Electric Flux

by Patrick Ford
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Hey, guys. So for this video, I want to talk about electric flux. It's a concept that is very important in electro statics. You'll definitely need it to solve problems, especially when we start talking about gas is law. So let's go ahead and check it out. So basically the flux of anything flux. It's just a measure of how much of something passes through a surface. The way I like to think about this is kind of like if this field here was like a river and you are to stick like a ring inside of it, how much water passes through the ring? That's sort of how I like to think about flux. So when we talk about electric flux, we're gonna be talking about the electric field and specifically, how much of this electric field will pass through a surface? Okay, so you've got these couple examples right here. Imagine these blue lines represent the electric field, and this represents just a surface kind of like a ring I was just talking about Well, in this situation, basically, the flux is how much of these lines will pass through the surface, and in this case, we can say that this ring has sort of, like caught all of these electric field lines, so that means the electric flux is going to be all or maximum or something like that. Whereas in this situation, now we're gonna have the ring. But instead of it being upright in all the field lines passing through it, what happens is that these electric field lines will pass directly over it. So imagine you were to turn that ring, and instead of it being upright, you would turn it on its side. No field lines would actually go through that ring that we kind of just go right over it or underneath it. So that means that the electric flux at this point is none or nothing. There is no electric flux because there's nothing actually passing through the surface. Remember, the electric field passing through the surface is defined as the electric flux. And then in this situation, we have somewhere in the middle. So some of the field lines are actually passing over it and under it, and then some of them are passing through. But at some angle here. And so in this case, the electric field line isn't all or nothing. It's actually just some. So it's, um, partial amount of electric flux. So clearly what we've seen in the three examples is that the electric flux depends on the angle of the surface. Now that we measured. This angle is, we say, the electric field lines make some angle with something called the normal of the surface. And the way I like to think about the normal is if my hand the back of my hand was a surface, then there is a vector that points directly perpendicular to that surface that's called the normal. And so, since the normal is the perpendicular of that surface, then the electric flux is going to be dependent on the angle that the electric field makes with that surface. And this angle here is measured between the electric fields, which is the blue lines and the normal, or the perpendicular vector of that surface. And if you have all those three things together, then the electric flux has an equation. Is gonna B e a times cosine of data. Now there's some units associate with electric flux. You might not need to know them, but you could always get them back from the electric field in the areas and things like that. And so if you have a bunch of surfaces together, not just one of them, you can calculate something called the total amount of flux, which is where we're gonna use later on in the chapter. So the total amount of flux through a closed surface is just going to be the sum of all. The flux is through the individual surfaces. Now, I want to be very, very careful about how explain this. But a closed surface you guys might be wondering what that is. Ah, closed surface is just sort of any boundary that encloses some volume. So the easiest one to think of is like a box. So imagine like this. Right? So I have a box, and Yep. So that means that if there were some electric field lines sort of passing through this box Well, this box has six individual surfaces. Right? So you have a flux that's going here. Flux is going here, here, on the bottom, on the fronts. And then also, I think I'm missing one, uh, somewhere over here. Right. So you have these individual flux is from these individual surfaces. But the closed surface represents sort of like that three dimensional object that I've made here. And so the total flux to calculate through this closed surface is just gonna be the sum of all. The flux is through the individual surface. And when we're doing that when we're calculating, total flux is we know that we can have. Sometimes you can end up with positive and negative flux is now usually in physics. Positives and negatives has to do with the direction. So let's go ahead and check out the two different cases. You're gonna get a positive flux whenever the electric field and the normal point in the same direction. Now, why? Because if you take a look at this equation right here, if we say that these electric field lines are e and this normal or this normal which we usually represent by a the area vector points in the same direction, then we know that the cosine of the angle is going to be zero and what's co sign of zero. It's just positive one. So that means it's just gonna correspond to a positive flux, whereas you're gonna get the opposite a negative flux whenever the electric field and the normal point in opposite directions. Now you can probably guess why. Because in this case, the cosine of the angle is 180 degrees and co sign of 1 80 is negative one. So the way I like to think about this is if the electric field lines is going out of a surface, it's gonna be positive. But if the electric field lines are going inside of a surface, then it's going to be negative. All right. That's basically last thing I want you to know about. Electric flux is, Let's go ahead and take a look at a quick example. So you got the electric flux through each surface of a cube, so kind of like the example that I showed you above is given below. So what's the total flux through the Cube? All we have to do is if you have the If you have a six individual electric flux is, then the net is just going to be the addition of all of them. So, plus one unify one plus Phi, too, all the way to 56 By the way, these Greek letters right here are the letter five. So sometimes I'll say that. So basically, all you have to do is just add all of these things up. The zeros don't contribute anything, so you just do 100 plus 20 minus 40 minus 80 and just go ahead and add all that stuff up. 100 plus 20 is 1 20 and then negative 40 and negative. 80 is negative, 1 20. So that means that the net electric flux here so fine nets is just going to be equal to zero, right? And that's it. So that's basically how you would add up together. These electric flux is Let's go ahead and take it. A bunch More examples in the next coming videos. All right, let me know if you have any questions.