Hey guys. So we're getting ready to start solving some more serious magnetism problems, but before we start, I wanted to do a video where I basically summarize the entire chapter. The reason I want to do this is that, in my experience, students tend to get very confused and overwhelmed with all the equations you're going to see in this chapter and all the different situations. But if you take a look at everything, you're going to actually see in this video that it's quite simple. This is my favorite video and after seeing this, I think you're going to feel much better about what's to come. So let's get started.
Alright, first of all, I want to remind you how electric charges both produce a field and feel a force. This is a central thing we're going to talk about in this video. If you have a little charge here, \( q_1 \), it produces a field \( E_1 \), and it goes in several directions. I'm just going to draw a few of them. And then if you have a second charge right here, \( q_2 \), that \( q_2 \) is going to feel a force and it's going to be repulsed. It's going to feel a force \( f_2 \). And the reason it feels a force is that \( q_1 \) is sending these field lines that are communicating that, hey, \( q_2 \), you're supposed to feel a force. The electric field here is given by kq_1r2, where \( r \) is the distance between the two. \( q_1 \) We call the producing charge because it's creating a field. The force on \( F_2 \) here, in charge \( F_2 \), if you know the field \( E_1 \), then it's just \( E_1 \times q_2 \). \( q_2 \) is what we called the feeling charge.
So if you have two charges, you're there, sending a signal to you, an electric field saying, hey, you're supposed to experience a force, and therefore you do. The reason why I experience a force is that you're also sending a field my way and telling me to feel a force. So it's very important that you understand that a charge at the same time produces a field and will feel a force from other charges. You do both at the same time. And that happens with magnets as well. If you have two magnets, and I'll make this part faster, north and north, they're supposed to repel. You're going to get field lines from north to south like this, remember? Right? Let's make a really big one here. So this magnet here is producing, it produces a magnetic field. By the way, the magnetic field is given by the letter \( B \) instead of \( E \), so it produces a \( B \) field. And this guy here will feel a magnetic force, \( F_B \), okay? And vice versa. So this guy here is producing and this guy's feeling, but actually, they're both producing and feeling. They're both producing feeling, that's why there is a mutual force.
Now, the reason this is important is that almost every magnetism problem is going to ask you to calculate the magnitude of either a new magnetic field that is being produced, so there's no magnetic field and then something happens that creates a new magnetic field or the force that you're going to feel from due to an existing magnetic field. Most problems are like this. So when you start solving a problem, the first question you should ask yourself is, are we dealing with an existing field, or are we creating a field? We're going to talk a lot more about that.
Alright, we're going to calculate fields produced by, as well as forces felt by either electric charges or electric wires. We're actually not going to calculate anything with magnets. We've talked about magnets before. The only thing you need to know about magnets is their direction. You're not actually going to calculate the magnitude of the force between two magnets, for example. The key difference here between magnets and these guys is that magnets will always produce fields and will always feel a force. Two magnets will always do that. But charges and wires don't always produce a field and don't always feel a force. Charges will only produce a field and feel a force if they are moving. If you have a charge going this way, and then you have a charge going this way, \( v_1 v_2 \), there will be some sort of magnetic force between them. But if charges are static, there's only electric force between them, no magnetic force. The same thing happens with wires. Electric wires will only produce a field or feel a force if they have current. If you think about it, what is current? Current is just the charge that is moving. So these two points are actually equivalents, right? So charges have to be moving. So if you have a wire, it means that the wire has to have a current through it so that the charges are moving. That's a very important distinction, and you'll see this in the equations as well. Alright. So in this chapter, you're going to see a lot of equations, and don't worry about them for now. You'll see these guys later, but I just want to kind of scare you ahead of time. This can also work for you as sort of an equation sheet that you can take throughout the chapter. We're not going to talk about any of these equations. I just want to make the point that these seven boxes are most of what you're going to see. And I'm going to do one video on every single one of them, but they're all very similar. I'm trying to sort of demystify the entire chapter. And what you're going to get is, you're going to get problems where you're producing a new field or feeling a force in an existing field. So again, the first question you're going to ask is, is this a charge moving to an existing field or is this a charge creating a field that doesn't already exist? And depending on the answer to that question, you're either going to be here or here. Notice how here you're trying to figure out what is the magnitude of the new field. Right? That's why all these equations are B's. And here you're trying to figure out the magnitude of the forces. Okay? So you have four different kinds of problems we're going to see, and this is the last point I'm going to make. First, you're going to have a moving charge. So like a \( q \) that is, let's say, moving this way with a magnitude of \( v \). And if you have a, if you have a moving charge that's moving to a magnetic field, I'm sorry, if you have a moving charge, if you have a moving charge, it's going to produce a magnetic field. And you can find the magnitude of that magnetic field using this equation. We'll get into details of those equations in other videos. Okay? But remember, charges can also move in a wire. And if you're a wire essentially just trapping charges inside of it. So you can have a moving charge or you can have a wire with current or a current-carrying wire. And these situations are identical. So now you have a wire and instead of \( V \) to the right, you have \( I \) to the right. Okay? And it's going to be similar that this wire is also going to create the magnetic field. So this is a quick example. Right here at point \( P \), there will be a magnetic field here. Okay? So this point here will have a magnetic field, \( B_P \). Okay? Because it's a certain distance away from that cable. You can also get a wire and make it into a loop. So imagine a wire and you just make a square out of it or a circle out of it. Something maybe like this, where you make a loop out of a wire. So that the current goes this way, goes all the way around, and then comes out this way. You can do that as well. That's the third thing we're going to talk about. And you can find a magnetic field right through the middle right here. Okay? Using that equation. And finally, you can make a lot of loops. You can get a wire and do a loop with it like this, that's a single loop. Or you can do three loops, that's three loops. Or you can make really long loops, and these guys are called solenoids. Something like this. And essentially, you're making something where this is really really long \( L \). So that it's bigger than just the radius of the circle. And that's sort of gets a different equation. Okay? So in this, these are the four situations we're going to talk about in this chapter. Some books actually break this up into two chapters where, this will be one chapter, and this will be one chapter. Sometimes it's in the opposite order, but it's all the same stuff over and over again. I really wanted to do this video because I think you'll see as we go through these that it's just the same stuff over and over. Cool? That's it for this one. Let's keep going.
