from that charge. Whereas over here, the electric field is going to point in this direction towards the negative test. Negative charge. And that's gonna be e minus. All right, In order to figure out those electric charges, I need the formula. I've got e equals k que over r squared. So I need to know the distances between the source charge or the producing charge Was the one cool. Oh, and the point of interest right here. Right. So I've got this little our distance over here and I have a triangle. I've got five centimeters and I've got eight centimeters here for the vertical piece. So I configure the high pot news of this triangle using the Pythagorean theorem. So you work this out, you're gonna get 9.4 centimeters. And if you were to do the same thing over here, you would have to do the same exact thing. You know, five and eight. And you have to figure out the iPod news. So this is actually starting to look like we have a lot of symmetry in this problem. So we have five and eight. We basically have this sort of, like isosceles triangle. So let's go ahead and see if we can use symmetry just like we did in the last video. To sort of reduce the amount of work that we have to dio. So we need these same charges. So, in other words, the same magnitude of the charges we got the one cool, um, in the negative one. Cool. Um, at the same distances. Which means they're gonna produce the same electric field, right? And if these things are symmetrically placed around this, these two charges then that means that when we go ahead and break up these electric fields into their components, so e x and the Y, we're gonna have the angle theta That's gonna be the angle. Theta is gonna help us break up these things into the components. But you're also gonna have components in the Y direction in the X direction from the negative. Cool. Um uh, the the negative piece of the electric field. And that's going to be an angle theta as well. So in other words, if these things, if he's test charges in the point of interest, are symmetrically placed, that we're gonna actually have the same exact datas for both of them and what that allows us to do is to eliminate the use of the vertical components. We don't have to. We have to worry about them because they're gonna cancel out. And instead, what that tells us is that the Net electric field is gonna point off in this direction. And it's just gonna be too times the electric field of the X components in which the X component of that electric fields or the X component of anything, is the magnitude times the cosine of the angle as long as your angle is relative to the X axis. So that means that our E nets are the Nets is just going to be too times I have the formula for the electric field over here. So we have cake you over r squared times the cosine of the angle. So I have all of these numbers are have case constant cues is the charge. And are is this distance right here This 9.4 centimeters all have to do is to go ahead and figure out what the co sign of this angle of this triangle is. So I have to go and use the triangle. So instead of using this angle right here, we'll have a whole bunch of stuff written out. E can also say that this angle right here is theta because these lines right here are parallel. So this is the same angle theta one in the triangle and in any triangle, the way we figure out co sign of Fada is if we have the angle, we can just plug it in. But if not, we can use it by relating the sides of the triangle together so we have could So Kyoto, Uh, by using so Kyoto we have co sign is the adjacent over high pot news three. Adjacent side is five. The iPod news is 9.4. Notice how I don't have to convert it to meters or anything like that. I could just plug it in. His meters are centimeters, because this thing is ratio anyways, So I've got 0.53 for my co sign. So that means that I can actually just plug in this number inside for co sign of theta. All right? And so now let's go ahead and just plug in all my numbers. I've got two times 8.99 times 10 to the ninth. Now I've got the queues right for the queues for both of them are just one Cool. I'm just gonna plug in the positive number. This our distance right here is gonna be point 094 because we have to convert m, it's gonna be squared. And now for this co sign of of theta right here, all you have to do is just substitute 0.53. Don't plug in co sign of 0.53. It's just 0.53 if you work this out, the Nets electric field is going to be 1.8 times 10 to the 12th Newtons per Coolum. So that's the final answer, and this net electric field points purely in the X direction. So this is one way that you guys can use symmetry, get very familiar with it. Watch this video a couple times. Just so you understand how I was able to work through this symmetry and I'll see you guys the next one, let me know if you have any questions.

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