Hey, guys. How's it going? So in this video, we're going to talk about a concept called magnetic flux. Now, this is going to be extremely similar to how we talked about electric fluxes. We talked about Gauss's law and electric fields. Now this video is going to be extremely similar to that. So, if you need a refresher, go ahead and watch that video again. Let's check it out. So when we talked about electric flux, it was basically just the amount of electric field lines that passed through a surface. So if you have these electric field lines that are passing through the surface right here, then we have 3 variables. We have the amount of electric field lines right here. We also have the area or the size of the surface that it was passing through, so that's the area. And then we also had the angle between them. And the electric flux was basically just the relationship between all of those three variables, e a times cosine of theta. And we also had the units associated. Well, the idea is that magnetic flux is the exact same thing, but instead of the electric field, it's the amount of magnetic field that passes through a surface. So literally this diagram is the exact same. The only thing that's different is that we have a b field or magnetic field instead of an electric field. And so what we do is we just replace these letters or the e with a b. So that means that the magnetic flux, which is given by phi b, is just going to be b times a times the cosine of the angle, where we have the strength of the magnetic field, we have the actual size of the object, and this theta, this angle right here, represents the angle between b and the normal of the surface. So, remember that the normal of the surface is that if I have the back of my hand right here, this pen sort of points in the perpendicular direction. So, in any surface, the normal is always going to be perpendicular to that surface. And if you have that, then this angle basically represents the angle between the b field, which points out this way, and the area vector. So that's going to be right here, that angle right here. Okay? So, the last thing that we need to know is that the magnetic fluxes are always going to be positive, whereas when we talk about electric fluxes, it could be positive or negative depending on whether we're going outside or inside. So magnetic fluxes are always going to be positive, and that's basically it. So let's go ahead and check it out because it's going to be very similar to how we dealt with electric fluxes. Cool?

So what is the magnetic flux through this square surface that's depicted below? So we have the strength of the magnetic field. We have a square surface that's over here. We're sort of looking at it from the side, and we're told what the side length is. So we're going to start off with our equation. The magnetic flux, which is given by phi b, is just going to be b times a times the cosine of the angle, in which this angle represents the sort of angle between b and a. Now if we're looking at this object here on the surface, then the normal vector is always going to be perpendicular to that surface. In other words, it's going to point towards the right. So if you have a surface like this, then that means that the perpendicular vector is going to point outwards like this. You're always also going to assume that it points sort of along the same direction as the b field because then you'll get a positive number there. So you have sort of a choice. You could have written it like this, but we're actually always going to stick to the right or alongside the magnetic field lines because then that would be perpendicular. So there that would be positive. Okay. So we have the electric, we have the magnetic field strength, what it is. And then how about this area? Well, this area right here, the area of a square is just given as side squared. So in other words, if the side length is 5 meters, then the area is just 5 squared, which is 25 square meters. Okay? So we have the area. Now we just have to figure out the cosine of the angle. So we're given this angle of 30 degrees. The problem with this angle is that this is actually the angle between the plane of the surface and the magnetic field. It's not actually the angle between the area and the magnetic field. This is the area, so that means that this right here is the angle theta that we need. So it's not going to be this 30 degrees. What we actually need is we need this angle right here, which is actually going to be 60 degrees because 60 plus 30 would be this right angle right here. Alright? So you have to be very careful with how you choose that angle. So let's go ahead and plug it in. So we've got this phi b is equal to we've got 0.05 Tesla, and then we're going to multiply this by 25, and now we have the cosine of 60. And if you work this all out, you should get 0.625, and the units for that are actually Webers. So I kinda talked I think I forgot to discuss it up there, but that's the unit for these. It's called Webers or that's equal to a Tesla times a meter squared. Alright? So that's it for this one. This is the answer. And, whoops. Let me know if you guys have any questions, and I'll see you oh, man. And I'll see you guys in the next one.