 Hi, I'm Zor. Welcome to Unizor Education. We will talk again about magnetic field related to electric current, straight line electric current, and we will have two electric currents parallel to each other. That's basically what we are talking today about. Now this lecture is part of the course called Physics for Teens. It's presented on the website Unizor.com. So if you go to this website, you have to choose the course Physics for Teens. And by the way, there is a math for Teens, which kind of prerequisite for this course. You do have to know math. And in the Physics for Teens, you might choose the electromagnetism subject. And when the next screen opens this is the magnetism of the electric current topic. And one of the lectures in that topic is this one. I do suggest you, by the way, to use the website Unizor.com, because every lecture, as you see it, it has nodes and very detailed nodes. It's basically like a textbook. And the site is completely free. There are no advertisements, no signing necessary, although you might actually do it, if you want, if you would like to participate in the process, in the educational process. All right, so let's talk about electric currents and magnetism. First of all, I would like to remind you something which we have been talking about. It's called Lorentz force. And the Lorentz force is the force which is exerted by the magnetic field onto the straight line current. Well, on any current, but we will talk, we were talking about straight lines. So if you have a magnetic field, this is magnetic field lines, and we are talking about uniform magnetic field. So all the lines are parallel to each other. Now, how can it be arranged? Well, consider you have some kind of a very big horseshoe magnet. So this is the north, this is the south. So in between the north and south you have relatively uniform field. And there are, obviously, some other forms. Now, let's consider you have this field, and you have perpendicularly to this field as straight line current. So this is magnetic field, and this is a straight line current, plus minus. It goes from plus to minus. This is the definition of the direction of the electricity, not related to electrons, obviously. So what happens? Well, when this is happening, there is a force which is perpendicular to both of them, to magnetic field lines and to the current line. So basically, since my magnetic field lines are parallel and lying in this plane of this board, and the current also lies, so it's two perpendicular directions. So what is the perpendicular to both? Well, it's this direction, perpendicular to the board. And the only question is, what's direction towards the board or outside of the board? Well, there is a rule of the right hand. Actually, there are two rules of the right hand, but I usually use the one which is magnetic field should be entering your your hand, and the thumb should point to the direction of the current, in which case the fingers points towards the board. So my force goes from here to the space behind the board. So that's the direction of the force. And the force is proportional to I, which is the electric current, amperage. It's proportional to L, the length of this current, and it's proportional to something which we called B, which is the magnetic intensity of the magnetic field. So that's basically the F, the Lorentz force. So this is just a very brief reminding of whatever we were talking before. Now we will use it for some very interesting purpose. So let's consider we have two wires, and let's consider them to be parallel and directed towards the same direction. What happens? First of all, as you know, and again, that's something which we have been talking about in the previous lecture, around each straight line current, there is a magnetic field which is formed by the mere movement of the electrons inside the wire. That's basically a condition when the magnetic field exists around this wire. So the magnetic lines going this way. Now that's another either the rule of the right hand, which means if you will wrap your fingers around the wire in such a way that the thumb points to a direction, then the fingers actually go in exactly the same direction as magnetic field lines. That's how we determine it. So the same thing here. So we have magnetic field around each straight line current. Now this magnetic field lines are circular. And by the way, they don't have Norse and South poles. This is magnetic field which does not have the poles because all of these lines don't have the beginning and end. They're basically circled onto themselves and there is no point where all of them are coming together. No matter. That doesn't really matter. What is important is the following. Think about how these magnetic lines and they are existing on obviously on every radius. It's like all the lines, magnetic lines of the same radius are making some kind of a cylindrical surface with the axis being this current. So if you will take a bigger radius, the radius which is actually exactly equal to the distance between these and let me look at this picture from left to right. So my current lines are just dots and my circular magnetic field is this one. So what happens with a magnetic field line around this one which goes through exactly through the point which signifies my current line. So my two current lines are perpendicular to the board. So I'm looking at this picture from this side and I'm talking about magnetic field around this particular current which is exactly on the distance equal to the distance between the wires. So the direction of this, you see it's this one. It's this one. So my current is this and the direction of magnetic line is this. At this point obviously they are perpendicular to each other, right? So because at this point direction of magnetic line is exactly downwards and the direction of this is towards the back of the board. Right? What happens? Well, we have a magnetic field which is perpendicular to the wire. There must be a Lorentz force. Okay, so let's think about what is the Lorentz force direction and magnitude. Well, again, my one direction, direction of the magnetic field is down. Direction of the current is towards the back of the board. So it's this one. So what is the perpendicular to both? Well, that's actually the surface of the board, right? If this is one vector and this is another vector which is goes behind the board, then the perpendicular to both is basically along this line on the surface of the board. Now, what's the direction? Well, let's talk again about this right-hand rule. I have my magnetic field going into my hand, so it's this way and my thumb is supposed to direct towards it's towards the back of the board, so it's so it's this way, which means my direction of the force is this way. So there is a force which is directed along the surface of the board towards perpendicularly to this one, which means perpendicular to the tangential line, so it goes straight to the center of the circle, which is this particular wire. So at every point of this particular current, there is a force which is pushes this wire towards this center of this circle, which is this wire. So every point of this wire is attracted towards this wire. That's what's happening. Now, the situation is absolutely symmetrical. If you consider the magnetic lines around this and how they affect this, so let's consider this magnetic line. It's exactly the same thing. So magnetic line at this particular point is vertical up, right? The tangential line. The current goes perpendicular to the board behind the board. So what is the line which is perpendicular to both? Well, that's the line which is on the surface of the board along this line. And what's the direction? Well, let's again use the right hand rule. So my hand is supposed to be receiving the magnetic lines, okay? My thumb is supposed to be directed towards the current, which is behind the board. So my fingers point this way. So this is. So when you have two current lines parallel to each other, from each point there is a kind of attraction to here and from here to here. So the whole lines are actually are trying to get together. They are attracting to each other. So two parallel lines with the same direction of the current are experiencing this force which basically pushes them together. This is an experiment which is actually was made by Ampere, the French mathematician and physicist. Some time ago, like 200 years ago, whatever. And the force which actually exists between these two wires is called the Ampere force. Well, not always. I think there is some kind of attribution problem. Certain things are the Lawrence force sometimes is also attributed to Ampere like an Ampere law or Ampere force. Well, right now that doesn't really matter for us. I mean, it's probably a matter for those guys. But they're not here anyway. So the force exists and in this case it attracts each other. Well, let's change slightly the picture. Let's direct one of them towards this and another towards opposite direction. So again, it's two wires and they are parallel to each other, but the direction is opposite. Now, what happens with these forces? So, in this case, we will have the following. First of all, the direction. Let me just wipe it. So again, we will look at the picture from the left. Now, the top one will have this is the point of the top one and it goes behind the board. And this is the bottom one. It goes towards us perpendicularly to to the board. Usually, schematically, it's usually it's represented as it's at the back of the arrow and this is the front of the arrow. All right, so you have the bow and arrow. So this is where the tail of the arrow is. Okay, so this one goes this way and using the rule of the Lorentz, the magnetic field is directed this way. I usually use, by the way, the corkscrew, the corkscrew rule, which means if you are turning the corkscrew this way, it goes towards behind the board. Now, this is the erection. So now let's talk about the direction of the force, the emperor force. Let's call it this one in the field of this guy. So the field is directed this way and the current is directed towards us perpendicular to the board. So what is the line which is perpendicular to both? So I need the perpendicular to this one. And two. So one vector is this way, another is this way. So the perpendicular to both is lying inside the board, inside the surface of the board. That's basically a perpendicular to both this one and this one, right? So what's the erection? Again, let's use the rule of the right hand. My field line is supposed to be part of the, it's supposed to come into the hand. So how can I arrange it this way? This way it comes into the hand. Now the direction of the of the current is towards us. So my thumb is supposed to be this way, right? So my thumb goes this way, outside of the board, towards us. My magnetic line comes into the hand, so the fingers point this way. So this is repelling force, you see. Now, absolutely symmetrical if you will consider the magnetic field of this guy. Of the bottom wire. Now it points towards us, right? So magnetic field is supposed to be directed How? If it points this way, then I should, okay, this is my corkscrew rule, right? So that's the vector of magnetic field. Now my right hand goes this way and my thumb goes behind the board. So that's the direction. So my fingers point upwards. So as you see, we have a repelling force. So in this case, forces are repelling. So again, two parallel lines with the current, two parallel wires, if you wish. If they are, if they have the current directed the same way, they attract each other. If the currents are opposite, they repel each other. And this is the ampere force, okay? So this is something which the guy called Amper, Ampere, was researching and at that particular time people didn't know that electricity is related to electrons or anything. It was just something and something needed to be measured. What's interesting about this, that obviously if you have certain value of the current, and let's say it's the same value, the same current, let's say we have the same battery, the same battery, plus and minus, and you have connected to both. One line and another line. So this is minus, plus, minus, plus. So that goes this way. No, sorry. Where is my plus? This is minus, and this is minus. I think I'm, no, we don't need this. We have two wires already. And these are going to this. Okay. So we have two wires, this one and this one. Parallel to each other. Direction is the same. Since it's the same battery, the intensity of the electric current is exactly the same. Now, what's important is, and Ampere obviously understood it, the greater amount of electricity which is going through these wires, well, in our language the greater amperage, and amperage is obviously called after Ampere. So the greater the force must be. And obviously experiments show this. So if they for instance put one battery and observed certain force, and then they put two batteries parallel to each other, so contributing to each other, and they have, or rather sequentially, then to increase the voltage, right? You have to put it sequentially. So the greater electric power, the greater amount of electricity going through the wires, the greater the force will be. So he was thinking about this from a different perspective. He didn't know what is the electricity that's caused by electrons. Electrons have certain charges, and the amount of, basically the amount of electrons moving at the same time through some kind of surface, that would actually constitute the electricity. He didn't know what it is, but he wanted to measure it. And what's interesting is that the force of attraction or repelling, whatever you connect these things, is dependent on the electric current. So he was thinking that he can measure the electricity, the strengths of electricity, the strengths of the flow of electricity by the force. And he has established a unit of electricity. So he took some kind of a measurement, and as a result he was saying that, for instance, the unit of length of the wire, which positioned, when the wires are positioned from each other at the unit of length distance, and if the force of attraction or repelling is equal to one unit of force, whatever the unit of force he was using, definitely not Newton, that would constitute the unit of electric current. So that's what he said exactly. So the unit of length of the wire, here and here, positioned at the unit of length distance, if they are attracted to each other at the unit of force, then the current which is going through these guys is a unit of electricity. So you can measure it. So he assumed that the force is proportional, first of all, the force between these two wires, repelling or attracting force, is proportional to the electric current. That was his assumption. And based on this assumption, he established the unit of electric current, called one ampere. Well, nowadays we are basically using the same unit that we defined this unit differently. We are defining unit as basically one cologne per second. But at the same time, we have established the cologne in a special way, in such a way that one cologne per second would constitute the same amperage as ampere some time ago, established for his unit called ampere. I'm not sure actually he called it ampere, but anyway he has established the unit of electricity, which right now we call ampere. And we are basically using exactly the same unit of electricity, and we have established cologne to be such a unit of electric charge that cologne per second is equal to ampere, one ampere. By the way, it's something which came to my mind. How do you measure the force between these two attracting or repelling force? Well, you can think about very simple experiment. I mean, it's just basically how creative you are. But this experiment just came to my mind. What if you have two wires, and let's say this is connection, and this is the wire which goes perpendicularly. And this is another connection, this is another wire. So basically you have to have two connections. Let's say you have one connection from this to this, and you have another connection from this to this. So you have two wires. They are hanging by these two threads from some kind of support, and there is an electric connection through this. Let's say plus, minus, plus, minus. So you have these two wires. But now I'm looking for this side. Now, they are hanging freely. They are freely hanging on the threads. And there is a current which comes through this. So what happens in this particular case? Well, if let's say the current is in exactly the same direction, then this thread will go to this position, and this one goes to... And they are attracting to each other, right? So they are swinging on these threads, and they will swing closer, right? Well, if they swing closer, if you know the weight and know the angle, this is the same angle, and you have the weight, mg equals p. So basically what happens here? You have weight, p. You have attraction, f. And you have tension, t. And you have an angle. This is the simplest mechanical problem which we have basically solved many times when I was during the lectures on the mechanics subject. That's very easy to establish what is the value of f, force f to have this angle phi knowing the weight of the wire. So if you have the weight of the wire, you can definitely find this particular force. That's it. And now you can establish basically by putting different electrical current to these wires, you can establish the connection between the wire, the current and the force, and that's how you measure the force, and that's how you measure the current. Basically that's it. So my purpose was to explain this unfair force and parallel law that two wires, if they are parallel with the current, direct current in each of them, they are either attracting to each other if the current is directed the same way or repelling if the current is in opposite direction. Read the notes for this lecture on Unisor.com. That's probably just another view for the same things. And I put some pictures there so that probably is also beneficial. Much better pictures than I was drawing here. Okay, that's it for today. Thank you very much and good luck.