Flux and magnetic flux

- [Voiceover] What I wanna do in this video is give ourselves an introduction or an intuition for the term Flux in general. And then think about how it applies to the idea of magnetic Magnetic Flux. So, first of all, when people are just talking about flux, and this is the easiest way that I know how to conceptualize it. They're talking about how much of something is flowing through a surface in a given amount of time. So if you imagine that this is, this is, I'm just defining a volume of air right over here. And let's say the air is denser near the bottom of this volume of air, so there's more air down here than there is up here, which is generally true. Air density goes down as you increase altitude. So there's very low density up here. This is in between. I don't have to draw all the air particles, but you get the sense. Lot of air, lot of air down here. And the air is moving. And so let's say that the air, let's say the air is... Let me do the velocity vectors in a different color. So, these are some of the velocity vectors of the air. Let's say the air on this side is moving is moving at let's say, a medium velocity. So right over there. But as we move more in that direction, the air is moving faster. So they have larger velocity vectors like that. We see that in general, all of the air is moving in that general direction, that's the way I'm drawing it. And I can draw the velocity vectors over here. The air is less dense. But the trend in the velocity vectors, when I go from the left to the right is roughly the same. So that's the flow. Now I'm just sampling some of the velocity vectors there. So let's talk about flux. And the thing about flux, really of any form, you have to think about a surface. So let's imagine you were to put some type of a net. Let's say you were to put a net right over right over here, right over here. And if we think about the flux, we would say, well how much air is traveling through that net in a certain amount of time? We could say how many molecules are traveling in say, each second. And so this would have some flux associated with it. Relative to the air. But what if we were to take that same net. And we're assuming it's some type of theoretical net that actually does not impede the air flow. But it helps us visualize a surface. What if we were to move that net a little bit to the right where the density is the same, but the particles are just moving faster. Well now, our flux would increase. So this is larger flux. Larger, larger flux. Why is our flux increase? Because, well, the density is the same, but in any given amount of time I'm gonna have more things going through that surface. Now what if I were to put that same net and move it up to this high altitude, right over here? That high altitude. Well, the velocity of the molecules are the same, and they're going in the same direction. But there's just fewer of them. So you're going to have less fewer molecules traveling through the surface in a given amount of time. So this is going to have smaller flux. And this is all relative to my first one. Smaller, smaller flux. Now, what if you were to take the same net and instead of the direction of the air being perpendicular to the surface, be normal to the surface, what if you were to take the net and reorientate it so that the air is going in the same direction of the surface. So what if you were to take the same net and you were to make it like this. So that it's the same net. I know it doesn't look exactly the same. But it's the same net, and you're to make it like this. Well now how much air is traveling through that net in a given amount of time? Well now very little to zero air is gonna be traveling through that net in any given amount of time. The air is going along the surface, not through the surface. So this one, let's just say that all the air is going exactly in the same direction as the surface, so nothing is going through the surface. We would say that this one has zero, zero flux. Now let's say that this theoretical net that actually does not impede the air flow, let's say we can stretch it or contract it. So if we stretch that net, in the same, let's say we were to do it, let's say we were to stretch it up like this. So it becomes a bigger net. So it becomes a bigger net like this. Well now this thing's gonna have larger flux because there's just more area. There's more to flow through. So now, if you said for this surface, you're gonna have a larger flux because there's just gonna be more air is going to go through that in any given unit of time. So as you can see, when we think about how much of something just flux in the traditional sense. How much of something goes through a surface in a given unit of time. It depends in this case, the density of the substance. It depends on it's velocity. Both the magnitude of the velocity and the direction of the velocity. We see if we orient the surface or if we oriented the velocity. So it's not going normal to the surface, perpendicular to the surface. Well then, we can have our flux go down. And you can have things in between. You can have a net. Let's say we took that same original net. But the direction of the air is neither normal nor exactly in the same direction of the surface. Well this flux is going to be in between, is going to be in between that original flux. And this one right over here. There's gonna be air flowing through. There is going to be air flowing through the actual surface. But it's not going exactly normal to the surface. And as we will explore later when we get a little bit more mathy into it. We actually care about the component of the vector of the air that is exactly normal when we eventually calculate flux. But this flux is gonna be some place in between this one and the zero flux because the air isn't going exactly perpendicular. Well that's just the more basic, or for me the more intuitive notion of flux. But what do we mean by magnetic, by magnetic flux? Well, like regular flux, we're still dealing with how things are kind of, you could say going through a surface. But instead of thinking about air particles or water molecules or things like that, we're gonna be thinking about a magnetic field. So let me draw a surface. So I have, I have a little bar magnet. This is the north side, this is the south side. We see our field lines. And then I've drawn a couple of the magnetic field vectors in white there. And let's say that we have a surface. We have a surface like this. And so, for this surface when we think about the flux we wanna care about... things are actually moving when we think about magnetic flux we aren't actually thinking about actual physical things moving through the surface. The way we did when we thought about, I guess you could say, traditional or more, or flow-based flux. But it's a similar idea. We care about the component of the magnetic field. And the density of the magnetic field that is normal to this surface. So let's say that this has a given flux. So let's call that, and the notation is phy. And, that's the flux of the magnetic field. And once again, it's based on, it's based on the strength of the magnetic field and specially the component of the magnetic field vectors that are perpendicular, that are perpendicular to this actual surface. So this would have one magnetic flux. But if I were to take the same surface and make it parallel, make it parallel to the magnetic field vecotrs instead of being normal or... Now the magnetic field vectors are parallel to it instead of being normal. So now our flux is zero. So this would have zero, or pretty close to zero. So approximately zero magnetic flux. Magnetic flux. Flux. Now if I were to take this surface and instead of orienting this way I just moved it further away. So instead of putting in here I would take it all the way out here where the magnetic field is weaker. Where the magnetic field is weaker. So we have a weaker magnetic field out here. The flux would also decrease. So it has a lot of the same properties as this more physical flux that we were talking about before. But instead of talking about, say, the velocity of the air molecules, no, the velocity vectors of the air molecules and how those relate to the surface, here we're talking about the magnetic field vectors. And how those relate to the surface. But the metaphor, the analogy is still the same. If they are perpendicular, you have larger flux. If they are going in the same direction, you might have zero or very little. You might have very little flux. If you have a weak magnetic field out here, the flux is going to be lower than if you have a strong magnetic field. That's analogous to, when you had high density and high velocity, that was a lot of flux. Versus low density or low velocity that is lower flux. And also, we can increase the total surface. So if we stretch that surface or we had a larger surface right over here, the flux through this surface is gonna be larger than the flux through this surface. Let's say this surface is analogous to a surface like this right over here. Let's say that the magnetic field is symmetric on both sides so the flux through this surface and this surface would be the same. So if you were to stretch it out to be a larger surface, well now you just have more of the magnetic field that is now normal to the surface. So hopefully this gives you at least a beginning ideas of the notion of magnetic flux. And how it relates to, I guess you could think of more physical flux.