 Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about electromagnetic induction and the Faraday's Law, Faraday's Law of Electromagnetic Induction. This lecture is part of the course. The course is called Physics for Teens. It's presented on Unisor.com website. If you found this lecture on YouTube or somewhere else, I suggest you to rather go to the website because the website Unisor.com contains the course, basically, which means all the lectures and every lecture has a very detailed notes, basically like a textbook. And there are exams for you to self-check or maybe your supervisor can check it or teacher. And the site is completely free and there are no advertisements, no strings attached. So it's much better to look at the whole course, actually, and to know what exactly you might need. Or take the whole course, actually. On the same website you can find the prerequisite course called Math for Teens. I do consider the mathematics very important for physics. And, for instance, in this lecture I will also use some mathematics, some calculus, for instance. Just a little bit, but still, whatever the level is, math is important for physics. Okay, back to business. Now, before going into electromagnetic induction and Faraday's Law, I would like to very briefly repeat what we have learned about interaction between magnetic force and electric current. Basically, most important thing is so-called Lorentz force. If you have magnetic field, and I will represent magnetic field with magnetic lines, and you have an electron or any other charged political moving, for simplicity we will always use perpendicular direction. Then there is an interaction between the electrically charged particle and the magnetic field. Magnetic field will generate a force which is acting perpendicularly to both direction of magnetic lines, and the trajectory of the charged particle. In this case, the perpendicular to these both, they are in the plane of this board, which means the perpendicular to both will be perpendicular to the whole board. So it's either this direction or that direction, depending on what exactly is the particle. If it's positively charged, it's one direction. If it's negatively charged, it's another direction. But anyway, every particle will have a force in this particular direction, either this way or that way. That's the Lorentz force. Now, based on this, we were talking about the force with which magnetic field exerts onto the wire with the current. So if this is not just a particle, but a wire, and there is an electric current running in it, what does it mean? Well, it means that there are a lot of electrons actually going along this wire in one direction, which means on every electron there is a force from the magnetic field. Again, it's directed perpendicular to the direction of the wire, and if it acts on every electron, it basically acts on an entire wire. So an entire wire experiences the force in this direction, depending on the direction of the electricity. And there is the rule of right hand, which basically helps to determine which direction, but that doesn't really matter right now. What matters is there is a Lorentz force between the magnetic field and every charged particle or the wire with electric current in it. Okay, now let me remind you how we quantitatively characterized that thing. Now, we have introduced basically the equation which quantitatively defines this force as the product of the current which is running in the wire, lengths, and intensity of the magnetic field. Well, I used the plane multiplication here because I am assuming the perpendicularity. In the vector form, it will be a little bit more involved. It will be I as a vector, L means lengths of the wire, and B should be a vector product here. So B is a vector in this direction. I is a vector, in this case, on this particular picture in this direction perpendicularly to the lines of the magnetic field. So F is the force which is a vector product of current vector times the lengths of the wires. Well, obviously it should be multiplied by lengths of the wire because force is acting on every electron inside the wire. So the longer the wire, the greater the force will be. So that's why it's proportional. And it's proportional to I which is basically the speed of electrons. Current is amount of electricity per unit of time. That's the speed of moving of electricity. And the B is the intensity of the magnetic field. Basically, this is how we defined in the very beginning what is the intensity of the magnetic field. If the length is equal to 1 meter and current is equal to 1 ampere, which means 1 cologne per second, and the F is equal to 1 newton, then we are saying that the intensity is equal to 1 tesla. In any case, so this is defined. Now, so this is for the piece of the wire, actually. Obviously, we can modify this per particular single electrically charged particle how it can be done. Well, let's say you have a particle, only one particle with a charged Q. Well, if it's an electron, it's the charge of electron. Now, if it's only one particle moving, what is I? I is Q divided by T. Now, if it's moving with a speed V, then the L is equal to V times T, right? So the whole current of the length L will be covered in time T. And if me is the speed, then the length of the wire is speed times time. And at the same time, if the same charge Q during the time T covers the whole length, it means that Q divided by T is the current, which means the F in this case is equal to Q divided by T times V times T times V. I'm using this formula for perpendicular direction, because it's perpendicular than this multiplication means times sine of the angle, if you remember, the vector product and sine of the 90 degrees one. So that means we have QVV. So this is the formula for one particular charged particle. And this is for the wire of the length L. And again, they're talking about perpendicular direction, perpendicular direction of the wire or perpendicular direction of the charged particle relative to lines of magnetic field. Also, let me talk about terminology which we will be using. We will be talking about something like crossing magnetic field lines. What does it actually mean? I mean, there are no magnetic field lines. I mean, it's our representation of the magnetic field. Well, in this particular case, for instance, if a charged particle is moving across magnetic field lines, it means that the force, magnetic force is actually, if it's a magnetically charged, then it will be either attracted in this direction or repelled in this direction. That's what these magnetic field lines are. And usually the density of these lines characterizes the strength of the magnetic field, the intensity B. And when we are talking about crossing, then I might actually use the more magnetic lines we cross, let's say, during a certain period of time. What does it mean? It means actually that the stronger magnetic field is because the strength of the magnetic field is represented with magnetic lines. And using the language of magnetic lines helps to determine the direction of the magnetic field. So that's why we're using this kind of a terminology. So crossing magnetic lines perpendicularly means that, well, there are certain forces of the magnetic field which act on other magnets and these are direction of these forces. And the electrical forces are perpendicular to this. That's what basically it means. Okay, so this is preambula, which means I just want you to understand, in particular, this formula, rather this formula, because we will use everything in a perpendicular direction for simplicity. Because it will be very, very important for understanding the electromotive induction. Now, okay, so what happened in this particular case when we have a wire with electric current running in it? And it causes basically the force and the force is moving the wire in this direction, right? So this is the wire, this is magnetic force. Let's say this is north and this is south and this is i. Then the force would be perpendicular to i and to magnetic field lines. Okay, so what happens in this case is the following. Movement of the electrons inside the wire, which means the current, electric current, causes the movement of the entire wire perpendicularly to both directions of magnetic field and the direction of the current. Now, usually in nature everything is symmetrical in harmony, so to speak. So my question is if current in the wire in the magnetic field causes the force and movement of the entire wire, can it be reversed? What if I will move the entire wire? Will it cause the current? So that's how we will try to basically make this kind of inverse logic. And this is what actually the person in the name Faraday did. And that's how he uncovered that yes, there is such a connection, there is such a symmetry, if you wish. Current in the magnetic field causes the movement of the wire. But now he has discovered that movement of the wire has caused actually the appearance of the current inside the wire, basically generating the electricity. Now, that's very important because this is exactly how we generate electricity. From mechanical movement. Movement of the wire is mechanical and it generates electricity in this wire. That's the electromagnetic property of the thing. And that's how we use basically because of this discovery, we have the electricity around us. So that's why it's very important. Okay, so let's just, one more thing I forgot to tell. Existence of the current in the wire, what does it mean? Well, it means that there is certain voltage actually on the ends of this wire. So if there is a difference in potential, there is a difference in potential or voltage, or electromagnetic, or electromotive force, we will use electromotive force. So voltage and electromotive force basically are the same thing. And so what I'm saying is that the current inside this wire means that there is some kind of a voltage on its ends or electromotive force. If we are talking about generating the current, which means basically we are forcing the charges inside electrons to move to one side of the wire, that means we're generating electromotive force. So that's the language kind of which I will be using. If the wire is somehow connected and there is a loop closed circuit, then there will be movement of the electrons all the time. But if there is none, there is still a difference in potential which might actually be generated. And that's what we're talking about. What's important is we're generating the EMF, the voltage, the electromotive force inside the moving wire. Okay, now we will talk about a concrete experiment. And I will use a different picture. In this case my force is perpendicular to the board. I will change the picture in such a way that magnetic lines will be perpendicular so the force will be along the board and it will be better visible. So experiment is basically exactly the same as before. Now let's consider my magnetic field are directed perpendicular to the board. So let's say my north pole is here, my south pole is behind the board. So magnetic field lines usually are represented as, well, if you wish it can be viewed as an arrow if you view from the tail versus this representation of the arrow if you look from the head. But in this case we're looking from the tail. So magnetic north pole is on this side of the board, magnetic south on that side of the board. Okay, now what we do is we will have a closed circuit which contains two rails, some kind of resistor connecting on this side. And on this side we will have some kind of a rod which can, this is a metal rod which is moving parallel to the other to itself on these rails. So it's moving this way. And I suggest that we will move it this way with a speed V. So that's basically the setup of the experiment. Now we have the movement of the rod, we have magnetic lines and let's see what happens. Why do we have this generation of electricity? Well, everything is related to Lorent's force. Let's just think about it. Inside of this metal rod there are electrons. Now electrons are connected, they're rotating around atoms. Usually in metals at least around the atom the electrons are rotating in different orbits. And the outer orbit is less electrons on outer orbit is less attached to the nuclei. Nuclei are more or less stable inside the material, inside the metal. Let's say it's copper. But electrons on the outside they're not as strongly connected and there are some free electrons. One or two electrons of each atom are, well, they can actually move relatively free. They can jump from one atom to another electron from that atom maybe goes back to the first one. So there are some, we will call it free electrons. It's not really free but they're very loosely attached to their atoms. And the strong force can actually move them into one or another direction. If there is a strong force, electrostatic force or some other force. So what happens here? Well, look at this. We are moving the whole rod, which means we are moving with this rod, we are moving all the electrons inside all the atoms actually, nuclei and electrons, et cetera. Well, and we know that if we are moving electrically charged particle inside the magnetic field and this is magnetic field and we are moving across magnetic field lines, which means perpendicularly to lines. So every electron right now is moving where? This direction. Now magnetic field is this direction. So it's perpendicular. There is a Lorentz force, which basically acts on each electron. Well, some electrons are relatively attached to their atoms, but the free electrons are not that much attached, right? So Lorentz force might actually kick them out from their orbits and move where? Well, let's think about it. Lorentz force is always perpendicular to magnetic field lines and perpendicular to trajectory. Trajectory is this way. Lines, magnetic lines are this way. So what's the perpendicular to both? Well, that's the direction of the rod itself. The rod is perpendicular to the direction of each electron inside it and it's perpendicular to magnetic field lines here. So electrons will move in the rod into one of two directions depending on the direction of movement of the rod and direction of the magnetic field lines. Now in this particular case, let me just think about it. It's a right hand rule, so I think that I have to put my hand like this so magnetic field lines are going into the hand. The thumb goes towards the direction of the movement of electrons, so the electrons will move up. So the electrons will move within the rod from each place where they are towards this end. And now since it's connected, they will start rotating. This is a circuit. This is a closed circuit. And that's what basically electric current is. So as long as we are moving our rod, the Lorentz force, which is acting on every electron, will push these electrons here and they will move around the closed circuit and continue moving. So the current exists as long as we are moving the rod. And this is something which was discovered by Faraday and called electromagnetic induction. We are generating the current in this particular rod by moving it perpendicularly to the lines of magnetic field. So the movement should be perpendicular and the wire itself should be stretched perpendicularly. So that's the case which we are talking about right now. Now, let's try to quantify what we are doing right now. Let's consider that because of our movement, there is a current I generated in this circuit. Now, L is the length of this wire and let's call this distance x. Because we are moving, so x is basically function of t, right, of the time since we are moving. And v is dx of t. The first derivative, speed is the first derivative of the length which we are covering. So b is given, that's the magnetic field intensity. Consider that we are generating I. Now, what happens? Well, as we talked about before, the Lorentz force which is acting on every electron and forces to move it this way, this generates the electric current. So electric current moves this way. Which means that the Lorentz force which is acting on the entire wire now. What happens in this particular case? Well, in this particular case, let's just think about it. My current is this direction. Now we are talking about an entire current in the field. My magnetic field are this direction. So the Lorentz force on an entire wire, an entire rod, whatever, is acting perpendicularly to both. Perpendicular to this direction and perpendicular to this direction. And what is this? Well, that's this direction. But let's think about what's exactly a direction. My field comes into this. My electrons now are coming this way. Which means my force is, my Lorentz force is directed this way. So when we are moving our rod with a constant speed b, we have to actually work. We are working against the Lorentz force. So the Lorentz force on one hand forces the electrons to go this way. But as soon as they go this way, the Lorentz force moves the whole. Well, it's not moving. We are moving. But there is a force which is actually directed against the movement. Well, on one hand, you obviously understand that that's exactly how it must be. Because if the force is directed in a different direction, not against our movement, then it will help us. Which means we will have free energy. We will just move our rod, just push it a little bit in one direction. And then the Lorentz force will start moving it further and further and further and faster and faster and faster. Right? No such luck. No free energy. There is a law of conservation of energy. So we are generating electricity but we must do some work against this force. So the force is equal to this one, which means our work must be equal to this. So we are working by pushing our rod this way. Okay. Now, what happens with energy which we are spending? Well, we can say that it's generating the electricity. And where is this energy now? Well, we have this resistor and resistor actually is heating up. Electricity is converted into heat and that's what happens. So we know how energy is, well, consumed by electric circuit. If you are remember, it's I times U times T times T. So I times U is a power, W is work, so power times time is work. Now, if you remember this, you definitely have to go to electricity part of this course, because that's covered. So this is the work which electric current in a loop is exerting. Exerting, exerting, sorry, exerting. Okay. So we are spending certain amount of work by moving with a constant speed against this particular force. And this amount of work is converted eventually in heating of this resistor. Right? So that's what's happening. Now, okay, so we can basically make some kind of an equation. The work with which this force, let's say we are moving by certain distance dx. So what's the differential? What? Differential. So what is the work which Lorentz force is doing, which we have to overcome, which means we are doing exactly the same work, basically pushing the rod in this direction. Well, that's the force, which is this one, times the distance. Right? So it's I times L times V times dx. So this is the work which we actually have to perform. And because of that work, there is a current I and there is a difference in electric potential. There is a voltage, there is a electromotive force between these points. So that should be equal to I times U times time. Time is dt. That's during infinitesimal a small amount of time. We are moving the rod by infinitesimally, infinitesimally. So that's what we're doing. So this is our short distance parallel to itself. So this is our equation, from which we derive very simply dx and dt will divide to dx, we will have V. I will go out and what we will have, we will have that L times V times V. V is dx divided by dt is equal to U. So this is a voltage which is generated, the EMF, the electromotive force. And it's generated by moving our rod of the length L, which is perpendicular to the magnetic field lines, moving it perpendicularly once again to magnetic field lines with the speed V, where V is the intensity of the magnetic field. Now, let's think about this formula a little bit. It's not the final formula. It's almost final. What is L times V? This is how it was done, right? This is L, this is V, which is dx divided by dt. So if this is dx, L times dx is area. So when we're talking about L times dx divided by dt, which is this one, L times V, V is dx by dt. So what is this? This is the area of by dt. So this is the area of by dt. And so we can change this formula into V times the area of dt. Well, it is area indeed because the longer the rod, the more magnetic lines we will swipe across when we're moving it, right? So it's very important actually because let's just think about, in this particular case, B is a constant. So I can actually say that this is equal to DB times A divided by dt, which is speed of changing the B times A. So if B intensity times the area, in this case area is increasing, so B times A is obviously increasing. So B times A, the intensity of the magnetic field times the area which are actually encompassing certain area of the field. You see, with this wire frame, we are cutting certain area from the magnetic field. And we are multiplying this area by the strength of the field, by intensity of the field. Now this thing is called magnetic flux. So B times A is a magnetic flux. Now let's think about what is magnetic flux? Well, magnetic flux can be basically visualized as the number of magnetic field lines per the particular, within a particular area, right? We are talking about magnetic field lines as a representation of strength, of intensity of the magnetic lines, right, of magnetic field. So that's why we can say that this multiplication area times the strength of magnetic field lines, or density of the magnetic field lines, if you wish, is the flux. That's when it's flowing, the magnetic energy is flowing through this particular area. So if the area is changing, as in our case, for instance, it's expanding, we are changing the magnetic flux through this frame. Well, there are many different ways we can change the magnetic flux. This is one of them. So if my frame is perpendicular to magnetic field lines, we can just expand the area. Or we can do it differently. If this is magnetic field lines and this is my area, I can turn it. And as you see, the amount of energy, magnetic energy, the number of magnetic lines, actually, which are going through the same contour, but turned at the angle is changing. So we are changing the flux, magnetic flux. And that also is basically equivalent to shortening our, so instead of turning it this way, we can just shorten it. And again, it will be exactly the same effect. So expanding or shortening of the wire loop is basically the same thing as turning it in such a way, or in such or another way. And that's exactly what I will be talking during the next lecture probably, where I will explain how we will really generate the electricity, because it's kind of an awkward way to generate by moving some rod. There is a better way, basically, but it means exactly the same. We are changing magnetic flux. So magnetic flux, when it's changed, and this is some kind of frame, a contour or whatever you want, it generates electricity inside this circuit. And this is basically the Faraday's law, that electromotive force generated is equal to the speed of changing of the magnetic flux through this particular closed circuit. So closed circuit gives you some kind of an area. And as long as this area changing, maybe expanding, maybe turning, turning will be the next lecture, then there is an electricity generated in this circuit. This is the Faraday's law. And this is extremely important for generating electricity, which we are using, because that's how it's generated, basically. Okay, that's it for today. I do suggest you to read the notes for this lecture. So you go to unizur.com to Physics for Teens course, the Resolute Electromagnetism part. And that's the first lecture in electromagnetic induction. Thank you very much and good luck.