ЭЛЕКТРИЧЕСТВО для ЕГЭ по Физике с нуля! Вся теория! Электростатика, Магнетизм, Закон Ома!

Hello everyone on VK, hello everyone on YouTube. Please write in the chat how well you can hear me, how well you can see me, and let's get started. Okay. Well, it seems like everything is going well, right? Guys, plus in the chat if everything is good with the quality, with the video, with the picture, with the sound, with everything. And we begin. So, what do we have planned to discuss today? Today, I want to, first of all, briefly explain all the theory of electricity to you. Briefly doesn't mean there will be only formulas. I will really try to explain to you for understanding how everything works, what an electric field is, what a magnetic field is, how they work, how to work with them in problems, right? I will also explain all the main formulas and all the main laws. And I initially thought of making the stream only about theory. However, I decided to add a little bit of practice. I'll spice it up a bit. I will add, therefore, a few problems purely for understanding. We will solve about 10 problems from the first part to consolidate what we will be studying today from a theoretical point of view. So, well, shall we fly? Let's fly. So. Guys, I remind you that first, by the link in the description, there is my Telegram channel, which you must subscribe to if you want to pass the Unified State Exam. Good, because in it I publish all my open broadcasts, which I have been conducting really every week lately, in which I publish free methodological guides on various topics. Recently, I published a huge 22-page guide on mechanics, which is very useful. Plus, there is also a file in the description with all the formulas for the Unified State Exam in physics that you must know. So, go ahead, take it, and prepare. And also, by the link in the description in my Telegram channel, you can wait for the opening of the seven-month physics course. We have already closed the eight-month one because, well, there is less time until the Unified State Exam, so it is planned, I will tell you. the opening of the next course, which you can still sign up for. Therefore, follow the link in the description to Telegram and wait. And who hasn't signed up? So, will there be a recording? Most likely, there will be no recording of the stream because I doubt we will get enough likes. Let's set a goal to get 100 likes to get the recording of this wonderful stream. The stream is truly wonderful, guys, because it will be very useful. Be sure to watch until the end so as not to miss anything. Because at the end, we will have the Lorentz force, the Ampere force, the right-hand rule, electromagnetic induction, which no one understands, self-induction EMF, which absolutely no one understands. In short, the stream will be very useful, very rich. So, let's fly. We will start with the very basics. We will start with electrostatics. What is this section about, guys? Electrostatics is the study of the interaction of electric charges. What is an electric charge in general? Well, let's give you an example, purely for understanding. In physics, there is a concept like mass, right? It is measured in kilograms. What does it show? Mass shows the measure of inertia, right? That is, the greater the mass of a body, the harder it is to change its speed. That is, conditionally, the heavier an object is, the harder it is to accelerate or stop it, right? That's mass. You understand this? Mass, a characteristic of a body, right, some kind of characteristic. And there is a characteristic like electric charge. And it shows how this body interacts with other electric charges, so to speak. Like that. That is, electric charge is a thing invented by physicists to explain the behavior of bodies. What is electric charge measured in? It is measured in coulombs and is denoted by the letter Q. The first thing you need to know, I think you all know this, is that electric charges interact with each other. There is a formula called Coulomb's law. It looks like this. And now I will briefly explain what is what in this formula. Imagine you have two electric charges. Electric charges have a sign, but we'll talk about that later. There is a charge Q1, for example, and there is a charge Q2. The distance between these charges is, for example, R. So, these charges will interact with each other, that is, attract or repel. We will talk about the force now. K is the proportionality constant in Coulomb's law. It is a tabulated value. Q1, Q2 are the charges, respectively. Note that we take the absolute value and divide by the square of the distance between these charges. That's it. With this force, they will interact. Question: how exactly will they interact? Attract or repel? It's all elementary here. Unlike charges attract, that is, plus with minus, and like charges, that is, plus with plus or minus with minus, will repel each other. Okay. I think everyone knows these points, right? Everyone knows Coulomb's force, it's understandable to everyone. Nothing interesting here, right? Let's plus in the chat if you really knew this formula. Uh-huh. Guys, in terms of time, I think it will be about two to two and a half hours, something like that. Okay. Alan, you scoundrel, late again. Well, look, I have a different Alan. Okay, then I have no questions. So, good. Next. This is all very cool, guys. This is how it's explained in school. You learn this formula, and then bam, electric field. Like, suddenly. Moreover, I think this formula appears in the ninth grade, and in the tenth or eleventh grade, the electric field appears. It just appears out of nowhere. There's no logic. What's the deal? I'll explain. Now, pay attention. Any interaction doesn't just happen. That is, let me explain, for example, gravitational interaction, right? For example, the Earth attracts all objects on its surface, right, and it attracts the Moon, right, and it interacts with all other bodies in the Universe. Because, as we know, according to the law of gravitation, according to the law of universal gravitation, which Newton discovered, any two objects in the Universe possessing mass attract each other. And there is even a force that is very similar, it is calculated like this, the force of gravity, which is calculated as the gravitational constant, the mass of one body, the mass of the second, and divided by the square of the distance between them. It's a copy, the formulas are almost indistinguishable, right? And this gravitational interaction happens not just like that, but through a gravitational field. That is, there is some kind of gravitational field that every object with mass creates around itself. So, for example, there is the Earth, and it creates some gravitational field around it. What is it? It is a special type of matter, through which and through which bodies interact, you understand, right? So it's like how to explain it? Well, it's like some, for example, a good analogy. It's like some kind of jelly, right, which has different densities. That is, there are denser lumps, and there is a more liquid space, right? It's roughly the same. And if we describe the gravitational field, it will look like this. That is, where there are some heavy objects, it will be denser, and the further away from heavy objects, the more liquid it will be, so to speak, right? And it's the same with the electric field. That is, the electric field, let me write this down, the electric field is a special type of matter. matter, through which the interaction of electric charges occurs. That is, let's write it like this, through which electric charges interact. And now it's important, every electric charge creates its own electric field around itself. And at the same time, every electric charge interacts with the electric fields of other charges. You understand, right? So it turns out that the electric field is like a network that connects all electric charges in the Universe. You understand? The scale, right? Guys, no, you don't need to memorize this. I'm just explaining it so that it's easier for you to understand what formulas I'm about to write. And now, with this understanding, however little it may be, about what this electric field is, what it is, we will now write down a few formulas, a few key points. So, look, there are two ways to describe the electric field in a specific point in space. There are two characteristics: a force characteristic and an energy characteristic. Let's start with the force characteristic. It's the simplest. So, look, the force characteristic of an electric field is its strength. What does it show? So, again, right, imagine that we have some electric field. That is, it is some kind of three-dimensional matter, so it exists in all space. And in each point, it's, well, different, right? That is, conditionally, the closer to the charge, it has one kind of force characteristic, the further away from the charge, it has another, that is, it is not uniform, inhomogeneous matter, right? So, like air. Imagine that we are, if we could magically learn to see the electric field, you open your eyes and you see that you are in some kind of substance that surrounds everything. And, for example, my camera emits its own electromagnetic radiation. The closer to the camera, the denser it is, this field. The further away from it, the weaker it is. You should imagine something like that. And, so, the main force characteristic of an electric field is its strength. What does it show? It shows with what force the electric field acts on a point charge placed at that point in the electric field. That is, again, I choose some random point, right, I take it, oops, oops, oops, here, I want to know the field strength at this point. I place a point charge like this in this point, and I measure with what force the electric field will act on this point charge. And thus, I get the field strength at that point. It is measured in volts per meter, or as an alternative, newtons per coulomb. Okay. So, guys, is the main idea clear here? So, pa-pa-pam-pam. I updated the sound a bit. It should work well now. Uh, so, regarding the fact that this is crazy, well, I wouldn't say it's crazy, guys. It's just that physics is really not easy, so I'm explaining as best as I can. Okay. Uh-huh. Everything is clear now, right? Next. It's important to understand that every electric field has lines of electric field strength. They are usually denoted like this, right? Well, that is, some line, each line has a direction, naturally. Right. And, look, the force from the electric field. If the charge is positive, unfortunately, I don't have a red chalk, only pink. Well, let it be pink. If the charge is positive, then the force from the electric field acting on it will be directed in the same direction as the electric field strength. And if the charge is negative, then the force will act in the opposite direction. That is, you see, right, the lines of strength are directed to the right in the figure, and the force from the electric field acting on the negative charge will be directed to the left, i.e., in the opposite direction. Okay. No, no, no, guys, it's not a disconnect. I just updated the stream so that we don't have a sound delay. I don't know, I've been fighting this problem, fighting it, fighting it. Sometimes this happens. Especially with VK, with YouTube, when you stream to two platforms. Okay. The force characteristic, I think the main points are clear. Regarding the energy characteristic. This is where the real craziness will start, guys. Potential, so the energy characteristic of an electric field is potential. It is measured in volts. And what does it show, guys? Essentially, potential, let me write this formula, is the potential energy that a point charge has at a given point in the electric field, divided by the magnitude of that charge. In other words, it can also be said that the potential is equal to the work done by the electric field in moving a single point charge from a given point to an infinitely distant point. So, again, essentially, remember, probably, potential energy. What is it, guys? When you have some object, for example, this chalk, right, we have chalk, it is at some distance from the floor, so it has some potential energy, right, mgh. And what does this mean? Essentially, mgh means that if I release this chalk, it will fall to the floor and the gravitational field will do work equal to the potential energy. Right? It's roughly the same here. That is, conditionally, the electric field tends, depending on the sign of the charge, either to push it out or to attract it to the source of this electric field. And it has this energy. So, I think the main idea is clear. We will move a little further, and it will become even better and clearer. It is also important to mention here that there is a formula for the work done by an electric field, which is calculated as the charge multiplied by the potential difference between two points. That is, again, if you have two points, well, for example, there is point one with potential φ, then the work that needs to be done, or rather, that the electric field does in moving a charge from one point to another, can be calculated by this formula. And one more important formula is, of course, voltage. Voltage is precisely this potential difference. That is, it is φ1 - φ2. The potential difference between two points. From this, by the way, an important point that we will use a little later is that voltage is always measured between two points. That is, to state the voltage, we cannot say the voltage at point A. We must say the voltage between point A and, for example, some point B or point C. We will talk about this again a little later when we move on to electric circuits. Okay. Okay, guys, I remind you, don't forget to like, because you probably want the recording of the broadcast, right? So, what's important to talk about now, guys? You can screenshot this, in principle. And let's move on slowly. Let's move on slowly. I'll erase, erase, erase, erase, probably. Like this. Now we will draw the lines of electric field strength, and also talk a little about the electric field created by a point charge. Look, let's start with the charge itself. First, imagine you have some point charge. Let's draw for two types of point charges, i.e., for positive and negative. Or rather, negative and positive. Like this. I show one thing, say another. So, I already said, right, that every point charge, right, in general, every charged body electrically, creates its own electric field and at the same time interacts with the electric fields of other charges. How does the electric field of a point charge look, so to speak? If this charge is positive, then the lines of strength are directed like this, in all directions from it. Here they are, the lines of electric field strength. If it is a negative charge, then it attracts to itself, so to speak, right, so the lines of strength will be directed from infinity to this charge. Like this. Understand, right, guys? And now, by the way, this point becomes clear why positive and negative charges attract each other. For example, remember that the force from the electric field acting on a positive charge will be directed along the lines of strength, i.e., in the same direction as the lines of strength. Now imagine that we take a positive point charge and place it here. The lines of strength are directed towards the negative charge, and it will be attracted to the negative charge. And if we take a positive charge and place it here, for example, the lines of strength are directed away from the second positive charge and will repel it, you understand, right? So the logic holds up in general. Okay. Good. What else is important to say? Naturally, strength. So, let's take a point now. Well, for example, here. At some distance from this point charge. Uh, yes, an important point, guys, I wanted to say that the lines of strength are just depicted like this. In reality, there are no lines of strength. They are just in textbooks. And in general, scientists depict these lines to visually show, right, that somewhere the electric field is denser, the lines are denser, so the field is stronger, and the further away from the charge, the weaker the field. But this does not mean that the electric field only exists on these lines. No, the electric field exists everywhere. And the lines simply show by their density that somewhere the field is stronger, somewhere weaker. In reality, as I said, a good, really good example is to work with, first, to understand that this is all happening in 3D, not in 2D, right, not in a plane, but in volume. And, secondly, to understand that, as I gave the example with some jelly with lumps, right, you have a lump of denser electric field, and the further away from it, the more liquid and weaker the field is. And let's try to find the electric field strength at a specific point at some distance from a positive point charge. KQ divided by R squared, naturally. Uh, yes. And here let's take the absolute value, because if we have a charge, that is, again, right, that K is the proportionality constant in Coulomb's law, a tabulated value. Open the textbook, open the textbook, or look at the beginning of the Unified State Exam. Q is the charge of this charge for which we are looking for the electric field strength. R squared is the square of the distance from this charge to the point where we are looking for the electric field. That is, again, this is the strength at this point. We can say, let's find it at this point. Measure the distance to this point, calculate using the same formula. Understand, right, guys? So, guys, are there any more questions? You're talking appetizingly. Tyn-tyryn. Why is the person blurry? Black rascal. We'll sort that out later. Uh, although, okay, yes, later. Let's save the questions for later. Okay. Why is Q in absolute value, Yaroslav? Because Q is an electric charge. It can be both positive and negative. Well, you can see from the picture. Uh, uh, and, accordingly, we are looking for, uh, the magnitude of the strength. Well, that is, our strength cannot be negative. It has a direction, but it cannot be negative. Therefore, we take the absolute value. Okay, let's, guys, plus if this is clear so far. The next formula, another one, is the electric potential at the same point, let's call it point A, right, so that it's clear what we're talking about. The electric potential at this point will be calculated simply as K Q over R. That's it. That is, again, K is the proportionality constant in Coulomb's law, Q is the charge, R is the distance from the charge to the point where we are looking for the electric potential. Okay. Good, guys. I hope you are taking notes in parallel so as not to miss anything, not to lose anything. So. Okay, okay, okay, okay, okay. Uh-huh. Then the real madness begins. Let me try to draw something. Let's imagine that we have, I'll erase this, probably, you've already written it down. Imagine that we have some charge, again, right, which emits an electric field around itself, so to speak, right, this is conditional. That is, it simply creates an electric field around itself. Some charge, it's really important. There is an electric field around it. It goes in all directions like this. We can see from the density of these lines that the further away from the charge, the weaker the electric field. Okay. Good. And there is a concept, guys, called an equipotential surface. What is it? What is an equipotential surface? Let me write it somewhere. Equipotential surface. It is a surface on which the potential is constant. In our case, let's try to build such a surface. To build this surface, you need to understand that it is always perpendicular to the lines of strength. That is, in our case, it will be, for example, look, like this, right, we build, for example, here, you see, right, a right angle here, here, here, here. Well, and, accordingly, it turns out like this. Moreover, the surface, again, we are talking about 3D, so we are building on a plane, but in reality, it will be some kind of sphere, right? And at each point of this surface, the potential is the same. Well, let's call the potential φ1. And if we build some second equipotential surface, well, it will have some potential φ2. And it's important to understand that along the lines of strength, the potential will decrease. That is, the further away from the charge, the lower the potential will be. Understand, right? So φ2 is less than φ1. This is a very important point, guys. Even in the first part, I think today, yes, we will definitely solve a problem today where there will be such a question, something like comparing potentials. And you need to remember very well that along the lines of electric field strength, the potential decreases. That is, the further along the line of strength, the lower the electric potential. So, good. Uh, pa-pam-pam. Uh-huh. Uh-huh. So, guys, I will answer questions a little later. Now we will finish this section, and I will answer the questions, of course. So, and probably the last thing I wanted to tell you is about a uniform electric field. Uniform electric field. What is it? It is a field whose strength is constant. That is, the lines of strength are parallel to each other, and the strength is the same at all its points. That is, conditionally, in our analogy with jelly, it's ideal jelly, which was made not in a canteen, but which your grandmother cooked without lumps, without anything, with ideal uniform density. That's what a uniform electric field is, right? It's a field where the strength is the same at every point. Then, if we take two equipotential surfaces again, well, we just build two perpendiculars to the lines of the electric field, right, not even perpendiculars, guys, but planes. Two planes perpendicular to the lines of the electric field. Here, for example, we will have potential φ1, and here potential φ2. And there is such a thing that voltage equals strength multiplied by the distance between these two equipotential surfaces. Something like that. This formula will work very well in capacitors. We will need it. So. In principle, guys, that's all for electrostatics, for the main theory. We will consider capacitors separately a little later. I will move them aside a bit. That's probably all for electrostatics, for the theory. Let's gradually move on to practice and solve problems so that I can show you that I wasn't telling you anything extra, but was speaking strictly to the point. Look, I have, I think, how many? Three, four problems on electrostatics. Four problems. Two of them are super easy, and two are quite unpleasant. Quite unpleasant. So, here's a problem. Number one. By how many times will the acceleration of a charged dust particle moving in a uniform electric field increase if its charge is halved, and the field strength is tripled? So, let me erase the board first, right? Guys, you can suggest, in principle, what formula will solve this problem. So, again. The charge was halved. Let Q2 = Q1 / 2, right? And the strength was tripled. So, E2 = 3 E1. Uh-huh. We are asked by how many times the acceleration will increase. So, a1. It is unknown by how many times the acceleration will increase. The first thing to understand is that the acceleration of this dust particle is caused by some force. And this force is, naturally, the force from the electric field acting on the dust particle. So, first, we recall, right, that according to Newton's second law, the force acting on the dust particle will be equal to its mass times its acceleration. Therefore, the mass of the dust particle, naturally, does not change. The dust particle itself does not change. So, if the force increased by some factor, the acceleration will increase by the same factor, right? So we can say that a / a1 = F2 / F1. Well, since the mass is constant. Okay, good. And how do we know with what force the electric field will act on the dust particle? That's from the definition of strength, right? The force of the electric field is equal to the electric field strength multiplied by the charge. Well, in the case of our dust particle. Uh-huh. That's it. So, it turns out F2 is E2Q2, and F1 is E1Q1. So. Okay. Uh, that's it. Now let's substitute E2. Let's immediately substitute it as 3 E1. Q2 as Q1 / 2. Well, we'll leave E1Q1 here. It's clear that E1Q1 will cancel out. So, essentially, it's 3 / 2 / 1. Well, it turns out to be 3/2, which is 1.5. That's it. By this factor, the force of the electric field will become larger in the second case, and therefore the acceleration of the dust particle will become larger by the same factor. So. Uh, good. No, what 25th problems, guys? Don't tease me. I'm telling you, the first part is the eleventh problem of the Unified State Exam. We just solved this. We definitely won't get into the second part today because the problems are very, well, not very difficult, but they take a lot of time to solve. And

Today, my goal was simply to explain the theory to you. Alright, Alan. No, look. Good question. Why isn't this formula here, right? Why isn't this formula here, but the one I indicated? Yes, not this one, but this one. What's the difference, guys? What is this formula for? This is the formula for the electric field. The electric field strength created by a point charge. We were interested in the electric field. that this charge creates. In general, no. We were interested in how this charge interacts with an external uniform electric field. They tell us, yes, a dust particle moving in a uniform electric field. So, there was some external electric field into which we threw a dust particle, it moved somehow, we changed the strength of the external electric field and the charge of the dust particle, and something happened. That's why this particular formula was needed here. Okay, good. Next task. Ah, the next task, guys, I'll explain right away. If you want a lot, a lot of practice, if you want me to rush less with the theory, yes, to explain in more detail, so that there is a lot of practice, so that we analyze every problem in the most detailed way, so that we solve all the prototypes of the Unified State Exam from the first part, all the prototypes from the second part, that is, all, well, all the main ideas, problems that can be encountered on the Unified State Exam, then you should go to my physics course. Follow the link in the description to my Telegram and wait attentively. I think that in the next few days, registration for the course will be open. What will be there? So, first, the course will naturally include all the theory for all sections from scratch. That is, even if you are a complete beginner for now, you will be able to figure it out. Secondly, there will be an analysis of all the main ideas of the problems, that is, all the main prototypes of what can appear on the Unified State Exam. That is, everything that the compilers release, like Fipi, in Dimidiova's collections, and so on. We will, of course, analyze all of this. Yes, by the way, I am the one teaching the course. Well, just in case. Next, on the course, there will be an individual plan tailored for everyone. That is, you enroll in the course, take an entrance mock exam, and your mentor helps you adjust an individual plan for yourself. That is, if you, for example, already know mechanics perfectly, then the curator says: "Okay, then do, do these sections." If something is lagging, he will focus on that. That is, you won't have a situation where a lot of information is just dumped on you and you don't know what to do with it. Next, naturally, there will be homework for each lesson. That is, how our lessons go: theory, practice, and then reinforcing all of this with homework. Homework with checking. That is, if you are on the Standard or Premium tariff, that is, the tariff with a curator, your problems will be checked directly on our platform. Great. Next, there will be mock exams. Well, how will they be, there are already guys who have signed up, mock exams every month. And the closer to the Unified State Exam, I think we will increase the frequency of mock exams even more, so that you get even more used to the format. So, yes, what else? What else? What else? Naturally, I have incorporated repetition into the course. That is, we have now, for example, completed a section of mechanics, then we start the next section, but we periodically return to the ones already covered, so as not to forget them, not to lose them. Naturally, immediately before the Unified State Exam, there will be a review of everything we have covered, all the theory. We will briefly review and solve the main prototypes again, so that it all refreshes in your mind. Well, and plus, if anything, we will also provide assistance with appeals. Therefore, guys, who wants to prepare for the Unified State Exam with me, who wants a quality result, a quality result, why do I say this? Because, firstly, I have been preparing guys for 5 years myself, and secondly, because last year my students scored 80+. I didn't even really count the 80+. I was like, 80, go. Oh, weak, weak. Undeserving, actually. An awesome result, but for some reason I'm already fixated only on 90+, 95+. That's what I'm aiming for. And yes, my students, last year there were many students who scored 90+, 95+, and several people scored 98. And there was even a perfect score last year, so you can also find reviews in my Telegram channel. Go, subscribe, and wait for messages about registration for the course. Okay. All right. Let's move on. Ah, regarding formulas, why, when we calculate potential, we write R, and when we calculate field strength, there is R²? Ah, well, because physics. Well, that is, you can try to derive these formulas. Well, we will derive all of this in the course, there will be answers to this question. But for now, I just don't see the super point in delving into the very, very, very depths, deriving all these formulas ten times to show you the connection. There's just such a formula, it works like this. So, how many points can you score on the Unified State Exam in physics? I know mechanics, molecular physics, and electricity. Yes, a lot, because essentially these are the most important sections. Then there, ah, well, electricity, I assume you don't mean optics. Optics can be quickly covered, and quanta must be covered, because it's an easy section that will bring you points. And that's it, you can definitely aim for 90+. So, let's move on. Let's move on, guys. The next problem is already on the board, on the screen. The force of electrostatic interaction between two small identical metal spheres, having charges Q1 and Q2, which are written here, yes, equal in magnitude to 18 micro Newtons. What will be the magnitude of the interaction force if they are brought into contact and moved apart to the previous distance? So, let's do this. F1 = 18 micro Newtons. Q1 = -80 nanocoulombs. Q2 = 40 nanocoulombs. Okay. What will be the magnitude of the interaction force if the spheres are brought into contact and moved apart to the previous distance? A very cool problem. Let's first say that initially this force F1, what is it? It's Coulomb's force, right, which is calculated as K Q Q1 Q2. Don't forget to put the absolute value, because otherwise the force might turn out to be negative. It would be strange. Divided by the square of the distance between these spheres. Okay. Now, in the second case, we brought them into contact. What will happen if two charged spheres are brought into contact? Charge redistribution will occur. Again, we will talk about charge distribution, redistribution a little later. Although no, let's, I think, this is the most ideal time. So far, we have talked about point charges. Most often, it will probably be, well, a point charge. Most likely, it will be some kind of electron or proton, that is, some elementary particle. But here they are talking about some spheres. So, a sphere is some kind of substance that contains more than one particle, right? That is, several molecules, several atoms, perhaps even several thousand or millions of atoms. And how to understand, like, not even how to understand, but why it can have some charge, right? Why? Here you need to remember that any substance consists of atoms. And what is an atom? An atom is a positively charged nucleus. around which negatively charged electrons fly, understand? And under certain conditions, these electrons can break away from atoms. And in the end, the total charge of a body, the total net charge of a body, arises because this body has either an excess of positive particles, that is, an excess of positive nuclei, or in other words, a deficit of electrons, or vice versa, an excess of electrons. That is, if a sphere is negatively charged, it means that the number of electrons in it outweighs the number of protons in the nuclei. And because of this, the sphere has a negative charge. If the sphere is positive, it means it lacks electrons, understand? Yes? And when we bring two spheres into contact, they start to exchange charges. That is, the charge begins to redistribute. And there is such a good rule that, well, let's say, the law of conservation of charge, that Q total, which equals Q1 plus Q2 and so on, is conserved. Moreover, they tell us that the spheres were initially identical. So, obviously, the charge should be distributed equally between them. If the spheres are identical, then the charge on each should become the same after redistribution. So, before distribution, they had charges of -80 and 40, meaning the total charge was -40 nanocoulombs. And dividing equally, we get -20 nanocoulombs on each. Let's write that Q1' = Q2' = -20 nanocoulombs. Each sphere now has this charge. Okay? Do you understand what I'm doing here, guys? What's with this sound, damn it? Uh, 17 micro Newtons. So, the sound should be normal now, guys. I updated it again. Well, it's an endless struggle. Okay, good. 18 micro Newtons. While the charges were, well, let's write it here, maybe there's no point. Well, let's write it, yes, like, here it was -80, and here it was 40 nanocoulombs. Uh-huh. Okay. It became two by -20, so F2. Let's write somewhere here that the Coulomb force in the second case became K -20 -20. The distance between them did not change. Uh-huh. Well, that is, we understand that initially, here in the numerator of the fraction, there was the product of the absolute value of -80, which is 80, and 40. 80 is what? It's essentially 3,200, right? And it became 20 by 20, which is 400, that is, eight times less. Agreed? So the Coulomb force should also decrease by eight times. And this means that F2 divided by F1, or rather, vice versa, we need to find F2, right? What are we looking for according to the condition, yes, what will be the magnitude of the force? F2, it turns out, is equal to F1 divided by 8. That is, 18 micro Newtons divided by 8. We get 2 and 2/8, that is, 2.25 micro Newtons. Here's the answer. 2.25. Uh-huh. So, Arseniy, I see, you solved it correctly. Okay. Okay. Good. Next. Electricity. Listen, yes, a huge number of problems are numbers eleven, twelve, thirteen, fourteen. Exactly. And in the second part, it can be numbers twenty-one, twenty-three, twenty-five. Ah, something like that. Something like that. So, it turns out that there can be about seven, definitely 6-7 problems on electricity. So, let's move on to the most interesting part. Oh-oh-oh-oh, Yaroslav, damn it. Re-watch, please, go back. I just explained the difference of eight. You can solve this problem differently, more laboriously, so that there is more math. I took the quick route. Go back, watch again. So, let's move on. The next problem we have is this one. And this is all, like, if such a problem appears on the Unified State Exam, it's over. So, look. A uniform electrostatic field is created by a uniformly charged, extended horizontal plate. The field lines of force are directed vertically downwards. Well, that's clear. So, this can be skipped. What's interesting here? We have five statements, and we need to determine which ones are correct. So, let's think. First. The potential at point B is less than the potential at point C. What should we remember here? Here we need to remember what I said 15 minutes ago. Along the lines of electric field strength, the potential decreases. Look, point C is located earlier along the electric field lines than point B. See? Point B is further along the electric field lines than point C. So, the potential at point B is less than at point C. First, yes? Second. The electric force acting on a positive charge placed at point B is directed vertically upwards. So, let's remember where the electric force is directed if we know where the field lines are directed. The field lines are directed vertically downwards. Well, judging by the figure, we place a positive charge at point B. The force from the electric field acting on a positive charge is directed in the same direction as the field lines of this field. Understand? Yes. Therefore, it will be directed downwards if the charge is positive. If the charge were negative, it would be directed upwards. So, the second one is not suitable. Third. The field strength at point A is greater than the field strength at point C. Who said that? If you remember what was written above, I'll scroll back a bit. A uniformly charged uniform electrostatic field. If the electrostatic field is uniform, it means that the field strength is the same at all its points. Therefore, the field strength at point A cannot be greater than at point C. It is the same everywhere. We dismiss the third one too. Fourth. The work done in moving a positive point charge from point A to point B is zero. Oh, this is a very interesting topic. Look, from the figure, it is clear, from the figure, it is clear that we, well, let's draw it like this. Here is point A, here is point B. From the figure, it is clear that both of these points are on the same equipotential surface. That is, you see, if we connect these points with a line, this line will be perpendicular to the field lines of the electric field. That is, these points lie on the same equipotential surface. And if they both lie on an equipotential surface, we can say that the potential at point A is equal to the potential at point B. Right? Because, by definition, the potential is the same everywhere on an equipotential surface. Okay. And then what will I say? Then I will say that the work done by the electric field in moving a charge is equal to q φ a - φ b. Well, that's the formula. Charge multiplied by the potential difference. Here are two potentials. If they are equal, then the potential difference is zero, and therefore the work done by the electric field is also zero. Fourth, yes. And finally, fifth. The plate has a negative charge. Yes. Why? Because, as we can see, well, they tell us that this electric field is created by a charged plate. And, as we can see from the figure, the electric field lines are directed towards the plate. And I remind you that positive charges create an electric field with field lines directed away from the charge to infinity, and negative charges, on the contrary, direct field lines from infinity towards themselves. Therefore, the fifth one also, naturally, will fit. Okay, good. Will the stream recording be available? Listen, well, I don't see that we have accumulated enough likes. I don't think there are 100 likes yet, so there's no stream recording. Yes, for now, we have around 80 likes. Let's reach it, and you'll get the recording. Okay. It will even be on TikTok. I'll post it. Well, I'll cut it into parts, and gradually post it. So. Ah, okay. We've dealt with this problem. Let's move on. Ah, here's another problem. Well, this is a basic basic, guys. These problems that we are solving today are, with very high probability, you will encounter them, with very high probability, you will encounter them on the Unified State Exam. Next problem. Or at least something similar, structurally. Ouch. So. At points A and B, located at the same distance from point C, two small spheres were placed and fixed, carrying charges +2Q and -3Q, respectively. See figure. From the list below, select all correct statements and indicate their numbers. First. If the spheres are connected by a copper wire, they will continue to attract each other. So, let's think about what will happen if we connect the spheres with a copper wire. What is a copper wire? A copper wire is a conductor. Well, wires are made of copper, yes, among other things. So, it conducts electric charges. So, our two point charges will exchange, well, not exchange, but the electric charge will redistribute equally between them, right? They tell us that, uh, two small spheres were fixed, so, well, we assume that it will be distributed equally between them. Accordingly, the charge will become of the same sign, because if one sphere is negative and the other is positive, the charges, well, that is, electrons, will flow until the charge is balanced and becomes equal in magnitude. Understand? Uh, so both spheres will be charged identically, positively or negatively. Well, most likely negatively, because, as we can see from the figure, one charge is -3Q and the other is +2Q. So, the negative charge prevails. And, accordingly, after charge redistribution, a negative charge will be established on both spheres, and they will repel, not attract. Therefore, we dismiss the first one, the first one is not correct. Second. The Coulomb force acting on sphere B from sphere A is directed horizontally to the left. Once again. Force on sphere B to the left. Yes, because spheres A and B attract each other. And, therefore, a Coulomb force is indeed acting on sphere B, directed horizontally to the left, towards sphere A. Yes. Second. Yes. Third. The field strength of the resultant electric field at point C is directed horizontally to the right. Ah, this is interesting. What's the trick, guys? So far, we have only talked about the electric field of a point charge, right? So, let's say we have charge A at point A, let's say charge +2Q. And its field lines emanate from it in all directions, right? If it's a positive charge, it directs the electric field lines away from itself. If it's negative, it attracts field lines towards itself. But what if we need to look at the electric field created by two charges? And here's the thing: if several charges create an electric field, there is such a thing as the principle of superposition of electric fields. The field strength at a certain point will be equal to the sum of the field strengths of each of the creating creating. Wait. Problems with the Russian language, I need to enroll in the course. So, let's take, for example, let me draw a second body here to show you with an example. Here will be the charge -3Q, right? It attracts towards itself, that is, the field lines will be directed towards it. So, let's take any arbitrary point, for example, point C here. Well, as per the condition. And we see that, essentially, guys, the fact that the lines don't reach point C is just how I drew it. In reality, they diverge to an infinite distance, right? And essentially, at point C, the field strength will be the sum of the field strengths of the electric field of the first and the electric field of the second charges. They, like, overlap, understand? Uh, well, and we see that for both charges, the field lines at point C will be directed to the right according to the figure. Therefore, yes, third, we write that we agree with this statement. Fourth. If the spheres are connected by an uncharged glass rod, their charges will not change. Yes, because an uncharged glass rod is not a conductor. Therefore, the charges of the spheres will not redistribute. Well, and fifth. The magnitude of the Coulomb force. Ah, yes, fourth, so we should mark as correct. Well, and fifth. The magnitude of the Coulomb force acting on sphere B is half the magnitude of the Coulomb force acting on sphere A. This is a basic misconception. What's the trick? Well, you start calculating the Coulomb force, like K QQ1 Q2 / R². You calculate something like: "Oh, this one is bigger, this one is smaller." Guys, the Coulomb force on the charge at point A and the charge at point B are the same, because it's the Coulomb force of interaction between charges. It cannot be that one charge acts with such a force on the second, and the second acts with a different force in response. It cannot be. Simply by Newton's third law. The force of action is equal to the force of reaction. Therefore, the Coulomb forces here will be equal. Okay, good. Not visible. Ah, devil. Wait, guys, please excuse me. Here, here's what I wrote above. Uh, sorry, I overlooked something, I didn't see that my recording was blocking the problem statement. Once again. The total field strength at a certain point is the sum of the field strengths of the electric fields of all bodies that, like, overlap each other at that point. That is, conditionally, each body emits its own electric field. All these electric fields overlap at some point, they converge. And to find the total field strength, we must sum the field strength of each field separately. Like this. Okay, good, good. Everything, now I'll tell you one last crucial point about dielectrics and conductors. And with that, we will definitely finish with electrostatics and move on to electric circuits, Ohm's law, and so on. So, we've been working for an hour, and we've managed to cover quite a bit, actually. So, what did I want to tell you? First, bodies are divided into materials, right? Let's say so. In terms of conductivity, they are divided into three groups: conductors, semiconductors, and dielectrics. So, what is what? Conductors. Let's start with conductors. These are substances that, as the name suggests, conduct electric current. Why can they conduct electric current? They can conduct electric current because they have free charge carriers. And here we need to move on to the definition of what electric current actually is. Look, imagine that we have some electric field. Some electric field. Like this, for example, right. Here are the field lines. If we place a charge, for example, at this point, let me draw it like this. We place a positive charge +Q at this point. An electric field exerts a force on it directed here. Here is the electric field force. Here it is. Okay. And so, if nothing holds this charge, it will move under the action of this electric field force. And if we make, conditionally, well, that is, this can be compared to a drop of water. We drop a drop of water, and it falls under gravity. Here, a charge will move under the action of an electric field, right? And what if, instead of one drop, we make a pipe or just a waterfall, right? That is, we make a whole stream of water? This is exactly what happens with charges. That is, we can make it so that not just one charge flies, but, uh, a large number of charges move. And this phenomenon, the ordered motion of electric charges, is called electric current. That is, we take, for example, some wire. We take some wire. The wire has free charge carriers. Well, if we take, for example, copper, well, or any metal, copper, aluminum, nickel, zinc, lead, gold, silver, blah-blah-blah from the list, they have free charge carriers. Well, whoever studied chemistry has studied chemistry. I myself didn't study it very well, but even from physics separately in the course, I will explain this point, that it just so happened that they have free charge carriers, free electrons. And this external electric field acts on these free electrons. And what do they do? They start, of course, to move. Look, guys, current is directed from plus to Oh, yes, current flows from plus to minus, guys. But in most conductors, the ones we will work with, electrons actually move. And electrons cannot move from minus to plus. Oh, on the contrary, from plus to minus. They cannot be attracted to minus, they will be attracted to plus. That is, conditionally, electrons will move against the field lines here, because electrons are negatively charged, and therefore the force from the electric field will be directed against the field lines of the electric field. But we will consider the opposite direction as the direction of the current, because the ancient Greeks knew nothing about the structure of materials, right, they knew nothing, they just said: "Let it be from plus to minus." And it has been like that ever since. And then, when it was discovered that it is not positive charges that move, but negative ones, and positive ones just stay in place, scientists said: "Well, should we change it?" No, we won't. Let our current continue to flow from plus to minus, but we will assume that, for example, in copper, well, in some metallic conductors, free charge carriers are electrons, negative charges, and they will move from minus to plus. Okay? Got it? So, conductors are simply materials that freely conduct electric current, in which there are free charge carriers. Let's depict some semiconductor, some conductor. So, for example, yes, basically charges are distributed uniformly in it. That is, there are positive nuclei, and all this is uniformly sprinkled with negative electrons. Okay. Good. Semiconductors, guys, we are not touching them at all for now. In general, you won't even need them much on the Unified State Exam. There will be one small nuance with these semiconductors, but that's a trifle, again, it needs to be discussed separately. In general, you don't need them much on the Unified State Exam. And all you need to understand about semiconductors is when one conductor is for two wagons. Next, dielectrics. Actually, semiconductors conduct current, but under certain conditions. That is, perhaps at a certain temperature, perhaps under some other conditions, it doesn't matter. Well, in short, they are fifty-fifty. In short, dielectrics, as you might have guessed, do not conduct current at all. Do not conduct current. And now let's try to predict,

What will happen to conductors and what will happen to dielectrics if we place them in an external electric field? Look, let's assume we place our conductor, this one here, in an external electric field. So, initially, the electric field strength here was zero, right? We place it in an external electric field. So, some field lines appear. Here they are, right? What will happen? Nuclei. Positive charges. Positive charges, essentially, are nuclei, right? So, we have, I think you've seen this picture a hundred times when a crystal structure is drawn, meaning there are nuclei at the nodes of the crystal lattice, which don't move anywhere, and electrons fly around them. So, in metals, it's exactly the same, right? Their positively charged nuclei are connected to each other by the crystal lattice, and they stay in place, they can't escape anywhere, you understand, right? They can only oscillate around these equilibrium positions in the lattice, around the nodes of the crystal lattice, and electrons fly around them. But electrons can move. And, as I've already shown, a force will act on the electrons, directed against the electric field lines. So, the electrons will redistribute to the left side. Well, judging by the diagram, right? And this means the right side will be charged. Well, there will be practically no electrons left on the right side. And therefore, an excess positive charge will arise on the right side. So, you understand, it's like when water recedes from the shore and pebbles are left behind. It's roughly the same here. So, the electrons have moved here, and an excess negative charge has appeared on this side. And on this side, since all the electrons have receded, it has appeared, it has formed, right, it has been induced. Sometimes they also say charge induction, right, an excess positive charge. So, that's how it is. Now, about dielectrics. It's even more fun here, guys. In dielectrics, there are no free charge carriers as such. That's why they don't conduct current. There's nothing to move freely under the action of an external electric field because everything is bound together there. But there are charged molecules. What kind of charged molecules? They are called dipoles. And they have two poles. Well, dipole means two poles, right, one positive, the other negative. And basically, they are arranged somehow chaotically. They are oriented chaotically like this, in an incomprehensible way. So that the electric field strength, initially speaking, is zero inside. But as soon as we place a dielectric in an external electric field, all these dipoles align themselves under the action of the external electric field. So that, so that, I drew two field strengths, that's too much. So that the negative poles of the molecules face against the field lines, and the positive poles, well, and it turns out to be something like this, you understand, right? They all line up, as it were, in accordance with the external electric field. And again, the picture is such that an excess negative charge forms here, and an excess positive charge forms here. Understand, right, guys? And, most importantly, perhaps, what else needs to be understood is that inside conductors, the field strength will be zero, because during redistribution, the charges will create their own internal electric field, which will balance the external one. And thus, the field strength inside will be zero, and the potential will be constant throughout the volume of the conductor. But in dielectrics, if they are placed in an external electric field, the field strength, well, let's say, inside the dielectric, will be a certain number of times less than the external field strength, than the strength of the external electric field. By how many times? External divided by epsilon, where epsilon is the dielectric permittivity, which is a tabular value that shows how many times this dielectric, this substance, weakens the external electric field. Understand, right? In principle, guys, that's probably all. I don't understand the exchange of Gofi. What don't you understand? Tell me, please, I'll try to explain. Friends, let's have a couple of minutes for questions now. Let me answer a couple of questions, because I understand that this is a kind of moment. Let's draw a line under electrostatics and then move on. About dielectric breakdown? I won't talk about dielectric breakdown because it's not really necessary for the Unified State Exam. I think it was in one problem, but it was just like, if a dielectric breaks down, it becomes a conductor, like, uh, something like that. But you don't need it. About EMF, of course, I will. Of course, we'll talk about EMF a little later, guys. Uh, Gofi, then look from the very beginning, if you just joined, look from the very beginning, because I explained everything in great detail there. Just put a like so that I leave the recording. And then watch from the beginning, don't rush. I think we'll get the likes. There's not much left, actually. Only six likes left to get. Superconductors are not semiconductors. Superconductors are superconductivity is a phenomenon that occurs at very low temperatures. They are essentially conductors with very low resistance. We'll talk about resistance now too, my friends. That's all, let's finish with electrostatics for now and move on to electrodynamics. Electrodynamics. Well, statics is like something static, right, it doesn't move, and dynamics is the movement of charges. So, now I'll take a new piece of chalk. So, so, uh-huh. The first thing we need to know is the concept of electric current. What is electric current, guys? Who can write what electric current is and how to find it? We just, literally 5 minutes ago, talked about it, right? Let's imagine we have some conductor. Let me draw it. Here's some wire, right? And electrons are running along this wire. Electric current is the phenomenon of ordered motion of charged particles. That is, if there is no external electric field, the particles will move chaotically. That is, they will fly in all directions, bustling around like this. In short, it will be like Makhachkala during rush hour, right? If we turn on an external electric field, for example, connect this wire to a battery, right, charges begin to move in an ordered manner. This is when a DPS officer goes out on the street, right, and everyone immediately drives neatly, right, smoothly, right? So, what is electric current? Electric current shows, if we cut the conductor like this, conditionally, right, not if we cut it, of course, the current will stop. But if we imagine cutting it and counting how much charge passes through this cross-section per unit of time, we will find the electric current. So, again, conditionally speaking, electric current shows how quickly charge flows through this conductor. That is, the amount of charge that has passed through the cross-sectional area of the conductor per unit of time. Electric current is measured, by the way, in amperes. So, again, the simplest example by analogy with water, the water flow is greater, the more simply drops of water, right, particles, water molecules flow through the pipe in, say, 1 second. The more liters of water flow through the pipe per second, the greater the water flow. Electric current is the same. The greater the charge flows through the conductor in 1 second, in some time interval, the greater the electric current. Understand? Yes. Okay. Good. Next. Every conductor has, guys, electrical resistance. It depends on several factors. Firstly, it depends on the material. Different materials conduct electric current differently. For example, copper conducts electric current well, silver and gold conduct electric current very well, and aluminum, for example, conducts electric current worse. This simply depends on the substance itself. Why does electrical resistance arise? Again, if we imagine that electrons are running not just on a highway like cars, right, but they periodically have to go around something. That is, open manholes. Imagine that they have to go around open manholes on this road, right? And these open manholes are essentially just nuclei. The nuclei of atoms that are in their path. And electrons, as it were, conditionally have to go around them. And some electrons collide with these nuclei and so on. And, consequently, electrical resistance arises. Electrical resistance also depends on the length of the conductor. The longer the conductor, the longer the road, the harder it is to travel, right? Thirdly, it depends on the cross-sectional area of the conductor. The thinner the conductor, the greater the resistance. Understand, right? What is the cross-sectional area? It's just like we take a sausage, cut it across like this, and calculate the area. That's it. So, do you want an interesting tricky question? What is the speed of electric current? The right-hand rule for now is not needed. Right-hand rule. Speed of light. Uh-huh. Speed of light. Yes, I agree. What if I tell you that the speed of electron movement in a conductor is, well, something like a few centimeters per second, something like that. That is, it's not large, let's say. So, the speed of electron movement in a conductor is not super high, but the speed of current is equal to the speed of light. How does this happen, guys? This phenomenon occurs, it's probably a bit above the level of physics for the Unified State Exam, it's somewhere there. But the idea is that each electron creates its own electric field around itself. We said correctly, each charged particle creates its own electric field around itself. And, consequently, it turns out that each electron. If it moves a little, it gets closer to the next one, its electric field increases, and it is transmitted. So, it turns out that the speed of electric current is determined not by the speed of particle movement, but by the speed of transmission of this impulse. One particle moves, as it were, pushes the next one. And with this domino effect, it turns out that the speed is equal to the speed of light, because the speed of propagation of the electric field is equal to the speed of light. Understand, right, guys? That's a cool thing. So, okay. Now, let me, perhaps, erase this a bit. Let's move on to a more familiar form. So, we draw resistance like this for the Unified State Exam and the Basic State Exam, and in school, and everywhere. Resistors. What is a resistor? It's some section of a conductor that has some resistance. Okay. There are three parameters. Electric current, we've already figured that out, resistance. And there is one more parameter called voltage. Voltage, as I've always said, right, it's always measured between two points. In this case, let's talk about the voltage across the ends of our resistor. And here comes Ohm's law for a section of a circuit, or for a specific resistor, right. It looks like this. The electric current through this resistor depends on two things: resistance and voltage. The higher the voltage, let me remind you, what is voltage? Voltage is, well, if you remember, the work of the electric field is charge multiplied by the potential difference. We just wrote, well, not just now, but half an hour, an hour ago. The potential difference is the voltage. Consequently, it turns out that voltage is the work of the electric field divided by the charge. The higher the voltage, the more work the electric field does to move this charge. The higher the voltage across the conductor, the harder the electric field tries to push the charge through the conductor. Consequently, the electric current will also be higher. That is, the higher the voltage, the higher the electric current. And resistance hinders the movement of charge through the conductor. And so we get this dependence, which is maximally logical, guys. In other words, how can we draw an analogy with something more understandable? Look, imagine that electric current, again, is a water flow. U is, for example, the height of the mountain from which this water flow flows. So, U is the height of the mountain. The higher the mountain, the faster the water will flow at the foot, right? And R is, say, the resistance to the flow of this water. That is, the narrower the stream, the greater the resistance, you understand, right? And here everything becomes clear that the water flow will be greater if the height of the hill is greater, and will be less if there is high resistance to the flow of this water. So, okay. Let me circle this. This is golden knowledge for us today. So, now let me rewrite it like this. And now I'll show you something else. Also an important point. Regarding the connection of several conductors, the simplest connection is the connection of two conductors. Well, because everything else we will connect will essentially be a connection of two conductors. Just combined options, right, in how many ways can you connect two conductors? So, imagine you have two pipes, how can you connect them? You can connect them one after another or in parallel. Consequently, you have series and parallel connection of conductors. Once again. Series and parallel. On diagrams, guys often confuse whether they are connected in series or in parallel. Series is if the current first flows through one, and then through another. Like one after another, right? And parallel is if the ends of the conductors are connected and the current comes to a junction and flows in parallel through both. So, what do you need to know about series connection? First: the electric current is the same, well, everywhere, on all conductors. In all conductors. Why? Because how much What is electric current? Yes, it's charge over time. How much charge do we have? So, conditionally, how many electrons entered the first conductor, the same number entered the second and flowed out further. Understand? Yes? So, the electric current is the same. Voltage is summed. Why? Because voltage is measured between two points. Let's say, there is point A and, let's say, point C. And here, let's say, point B. Do I need to explain that the voltage between points A and C will be equal to the sum of the voltage from point A to point B and from point B to point C? That is, this plus this equals this voltage. So, voltage adds up, and resistance also adds up. Total R will be R1 + R2. In parallel connection, everything is a little different. I would even say the opposite. Electric current, guys, let's say some current flows in here, and what happens to it? It comes to a junction. Part of the electrons, part of the current flows through the top, part through the bottom. Consequently, the total electric current is equal to the sum of the currents. And the voltage in each branch of this circuit will be the same. Why, guys, this is obvious. Voltage is measured between two points. Each of these points is connected to a resistor. So, they are both connected to the same two points. Therefore, the voltage across them is the same. But with resistance, it's a bit of a hassle. 1 over R total is 1 over R1 plus 1 over R2. Well, and further, if we have several more resistors connected in parallel, we add more such terms. So. And what does the strange letter like Q, but not Q, mean? This is rho. Guys, I understood, I understood the question. Yaroslav, I see. Rho is the resistivity of the conductor. I already said, right, it's a tabular value, it depends on the conductor material, whether it's copper, aluminum, silver, lead, gold, blah blah blah. So, you open the table, you see the resistivity of the conductor there and substitute it into this formula. That's all. So. Yes, I'll probably fold this up for now so it doesn't bother us. So, okay. And then, what else did I want to tell you, guys? In principle, uh, so, we've been talking about a section of the circuit, now we need to talk about, uh, Ohm's law for a complete circuit. Now the real craziness will begin. I'll erase the board, whoever didn't manage to screenshot, screenshot. And let's go on. Look, so, Ohm's law for a complete circuit. It will be interesting now, guys. It will be very fun now. In general, if you understand it properly once, then everything will go smoothly for you. Look, so, imagine that you, uh, before this, we took some section of the circuit, right, several connected resistors. Now we didn't take a source, so we didn't consider a source at all. Now we will take a source and, well, some external circuit that we connect to it. For simplicity, for convenience, we will draw the external circuit as one resistor R. In reality, you understand that there can be several resistors connected in some way, but let their total resistance be R. The trick is that any real EMF source, we'll talk about EMF separately in a moment, any real current or voltage source has internal resistance. So, here's the source. And any source consists of an ideal voltage source and internal resistance connected to it. Well, meaning any battery has resistance, any generator has resistance, any accumulator has resistance, and so on. What's the trick? The first thing to understand is what EMF is. EMF is electromotive force. That is, it's something that causes electric current to flow in a given circuit. And it is calculated as the work of external forces to move a charge divided by this charge itself that flows in the circuit. Okay? What is important to understand? Ohm's law for a complete circuit, of course. The electric current in this circuit will be equal to EMF divided by the sum of external and internal resistance. That's all. R is the external resistance, the resistance of the external circuit. r is the internal resistance of the source. That's all. So, remember, right, for a section of the circuit, voltage over resistance, for a complete circuit, instead of voltage, it's EMF. In general, EMF is also measured in volts. The essence doesn't change much here. And in the denominator, instead of one resistor's resistance, we now have the resistance of this and this resistor. Well, they are essentially connected in series, right, if you look at the diagram. One after another in series. Therefore, their total resistance is calculated like this. So, okay. And then let's. Ah, yes, conditionally, we can say that EMF is voltage. There's a nuance here, again, these are subtleties, depths. I don't want to overload you right now, honestly. We'll go into more detail about this during the year in the course, so that we can cover all the little things. For now, if I get too deep, we won't leave here in 8 hours. Therefore, let's stop at the level of understanding we have for now. Let's not get too deep, because you need to understand, guys, you need to understand that physics doesn't stop at the Unified State Exam level at all. That is, you go to university, and they explain the same thing to you three times deeper. That's where derivatives start, other additional things are piled on top, complex mathematics, and you delve even deeper. Therefore, in any case, school physics is like the tip of the iceberg of real physics, so to speak. That's how it is. Therefore, I can't tell you everything here under any circumstances, because there simply won't be enough time, and it's probably not needed for the Unified State Exam. So, what shall we do? Pam-pam-pam-pam-pam-pam-pam-pam. So, let's solve some problems, perhaps. Yes, let's solve some problems, and then I'll continue to tell you the theory. So, that's how it is. Let's start with this one. The length of a copper wire connected to a current source was increased by two times. By how many times should the voltage between the ends of the wire be increased so that the electric current does not change? Let's recall the formula for the resistance of a wire, right, a conductor. Rho L over S. What is what? Once again. Rho is the resistivity of the conductor. It doesn't change here. L is the length of the wire, it changes. S is the cross-sectional area. Well, they say it doesn't change, right? So, they say that the length of the copper wire was increased by two times. The length increased by two times, which means the resistance also increased by two times, with all other parameters unchanged. We are asked by how many times the voltage needs to be increased so that the electric current does not change. Let me remind you that electric current is calculated as voltage divided by resistance. Look, if the resistance doubles, we also need the voltage to double. So, it will be like, yes, 2U over 2R. Both have doubled. And it turns out that the total electric current has not changed. Therefore, we write two in the answer. The voltage needs to be increased by two times. Here's a light eleventh-grade problem for the Unified State Exam. Maybe the next problem. So, let's solve this one too, it's also, I think, an eleventh-grade problem. The figure shows the graph of the dependence of the electric current in a conductor on the voltage between its ends. What is the resistance of the conductor? Well, here we choose any point on the graph and calculate for it. If the electric current is equal to voltage divided by resistance, then resistance is equal to voltage divided by electric current. We choose any convenient point, but I think a convenient point would be 8 V and 2 mA. We get 4 thousandths. Well, if we convert milliamperes to amperes, we get 2 thousandths, right? 8 divided by 2 is 4,000 ohms. They ask for the answer in kilohms, so we write four in the answer. Next, what do we have next? Next, next, next. Here's what we have. Oh, and the graph shows the dependence of the electric current in a conductor on time T. Determine the charge that passed through the conductor in delta T seconds from the beginning of the time count. So, here, guys, a life hack. Catch it. If they tell you, here you have some graph of the dependence of electric current on time, specifically electric current versus time, in these axes, then the charge that passed through the conductor can be found as the area under the electric current graph. That is, we just need to calculate the area of this trapezoid to find delta Q. How to find the area of a trapezoid? Half the sum of the bases multiplied by the height. One base is 120. Well, if you look at the picture, right, 120. The second base is from 40 to, well, up to 100, so 60. Divide by half the bases multiplied by the height. Something I'm confused. Divide by 2, multiply by the height. The height is 5 mA. So, 5 * 10^-3 A. That's all. 120 + 60 = 180, divided by two is 90, multiplied by 5, we get 450 * 10^-3, which is 0.45 coulombs. Something like that, guys. Yes, there will be self-induction EMF, yes, today I will tell you everything about electricity. The only thing that belongs to the section of electromagnetism is optics, because it is related. There will be no optics today, neither wave nor geometric. Everything else related to electricity and electromagnetism will be there. And so, la-la-la-la-la. Let's move on. The electric current flowing through the conductor is 4 A. What charge will pass through the conductor in 5 seconds? Well, guys, do I need to remind you? Yes. What do we have? Electric current is delta Q over delta T. From this, delta Q is electric current multiplied by delta T. That is, 4 A multiplied by 5 seconds, which is 20 coulombs. Everything is easy. Just the easiest. So, and now what else did I want to tell you about this? Perhaps, perhaps, it's worth reminding about the power of electric current - it's voltage multiplied by electric current. Or, if you remember Ohm's law for a section of a circuit, you can express electric current or voltage from here and get these things. I²R or U²/R. There's also this thing. And then there's a concept called Joule's law. What is power for? Well, the power of some appliances, right, for example, the power of an electric kettle. Here's a kettle, it has power written on it, right, for example, let me remind you that power is measured in watts, for example, they write a power of 2,200 W. Hmm, I think, the voltage is 220 V, so what electric current will flow through it? Well, 10 A, right? So, power shows, conditionally speaking, the higher the power, the faster, for example, my kettle can boil water. Understand, right? Joule's law is, in principle, close to power. What's the idea? The amount of heat released in a conductor is calculated like this: U * I * delta T, that is, voltage multiplied by electric current and by the time interval during which the current flows through the conductor. Understand, right? So, when we take some conductor and pass electric current through it, it heats up. If the conductor has high resistance, it will heat up very strongly. Consequently, here's such a formula. And there are two more options, again, expressed through this thing, that is, I² * R * delta T, or U² / R * delta T. That's how it is. Vanya Ovchinnikov, how long will the stream last? Am I annoying you? Actually, I think it will last for another hour and a half. Well, probably at least an hour. At least an hour, if not an hour and a half. Honestly, I suggest taking a short break of literally five to seven minutes, so that, perhaps, you can relax a bit, make some tea, and I'll go drink something because my throat is a bit dry. Literally 5 minutes. Come on, I'm giving you this time. During this time, you can safely go to my Telegram channel, subscribe to it, and get the file with all the formulas. I'll explain where to do it. Here, by the link in

In the description, go to Telegram, and there, at the top, in the pinned comment, in the pinned message, in the pinned post, click on it, and there's just a ton of stuff. You'll click on it, and it will pop up separately for you. And regarding electrostatics, I have a methodology guide. Yes, yes, I do. And a file with all the formulas. And a super detailed methodology guide for mechanics. In short, there's a lot of good stuff without quotation marks. Exactly, really a lot of useful material. So, go and check it out. Also, if you subscribe to my Telegram, right after this stream, I will post there, uh, well, not post, but duplicate the recording of a five-hour review of all the ЕГЭ physics theory. That is, you get 5 hours of physics for free, please. Ah, and plus, in November, for the first time, I'm announcing, somewhere, pa-pa-pa-bam-pa-bam-bam, at the end, well, in the second half of November, I plan to hold a stream from scratch to 70 points. That is, essentially, a stream on the entire first part, an eight-hour long, difficult stream, during which we will break down all the theory from scratch and solve all the prototypes of the first part. It will be a bomb, guys. So, subscribe to Telegram and, uh, let's take a 5-minute break. We'll continue in 5 minutes. We have capacitors left to deal with, pam-pam-pam. This is the first, a separate topic. And with the forces of Lorentz, Ampere, and induction, self-induction. In short, overall, not too much is left, I think. We'll manage in an hour. That's it, let's not go anywhere. We'll continue in 5 minutes, guys. Success! Success! Hello, bandits. So, well, shall we continue? Let me record a short video for Telegram now to call everyone there, and we'll continue. So, people, that's it, we're continuing. So, we have one of the most interesting, important, and probably frequently used sections of electricity in the second part left to deal with. This is, first, EMF of induction, self-induction, uh, everything related to magnetism, Ampere's force, Lorentz's force, and, uh, of course, capacitors, we'll also briefly cover them now. So, jump in, let's continue. Everyone, I'm waiting. So, well, well? Uh-huh. Don't film me. [laughter] Turn off the camera. Filming is prohibited here. Okay, good, guys, let's move on. Let's move on. Let's move on. What else did I want to tell you? Probably the most important thing I need to tell you about capacitors. Let's briefly go over it. Uh, capacitors are a separate world. There's a lot to show in practice, yes, and to solve problems. Perhaps one day there will be an open stream on capacitors, also on the course. Don't worry at all, there will be 100 million of these streams on capacitors. Several streams for sure. So. For now, I'll give you the basic theory, the basic formulas, and an understanding of what a capacitor is and how it roughly works. Further, you'll need to delve deeper separately. So, what is a capacitor? A capacitor is two plates made of a conductor, between which there is a dielectric. What is a dielectric? It's a substance that does not conduct electric current. And the whole point of this complicated construction is to accumulate electric charge. So, look, if we charge one plate positively, for example, and the second negatively, then these charges attract each other. They cannot jump to each other because there is a dielectric between the plates. But at the same time, they attract and are held, do you understand? Yes, that's the point of a capacitor. Storing, accumulating, and preserving charge. The charge of a capacitor is equal to its capacitance multiplied by the voltage between the plates. Basic, basic. Next. The capacitance of a capacitor depends on several quantities. It is calculated as follows. I wrote epsilon naught S over D alpha beta gamma prime alpha gamma beta prime. In short, something from this opera, right? I'll explain what C is, what epsilon naught is, the dielectric permittivity of the substance that is between the plates, that is, the filler of our capacitor. What is dielectric permittivity? I'll remind you, it shows how many times the dielectric weakens the electric field within itself. Epsilon naught is a constant, a tabular value. S is the area of the capacitor plate. D is the distance between the plates. Everything is clear, right, guys? Let's give a plus to show that you've arrived, woken up, and are all present. Let's give a plus to the chat, who hears me, sees me, and everything is okay. Ah, here they are, the cunning ones, they didn't turn off the broadcast, but they all left. I knew it. So, VK, let's wake up too, wake up. Everything, everything, everything, I see. Okay. Good. There's activity. Let's move on. Okay. Next. A capacitor stores energy, right? So, there is some electric field between the plates of the capacitor. If there is an electric field, then there is energy of this electric field. Here are two formulas. Well, you can even add a third one. U squared over two. Three formulas for the energy of the electric field of a capacitor. You definitely need to know these too. This will definitely come in handy for you. Exactly. Now, let's talk about the types of capacitor connections. There are, again, series and parallel. What's important to know about series? Ah, well, let's draw it first, right? Series means they are connected one after another like this. Parallel means they are, well, respectively, connected parallel to each other like this. So, in series, Q total equals Q1 = Q2. That is, in a series connection, their charges will be equal. In parallel, the total charge is equal to the sum of charges Q1 + Q2. Now, voltage. Well, it's clear that here it will be U1 + U2, and here it will be U1 = U2. Okay? And the most important thing, capacitance here. Guys, the total capacitance is simply C1 + C2. And here it's calculated like for parallel connection of conductors. That is, one over C total equals one over C1 + one over C2. That's the story. Remembering all this is quite difficult. Because with conductors, well, with the connection of conductors, we remembered, okay, you can remember. Plus is often used, it's easy to remember. Here, to avoid mixing anything up, it's quite difficult to remember. First, you need to understand better what, how, and why. That is, for example, why the charges are the same here, right? Why the charges are summed up, this needs to be analyzed separately. And, of course, solve more problems. There can be problems in the second part. Problems on capacitors also appear periodically in the first part, but, as I already said, this section is quite difficult, and you need to work on capacitors separately. Uh, can you explain the formula again? Vanya Ovchinnikov, please tell me, which formula? I will definitely explain it to you. Uh, yes, ICE Mortis 1, well done. How does electric current flow if there is a dielectric between them? That's the trick. That's the trick of a capacitor, that it doesn't conduct electric current, by and large, because what is electric current? For there to be electric current, we need a conductor, right? Besides, electric current flows only in a closed circuit, right? So, we have a voltage source there, well, some electromotive force that causes current to flow in the circuit, and current can only flow in a closed circuit. Here, we have a break in the circuit, current cannot flow. But at the same time, if we connect a capacitor to a battery, for some time we will see that current is flowing. What's the trick? The trick is that the capacitor accumulates charge. And until it is charged to a voltage equal to the source voltage, that is, imagine, right, we connect a source, so, right, minus here, plus here. Like this, for example, right? Until the source voltage equals the voltage on the capacitor, the capacitor will be charging. What does this mean? It will absorb negative charges on one plate, and give away these negative charges from the other, that is, it will absorb positive charge, and current will flow in the circuit until the capacitor is charged. When it is charged to the same voltage as the source, current will stop flowing. Here's a very good answer from Fastline. A capacitor does not conduct current, it accumulates it. Yes, something like that for understanding, you can say. La-la-la. Regarding the capacitance formula, Vanya Ovchinnikov, I'm explaining. So, once again. Capacitance of a capacitor. Dielectric permittivity of the material that is between the plates, the dielectric, right, this one. A tabular value that depends on the material. Epsilon naught is a tabular value - it's just the electric constant. S is the area of the plate, that is, you understand, right, two plates, they have an area. Take the area of one, and substitute it here as S. D is the distance between the plates. Okay. Let's move on. Ah, let's move on. Let's move on. For now, let's probably wrap up with capacitors. And now let's start talking about magnetic fields and various phenomena related to magnetic fields. Now will be the real highlight. We'll probably start with Lorentz force, my friends. But before we get to it, we still need to talk about permanent magnets and magnetic fields. Let's do this, guys, who can tell me now what a magnetic field is? The definition. Without using Google, please, on faith, honestly, work it out. Honestly, write what you think a magnetic field is. By analogy with what I told you today about gravitational fields, about electric fields. What is a magnetic field? The thing is, scientists haven't invented anything new. A magnetic field is again a special type of matter through which magnets interact, essentially, right? That is, bodies possessing magnetic moment. Once again, a magnetic field is a special type of matter that magnetized bodies can create and which interacts with these bodies. Magnets have one quirk. They have two poles. Moreover, no matter how you break it, it will still have two poles: north and south. Magnetic field lines are always directed from north to south outside the magnet, and inside the magnet, respectively, from south to north. Like this, right, they continue. Again, these lines don't mean that the magnetic field only exists along these lines, and not between them. It exists everywhere. It's just, well, I hope you've seen, right, that picture when a magnet is brought to a sheet of iron filings, and the filings align along these beautiful lines. So. Naturally, the magnetic field also weakens as you move away from the magnet. Well, it weakens very much, it essentially extends infinitely far, but the further it is, the weaker, weaker, weaker it becomes, and at a distance of a few meters, it becomes very weak. So, it's practically imperceptible. Okay. There's such a thing as the magnetic induction vector. Magnetic induction vector. Well, just like the intensity of an electric field, right? It shows how strongly this field acts on electric charges at that point. Yes. Similarly, the magnetic induction vector at a certain point shows how strongly the magnetic field acts on, uh, moving electric charges. We'll talk about this now. And on magnets. The magnetic induction vector is measured in Teslas, in honor of Nikola Tesla, not in honor of Elon Musk's beautiful car. So, what do you need to know? You need to know, actually, probably one most important thing, guys. The most important thing, I'm explaining. First, memorize this picture. North-South, lines from North to South. Just like everyone wants to escape from the North to the South, the lines go like that. Now I'll erase it. What's important, guys, do electric charges interact with a magnetic field? Who can tell me? Ideally, it seems like no, because, well, a magnetic field shouldn't act on electric charges, it seems, right? And the correct answer is: both yes and no. Look, if an electric charge is stationary relative to the magnetic field, then the magnetic field does not affect it in any way. But if we have a magnetic field in which a point electric charge is moving, then the magnetic field acts on the moving electric charge. And this force, with which the magnetic field acts on moving electric charges, is called the Lorentz force and is calculated as QVB sin alpha. What is what? Q, obviously, is the charge, V is the velocity of the charge's motion, B is the magnetic induction vector, sin alpha is the angle between the direction of velocity and, uh, the direction of the magnetic induction vector. The first thing we must understand is that if sin alpha is zero, that is, if angle alpha is zero, that is, if the velocity of the charge's motion is directed parallel to the magnetic induction lines, the magnetic field will not act on the charge, because, well, sin alpha will be zero, so the Lorentz force will be zero. First. Second, an interesting point, where is the Lorentz force directed, guys? Left hand. Guys, remember how I remembered this? Ah, well, there's a paradoxical situation here. For the Lorentz force, for the Ampere force - it's a force, right? And our left hand is supposedly weak. I somehow made this parallel, like, paradox, hal, kek, as they say. I'm practically already a mellen, right, so you can say it like that. Like, it's strange, right, that the force is usually, like, the strong hand is the right one, but it's measured by the left. I don't know, that's how it formed in my head. You can remember it differently. You can remember, like, Lorentz force, left, L, left hand. Or a little later I'll explain to you that, in principle, one left-hand rule will be enough for you. You'll see later. So, Lorentz force. To determine where the Lorentz force is directed, we must take our left hand. Point the four fingers of your left hand in the direction of the charged particle's motion, here, well, somewhere in that direction. You should place your palm so that the magnetic induction vector comes out of it perpendicularly. Well, here we have, right, here. And by extending your thumb, we will understand where the Lorentz force is directed. That is, in our case, the Lorentz force will be directed towards us from the plane of the board. And here's a nuance. There are such images. That is, if the vector is directed perpendicularly to the drawing, towards us, it is drawn like this, away from us, like this. How to remember? A flying arrow. If an arrow flies towards us, we see the arrowhead flying into our eye. If it flies away from us, we see the fletching of the arrow. So. But the direction I indicated, right, towards us, it applies to a positive Q, for, well, if the charge is positive, if the charge is negative, then the direction will be opposite, that is, into the board. So, did everyone understand this point? Guys, let's give a plus to the chat, who understood about Lorentz forces and how to find their direction. Uh-huh. Let's repeat briefly once more. Let's take the left hand again, four fingers in the direction of the charge's motion. The magnetic induction vector enters the palm perpendicularly. Into the palm, not the outer side, but the inner side. Yes. Extend your thumb, and it shows us the direction of the Lorentz force, towards us. And this is for a positive charge. If the charge is negative, then in the opposite direction, that is, away from us in this case. Yaroslav just said: "If an electron flies, it has a negative charge, so the direction of the Lorentz force will be opposite." That is, if for a positive charge in this case it's towards us, then for a negative charge it's away from us. That is, you find it for a positive charge, if it were a positive particle, and then you just flip it 180 degrees. So, okay. Next, there's also such a thing as Ampere's force. Well, that's a masterpiece. Ah, look, essentially, it's the same thing. It's just that Ampere's force is calculated not for one particle, but for a conductor with current. That is, let me extend it like this. Here you have some conductor with current. So, everything is the same. B is the magnetic induction vector. Multiply by the current in the conductor, multiply by the length of the conductor that is in the magnetic field, and multiply by sin alpha, that is, the sine of the angle between, uh, the direction of the conductor and the magnetic induction vector. The direction can be remembered as Ampere beat his son, as an option. The direction is also by the left-hand rule. Four fingers in the direction of the current. Magnetic induction vector into the palm. The extended thumb shows the direction of Ampere's force. That's it. Ah, okay, Yaroslav, understood. Understood. I somehow didn't see that you asked. Okay. Well, I think it's all maximally simple and clear here for now. Let's move on. Let's move on. And next, we have a bit of a moment, that, guys, screenshot it, I'll erase a bit now so we have space. Ah, yes, I'll erase it. And the next moment is the following. The thing is, I just said, right, that a magnetic field acts on conductors with current, it acts on moving charges. But what if conductors with current themselves create a magnetic field? And yes, that's how it is. That is, if we have a conductor with current, it creates a magnetic field around itself. It creates a magnetic field around itself. Ah, and the direction of this magnetic field is found by the right-hand rule or by the screw rule. I advise you, well, to avoid confusing hands, either remember well what is where, that is, forces by the left hand, and the direction of the vector, the direction of the magnetic field created by a conductor with current, by the right hand. Or remember only that we determine forces with the left hand, and here use the screw rule. What's the logic? So, look, the magnetic induction vector, well, rather, the magnetic induction lines will be directed like this. Take your right hand, wrap it around the conductor so that your thumb is directed in the direction of the current. And, uh, the four fingers, like this, they wrap around the conductor and show us where the swirling magnetic field around this conductor, created by it, will be directed. Like this. Well, you see, right? I drew it. Like this. What is the screw rule? Imagine you have a conductor with current. You are looking, as it were, into this conductor. The current is flowing away from us. The current is flowing away from us there. Screw rule. Have you ever screwed in a screw, a bolt, a nut, something like that, a corkscrew, I don't know. So, like this, right? That is, when you screw it in there, you turn it clockwise, and accordingly, the magnetic induction vector will be directed like this. Well, it's clear that not the vector itself, but the magnetic field lines will be directed like this. Okay, good. Let's move on. Ah, now the most, probably, interesting thing. The most interesting thing, guys, probably our story is coming to an end about electricity. A little bit is left, you know, it turned out that, well, of course, yes, initially humanity began to "tame" electricity precisely in the order we study it, right? That is, first we started talking about, uh, well, scientists, ancient Greeks, in short, these philosophers, they noticed that if you rub, say, glass with wool, then for some reason they start to attract each other, right? Then the theory of atoms appeared, the theory of charges appeared, as I already told you, right, and that's how electricity began. But the main trick is that at the very end of the electricity section, we will now cover how humanity made electricity widespread. That is, well, before a certain event, before a certain discovery, electricity was, well, where, where would you get electricity? Nowhere. You would have to sit and rub some stick. Well, only for experiments, if only for experiments. Well, you could, of course, uh, charge lightning, right, from lightning, that is, install a lightning rod. Lightning struck it, you charged some object with this electric charge. Well, and that's it, that's where all the electricity ended. And that's why, guys, honestly, you know, my breath is taken away. I just, uh, when I realized how cool this discovery was, about which I'm about to tell you, how much it really changed everything around us, how much it made electricity widespread, and where would we be if this discovery hadn't happened? Well, it's really, it's powerful. It's really powerful. I consider it one of the most powerful discoveries in physics, in general. So, and this discovery is related to how we can generate electric current easily and relatively simply. Before I start talking about it, I want to tell you a little something. Context. Context. So, imagine that you have some kind of loop. What is a loop? Let's not call it a loop. Let's just call it, say, we have a window. Let's say we have a window. A window, in short, right, we have a window. And we need to calculate the flow of air that enters this open window. That is, we consider the window to be open, and we need to calculate how much air flow enters it. Let's call this flow F. What will the air flow depend on? It will depend, first, on the wind strength, well, the speed of the wind, right? That is, the stronger the wind, the more flow. Second, it will depend on the area of the window. The larger the window area, the more air will enter it. And third, it will depend on the direction of the wind. That is, if the wind blows parallel to the wall, it's clear that it won't blow into the room. If it blows perpendicularly, it will blow in more. If it's at an angle, then, well, something in between, right? And it works exactly the same way, guys, with magnetic flux. Don't ask why it's needed yet. You'll find out now. Imagine that you have some kind of loop, and we draw a normal to this loop. What is a normal? It's a perpendicular. It's a vector perpendicular to the plane of the loop. And, let's say, this loop is penetrated by a magnetic field. Here are the magnetic induction lines. Here they are. So, to find the flux of the magnetic induction vector through this loop, we must multiply the magnitude of the magnetic induction vector by the area of this loop and by the cosine of the angle between the magnetic induction lines and the normal to the plane of this loop. This angle is alpha. Here it is. Clear, right, guys? This is magnetic flux. It is measured in Webers. And now, and now the most interesting thing, guys, how can we, how can this help us, uh, generate electric current? Huh. The trick is, the trick is that there is the so-called Faraday's law of electromagnetic induction. What does it say? It's, well, you know, maximally stuffy, maximally incomprehensible, probably difficult for someone. But it says that if we take and start changing the magnetic flux through a loop, a conductor loop, right, in any way, then an induced EMF arises in this loop, which can be calculated like this. Minus the change in magnetic flux divided by the time during which we change this magnetic flux. That is, once again, essentially, minus the rate of change of magnetic flux. That is, once again, it turns out that if we take some loop and start changing the magnetic flux in it, in what way? By changing one of these three things, we can change, uh, simply the magnetic induction vector, right? That is, we can bring a magnet closer, move it away, the magnetic induction vector changes, the magnetic flux through the loop changes. We can change the area of the loop. Well, in some way, right, take it, stretch it, compress it, the magnetic flux will change. And the third way is to change the angle. This is probably the easiest way, which, by the way, is most often used, I'll tell you a secret. To change the angle between the direction of the magnetic induction vector and the normal to the plane of the loop. We change one of these things. The magnetic flux changes. The faster the magnetic flux changes, the greater the induced EMF that arises in the loop. And what is induced EMF? It's the electromotive force that causes current to flow in this loop. And now we can connect some light bulb to this loop and boom, it will light up. Or, if we make a large, powerful loop like this, right, and change the magnetic flux very quickly, we can connect an electric motor, we can connect anything. Do you understand, guys? And why is there definitely a minus sign? I'll explain now. Yaroslav, it's a subtle point, I'll explain now. Do you understand, guys, how powerful this discovery is? Most often, uh, essentially, based on this principle, probably 95% of generated electricity is generated. It's generated approximately like this. That is, uh, any, you'll say, nuclear power plant, uh, a hydroelectric power plant, right, and so on, they are all designed to simply rotate a generator. There's a huge generator there. What is a generator? Essentially, it's several of these loops rotating in a magnetic field. They rotate in a magnetic field, the cosine of alpha changes, the magnetic flux changes, an induced EMF appears. Do you feel it? And most of the generated energy is generated this way. Without this method, everything we would have, well, probably, it would be, uh, first, solar panels, which, well, you understand, depend on many factors and are very inefficient, very expensive, very harmful to the environment, and so on. And probably we would have, uh, how are they called, Oh, it slipped my mind. Mmm, now. Damn. I forgot. Uh, piezo, piezoelectric effect. Piezoelectric effect is when there are some materials that, when you compress them, they generate electricity due to compression. Well, that's also so-so. The technology is not the most scalable, not the most stable, do you understand? That is, this is the key to knowledge, guys, the key to electricity. So, uh, let's continue, let's continue to continue. Uh, I've updated it. It should be clear now, in principle. Let's now, uh, explain in more detail a couple more points. The most, probably, main question is really: why is there a minus sign here? The idea is that this minus sign, by and large, it would be quite simple to write it like this. The magnitude of the induced EMF is equal to the magnitude of

Delta F divided by delta t. This would be enough in most problems, but this minus sign is needed to show the direction of the induced current. Let me say right away what induction is. Induction is a phenomenon, well, from Latin, I think, it's something like birth, appearance, generation, something like that, right? That is, the creation of something, the appearance of something. EMF of induction, accordingly, the emergence of an electromotive force, right? And this electromotive force creates an induced current in this loop. And this minus sign indicates the direction of this induced current. Let me rearrange the picture a little. So, conditionally, let's say now that let's draw it like this. Let's. This will be the external, and this is B. Well, let's write B induced. So, look, we have, for example, some external vector of an external magnetic, vector of an external magnetic field, vector of the induction of an external magnetic field. Here it is, for example, it is directed towards us. It pierces our loop like this. If it starts to change, well, let's say that B external decreases, as soon as it starts to change, the magnetic flux changes. Because of this, EMF of induction arises, which creates an electric current. It creates an electric current in such a direction as to, attention, impede the change in the external magnetic flux. That is, the induced current should flow in such a direction as to maintain the magnetic flux in the loop. If, as we see, the magnetic flux is decreasing, since the vector of external m, the vector of magnetic induction of the external field is decreasing, then the induced current should flow in such a direction as to maintain it, that is, to flow like this, so that there is, yes, a vector of magnetic induction from the magnetic field created by the induced current. And for this to happen, I remind you, the right-hand rule. Here, for the vector of magnetic induction to be directed towards us, the current must flow like this, that is, counterclockwise. The induced current should flow like this. Understandable, right? And if the vector of the external magnetic field were increasing, then it would be increasing, which means the induced current would try to reduce it, to impede the change in magnetic flux. And the vector of magnetic induction would be directed away from us, and the current would be directed clockwise. This is provided that it is increasing. Such is this mess, guys. In short, here, uh, you need to, uh-huh, here you need to definitely, uh-huh, understand this in more detail, solve problems. We will now, uh, I think, solve two problems on this topic. In practice, you need to practice. So, I tried to explain to you, in practice, you need to practice. So, any questions, guys? Uh, so, Fastline, I don't quite agree with you here. This is a bit different. We'll talk about it a little later. Now the most insane thing squared. That is, if this is just insane, right, like, you need to comprehend it, spend time. Now it will be insane squared. But before we move on to insane squared, let's still, uh-huh, let's still, uh, solve some problems. We'll solve a couple of problems now. La la la la la la la la la la la. Now. Uh. Mm, so. Oh, so, yes, I didn't pick a suitable problem. Well, okay, then we won't solve it. And now let's. Okay, then we'll move on directly to insane squared. Look, I'm laughing very subtly now, not for nothing. Look, now let's imagine that we have some loop of a conductor, right? Well, some closed loop of a conductor, through which we have passed an electric current. Well, for example, like this, right? Here we have an electric current. So, this conductor, obviously, creates a magnetic field, right? How does it create it? Well, according to the right-hand rule, inside the conductor, the vector of magnetic induction will be directed like this. Right? Here. Op. according to the right-hand rule inside the conductor. Like this. Ah, okay. Good, good. And what if we decide to sharply change the current in the conductor? Mm, so, guys, once again. If some current flowed, it created some vector of magnetic induction, uh, yes, mm, you can even say more simply, it created some magnetic flux. Well, it's clear, here it's BS cosine alpha. So there's flux, right? This flux is calculated like this. Inductance of the loop multiplied by the current. And what is, guys, the inductance of the loop? A good question, probably, right? Inductance is precisely the quantity that shows how well a loop converts current into magnetic flux. That is, it converts the energy of electric current into the energy of a magnetic field. Inductance is measured in Henry. So, again, the higher the inductance, the greater the magnetic flux will arise in this loop, with the same, with the same current. So, okay. Accordingly, let's say we start changing the current, the magnetic flux naturally changes. And if the magnetic flux changes, EMF of induction begins to arise, which impedes the change in magnetic flux. And in this case, it will already be the EMF of self-induction, guys. That is, our system begins to influence itself. Do you understand the point? This is a complete mind-blowing thing. That is, well, essentially, the same formula minus delta F over delta t, only here delta F is essentially L delta I. Well, and it will be - L delta I over delta T. EMF of self-induction. That is, uh, again, let me try to explain for the last time. We initially pass some current. Here, some current initially flowed. And we, for example, start to decrease it. If we start to decrease it, you see, right, the current has decreased, the magnetic flux through this loop decreases. If the magnetic flux through this loop decreases, the loop says: "Stop, I don't like this. Let's not decrease the magnetic flux. I'm already used to it. Let's maintain it." And a current arises in the loop in such a direction as to maintain the magnetic flux. What direction? Well, according to the right-hand rule. The induced current, the current of induction, will be directed here, understand? Yes? And thus, it will turn out that, uh, how can I put it? It will turn out that a sharp change in current is simply impossible. Because if we sharply start to change the current in some way abruptly, it simply won't change, because the current will be maintained, that is, there will be, uh, like inertia in the system, understand? It's like a heavy object suddenly changing direction or speed of movement. It's the same here. That is, you can't sharply change the current, because the system will try to maintain the current, so to speak. Understand, right? Such is this insane thing squared. Let's have questions. Please like. I need to finish watching the recording. I'm playing Dota while this is a complete meme. Mm. Exponential graph. Mm, yes, by the way, probably, probably, to be honest, I haven't worked with graphs for a long time. It won't be particularly useful for you on the ЕГЭ, in short. Yes, this is how it will be. That is, uh, essentially, if we try to change it abruptly, well, let's draw it like this, abruptly change the current, uh, in the conductor, it won't work. We'll get something like this. It will smoothly decrease like this, then smoothly increase, then smoothly decrease. Something like this. It will be smoothed out a lot. So, okay. Uh, in principle, guys, we are coming to an end. Uh, next, there is such a concept as an inductor. Essentially, an inductor is just many turns of these connected in series. That is, well, wound wire like this, right, on some pipe, on a tube. Accordingly, this moment is amplified. The inductance is amplified. The more turns, the greater the inductance. Firstly. Secondly, if we insert something into the coil, some core, for example, uh, well, ferromagnetic cores are usually inserted, ferromagnets are substances that amplify the magnetic field. And if we also put a ferromagnet in the coil, then its inductance will be very high. And essentially, the higher the inductance, the, uh, slower, the smoother the current will change in the coil under external influence. Something like this, right? This is not something to grasp on the first try. It needs to be practiced properly in practice, guys. So, what else did I want to tell you? Let's briefly explain the oscillating circuit in a nutshell, what the idea is. And, uh, let's go solve some more problems. I have a few interesting problems for you. So, oscillating circuit. The simplest oscillating circuit looks like this, guys. So, it's an inductor and a capacitor. What's the idea? The idea is that the inductor stores some energy in the magnetic field, which is calculated like this. Inductance times current squared divided by two. Capacitor. Well, as you remember, Cu squared divided by two. So, uh, in an oscillating circuit, as you might have guessed, oscillations can occur. Oscillations of what? Electromagnetic energy, essentially, right? Imagine that the capacitor was initially charged, for example, right? Initially, the capacitor was charged, and we connected it to this circuit. What will happen? The coil is essentially a piece of wire that, by and large, conducts electric current. The capacitor starts to discharge and give, well, so to speak, right, discharge through this coil. But it's clear that the current in the coil cannot immediately rise to its maximum. It will rise very smoothly, because the coil has inductance, which does not allow the current to change instantaneously in it. Yes, remember, we just talked about this. And, uh, at some point, the current in the coil reaches its maximum, but at the same moment, the capacitor will be completely discharged. Everything, the capacitor is completely discharged. The current in the coil can no longer increase, because, well, there's nothing to push this current. But it cannot stop abruptly either, because the coil has, like, inertia. That is, it will still give off current for some time. And it will turn out that the capacitor is recharged. That is, if initially it had, for example, a plus on the right, minus on the left, then it will be recharged so that the plus will be on the left, the minus on the right, understand? Yes, it will change polarity. And then it charges, charges, charges, is charged, the current in the coil stops. It says: "Stop, let's discharge." And this process will go in a circle. That is, the capacitor and the coil will exchange energy. So, okay. Uh, in principle, that's probably all for the theory today, guys. That's probably all for the theory today. Uh, let's quickly go through some problems now. And, uh, and we'll wrap up. So, mm, let's probably start with a problem like this, guys. When a conductor moves in a uniform magnetic field, an EMF of induction of 4 mV arises in the conductor. What will be the EMF of induction when the speed of the conductor's motion in the same field is halved? So, again, they tell us here that the conductor is moving in a magnetic field. Let me draw that the vector of magnetic induction is directed towards us, for example. Yes. So, you'll say: "What does EMF of induction and so on have to do with this?" There is another formula, guys. I didn't tell you about it. It's derived. Interesting. Uh, well, for now, let me just give it to you. Uh, so, stop. Uh, BVL cosine alpha. So, what is what? B is the vector of magnetic induction. V is the speed of the conductor's motion. L is the length of the conductor. Cosine alpha is the cosine of the angle between the direction of velocity and the vector of magnetic induction. Accordingly, uh, if the angle alpha is, uh, now, guys, I'm having a slight brain freeze. Now, now, now, now, now. Cosine or sine? Now, a second, I need to remember. Ugh, this completely slipped my mind. It's still sine. It's still sine. BVL sine alpha. Damn it. BVL sine alpha. Sine alpha is the angle, the sine of the angle between the direction of velocity and the vector of magnetic induction. Uh, accordingly, if the vector of magnetic induction is perpendicular to the direction of velocity, as you can see from the figure, right, we will have the maximum value of EMF of induction. This is the EMF of induction arising at the edges of this, uh, conductor moving in a magnetic field. Uh, in principle, let's calculate it according to the problem, right? They tell us that the EMF of induction was 4 mV. Uh, how will it change if, uh, we halve the speed of the conductor's motion. Halve the speed of the conductor's motion, the speed has decreased, so obviously, uh, the EMF of induction will also decrease by half, becoming 2 mV. Easy. Next. Mm, Yaroslav in reality, yes, when the capacitor completely discharges to zero, the coil has maximum energy and vice versa, they should discharge to zero. So. Uh, next, next, next, next, next. Let's solve this one. A straight conductor with length L01 m, through which a current flows, is located in a uniform magnetic field with induction 0.4 Tesla, with induction 0.4 Tesla. So, and is located at an angle of 90° to the vector B. What is the current if the Ampere force is 0.2 N? Well, guys, you just need to remember the formula for the Ampere force, in principle, and that's it. That's it. Uh, what is what? B is magnetic induction, and I is current, L is conductor length. Sine alpha is the angle between the conductor and the vector of magnetic induction. So, let's calculate. So, from this, it follows that the current is calculated as the Ampere force divided by B L sine alpha. Uh, papam-pam-pam. Well, that's it. Then the Ampere force is 0.2 N, we divide by B, which is 0.4 Tesla, L, uh, 0.1 m. Well, and of course, sine alpha will be one, since alpha is 90. 0.2 divided by we get like 5. 5 A. So, the next problem. Well, uh, this is not an interesting problem. This is also not super interesting, probably. I would really like to analyze two interesting problems with you, guys. Uh, like these. Look, so, the electrical circuit consists of an aluminum conductor AB, suspended on thin copper wires and connected to a DC voltage source through a rheostat, as shown in the figure. To the left of the conductor is the north pole of a permanent magnet. The slider of the rheostat is smoothly moved to the right. This is a problem in which everything is very, very nuanced, in short, very nuanced. You need to solve it very carefully. Let's analyze it, please, because, well, the authors love it. And in general, I understand why they love it. Because the problem is really powerful, really good. Look. Uh, let me scroll down a bit. Somehow, I don't know, somehow I'll do it like this. I'll do it like this, probably. So. Aha. Let's start. Uh, I'll still draw it. Here's our conductor A. Here's the north pole of the magnet. If there's the north pole of the magnet, then the magnetic field lines are directed from north to south. So, in the vicinity of the conductor, they will be directed to the right in the plane of the figure, right? Well, from north to south. Like this. Like this. So, in the vicinity of the conductor, the vector of magnetic induction will be directed to the right in the plane of the figure. Okay. Perpendicular to the conductor. So. Uh, let's say further. They also tell us that the rheostat, what about the rheostat slider, it's smoothly moved to the right. What will happen? What is a rheostat? A rheostat is, essentially, a resistor with adjustable resistance. That is, uh, remember the formula, right? The resistance of a resistor is ρ L divided by S. And if we move the slider, the length of the conductor through which the current flows changes. That is, the current flows like this. And if we move the slider here, it will flow like this. Well, roughly speaking, yes, it's a rough analogy, but still. The further the slider is from this second contact of the rheostat, the greater the length of the conductor and the greater its resistance. The same is true in the figure. If we smoothly move the rheostat slider to the right, the resistance increases, understand? We move to the right, the length increases, the resistance increases. Therefore, the first one, yes. Second. The magnetic field induction lines created by the magnet near conductor AB are directed to the right. Yes, I just showed this. From north to south near conductor A, they are directed to the right. Second, yes, listen, a combo, a combo. Now we'll get the third one, and it'll be great. The Ampere force acting on conductor A increases. Oh, how. Let's think. The Ampere force is calculated as B I L sine alpha. So. That's how it's calculated. La la la la la. Okay. Does the magnetic induction vector change? No, we're not bringing the magnet closer. Uh, accordingly, the magnetic induction vector doesn't change at all. Does the length of the conductor change? It doesn't change. Does sine alpha change? Naturally, it doesn't change either. Only the magnitude of the current changes. Why do we increase the resistance of the rheostat? And I'll remind you, and I'll remind you, where the attack came from. EMF of the sum of external and internal resistance. If the external resistance increases, the current decreases. The current has decreased, which means the Ampere force has also decreased. So, the third one is incorrect. Fourth. The tension forces of the wires on which conductor A is suspended decrease. Interesting. Here, it would seem that the Ampere force has decreased, so probably the tension forces of the wires will also decrease. But, but there's a nuance. We need to clearly understand where the Ampere force was directed. Well, and where it will be directed now. For this, the Ampere force, the left-hand rule. Remember, right, four fingers in the direction of the current, judging by the figure, and we also need the direction of the current. Well, you're completely... The current flows from higher potential to lower, from plus to minus. Yes, electrons from minus to plus, but, as I said, we always take the direction of current from plus to minus. So, judging by the diagram, from point A to point B. The current is directed like this. Four fingers in the direction of the current. Left hand, right, vector of magnetic induction into the palm, here. So, the Ampere force was directed downwards. Right? If we decrease the Ampere force, it means it pulls the conductor down less, which means the tension force of the wires decreases. Yes. Four, right? And the fifth. The current flowing through conductor AB increases? No, because we just determined that it decreases. So, guys, any questions about this problem? Uh, Yaroslav Dorokhov, what is it? V, I understood you. I'll show you now, I'll tell you. I'll tell you, one second. Uh, the question I wrote there, like in the coil, it's L i squared divided by two. Guys, V is just energy. Well, in this section, energy is written as W, and in mechanics, it's E. Like, it's just energy. The same in joules. This is our favorite classic energy of the coil. Energy, well, in this case, it's the energy of the magnetic field stored in the coil, so to speak, stored, or rather, again, the energy stored by the magnetic field of the coil. You can say it like that. Well, and let's probably solve the last crazy problem for today. Now I'll bring it up. Ala, now let me somehow try to stretch it. Like this. Like this. The last problem for today. Let's go. Two parallel metal plates of large size are located at a distance D from each other and connected to a DC voltage source. So. Essentially, it's a capacitor, right? Essentially, it's a capacitor. Uh, let's choose the correct statement. They tell us that the electric field strength at points A, B, and C is the same. Here we have point B, point A, and point C. Yes, the field strength is the same. Why? Because we assume that the electric field inside the capacitor is uniform. Uniform electric field. That is, the field strength is the same at all points. So, the first one, yes. Second. The electric potential at point A is greater than at point C. Here it is important to understand that, first, judging by the figure, the right plate is connected to the positive pole, the positive pole, and the left to the negative. So, here we have a positive plate, and here a negative one. The field strength lines are directed from plus to minus. Here they are, right? Yes. Now let's remember that the potential decreases along the field strength lines. So, so, the electric potential at point A is indeed greater than at point C, because point C is located further along the line of electric, uh, along the line of electric field strength, even at point A. Right? It's further along the field lines. So, the potential is lower at point C than at point A. And at point A it is greater than at point C. Yes. The second one fits. Strange. Third. If the distance between the plates D is increased, the electric field strength at point B will increase. Interesting. Mm, here it is important to understand that the plates are connected to a DC voltage source. So. So. That is, the voltage does not change. And do you remember the relationship between voltage and field strength? This formula, where field strength and voltage are related, was valid only for a uniform electric field. In a capacitor, the electric field is always uniform. This is basic, basic. You must know this. Look, now they ask us, right, about the field strength U divided by D. So. The voltage does not change, as the capacitor is connected to a constant voltage source. So, it always maintains the same voltage. If we suddenly increase the distance between the plates, the field strength decreases. Understand? We increased the distance, kept the voltage, the field strength decreased. The field strength will decrease, so the third one does not fit. If the distance between the plates is increased, the field strength will not increase, but decrease. Third. No. Fourth. If the distance between the plates is increased, the charge of the left plate will increase. Hmm, interesting. Interesting. Uh, the charge of the capacitor is essentially equal to the charge of the plate, equal to Cu, that is, the capacitance of the capacitor multiplied by the voltage across its plates. And the capacitance of the capacitor is ε₀S / D. Look, if we increase the distance between the plates D, the capacitance of the capacitor decreases. Right? We increased D, the capacitance decreased. If the capacitance decreases, then the charge of the plates also decreases. Therefore, no. Here it is important to understand that, guys, the magnitude of the charge will decrease. The right plate had a negative charge, and it will become, essentially, larger. That is, it was, for example, -5, and it will become -3. That is, its magnitude will decrease, but its value will increase. Here they are asking about the left plate. The left plate is positively charged, and the charge will decrease. Everything is logical. The fourth one does not fit. And the fifth. Ah, guys, five. Sorry, I'm writing here, uh, and not showing what I'm writing. Uh, you need to know these formulas, like. So. Fifth. If the plates are completely immersed in kerosene, the energy of the electric field of the plates will remain unchanged. La la la la la la la la la la. So, the energy of the electric field of the plates. Let's think about how it can be found. The energy of the electric field of the plates is essentially the energy of the capacitor. It's Cu² divided by two. Uh, well, probably, yes, this formula will be optimal in our conditions. So, the voltage does not change. We understand this, because the capacitor is connected to a constant voltage source, right? What will happen to the capacitance? Look, if we immerse the plates in kerosene, we need to look at the dielectric permittivity of kerosene. Let me do this now. Now, a second. Well, it's about two, so to speak, and air, well, it's one, right? So, look, the dielectric permittivity of kerosene is twice as high as that of air, which was initially in the capacitor. So, the capacitance of the capacitor will double. So, the energy of the electric field should also double, according to logic, so the fifth one does not fit. And essentially, the answer is 1D. Something like that. Something like that. Guys, any questions? So. Hhh.Hh. Yes, everything is correct, everything is correct. Something I, uh, I'm used to in such problems there being three correct answers. I was thinking, damn, maybe I messed up somewhere, because the problem is not easy. No, everything is correct. The answer is indeed 1D. Everything is correct, everything is beautiful. Uh, I'm waiting for your questions if you have them. Uh, if there are no questions, let's start dispersing. I want to sleep. It's 06. Wow. Where do you live? In the Far East, I guess. Ice Mortis. Uh, Valery 1981, you need to know that, uh, in physics, not English letters are used, but Latin ones. So, as far as I remember, the Latin pronunciation of this letter V, Aha. was used. Aha. Aha. Aha. Well, in short, they write here that, like, it wasn't there, and there was a Greek A. What Latin? Greek, of course, they use Greek letters. Now, a second. It looks like Omega, I don't know. I've seen it very often, guys, again, it's important, these are not English letters, but Greek ones, right, mostly. So, uh, Greek, Latin, it seems they use. In short, I've often seen it pronounced as v, and it would be correct to pronounce it as v, honestly. Uh, Roma, please explain the fifth point in the problem again. Yes, let's. What, am I going to throw you somewhere? If the plates are completely immersed in kerosene, the energy of the electric field of the plates will remain unchanged. The energy is calculated by this formula. Well, this is the energy of the capacitor, essentially, this is the energy of the electric field of the capacitor. Cu² divided by two. C is the capacitance of the capacitor, U is the voltage squared, right, and divided by two. The voltage does not change, as the capacitor is connected to a constant voltage source according to the condition. So, uh, what happens to the capacitance? The capacitance is calculated as follows. Well, S divided by D. S is the area of the capacitor plates, it doesn't change. D is the distance between the plates, it doesn't change in the fifth point. Epsilon zero is the electric constant, a constant. In short, it's in the table, it doesn't change. Epsilon is the dielectric permittivity of the medium between the capacitor plates. And we are told that we are filling kerosene between the plates. I opened the table now and took the dielectric permittivity of kerosene from it. It is twice as high as that of air, which was initially in the capacitor. So, it has doubled, which means the capacitance has increased, and therefore the energy of the electric field has also doubled. Well, approximately doubled. Something like that. Thank you very much, guys. Yes, thank you very much to you too for the stream, for coming, for visiting the old man, as they say, you honored the old man with your presence. Uh, let's wrap up for today, guys, definitely. Once again, I remind you, subscribe to Telegram, because there is really a lot of benefit for you there, uh, both open content and streams. Also, wait for the opening, uh, of the course, definitely sign up, because, well, really, in terms of price, I calculated it to be about four times cheaper than with a good tutor. In terms of quality, it's just, well, like, it's three lessons a week for an hour and a half. There are homework assignments, curators, uh, individual plans, all the theory is explained in detail. Not like we are doing now, a whole section, right, in 3 hours, but very detailed, each small section, right, down to the smallest details. Explained 10 times, repeated. Second part, first part. We also analyze the formatting, mock exams, review. Uh, in short, everything you need, a full package to pass with 90+. Even now there is still time to start preparing and write. Well, 80+, I think you can prepare from scratch if you work actively. 90+, either work very actively from scratch, or, if you already have a decent basic level, then 90+ is still a real result if you work and join right now. You can't delay. Uh, recording? Yes, guys, I'm leaving the recording. That's all for today, friends. Let's disperse. See you, so to speak, with my course students in the course. Uh, see you in Telegram. And, of course, next weekend, I think I'm not planning. In one week, I think I planned some stream or next week, I don't remember. In short, all the info will be in Telegram. Everyone, bye-bye, and good luck.