 Hi, I'm Zor. Welcome to a new Zor education. We are continuing talking about electricity, and we basically start the new chapter of this, which is basically about electrical fields. Now, my first lecture in this chapter is related to Coulomb's Law. Coulomb's, Coulomb's different pronunciation, but in any case, that's obviously the name of the guy who basically invented this particular law. He made some experiments, etc., and came with a nice formula, which I'm going to talk about today. Now, this lecture is part of the course called Physics for Teens, presented on the website Unisor.com. I suggest you to watch this lecture from the website, because the website basically presents a course. So this lecture is part of the whole set of lectures, and there is a logical dependency between the lectures. There are certain thoughts about how to present this material. Plus, the website has exercises, problem-solving, exams, and other functionality. Obviously, the lecture itself is linked to YouTube or whatever else, wherever you found this particular lecture. So that's why you can watch it from the website exactly the same way. But again, the detail notes for each lecture is on the website, so it's much more beneficial to use the website. And by the way, the site is completely free. There are no ads, there are no financial strings attached, etc. Okay, so we are talking about Coulomb's Law. First of all, we do know by now that electrical charge is basically excess or deficiency of electrons relatively to protons in the object. So every atom in its neutral state has the same amount of protons and electrons. Protons in a nucleus and electrons are, well, we are considering this planetary model of atom when the electrons are rotating, circulating around the nucleus. Not exactly, maybe, true how it is in nature, but that's a good enough model for us. But the number is the same, number of protons and number of electrons. If there is an excess of electrons, we are saying that the object is negatively charged and use the sign minus. Obviously, it's, you know, just sign. There is no negative or positive electricity. It's just our convenient model. Excess of electrons is the same as we are calling the negative charge. Now, deficiency of electrons, when the number of electrons is less than the number of protons, we designate as a positive charge. Now, what's important is, and again, we were talking about this before, electrical objects which are electrically charged do have certain forces among them. For instance, if you have two positively charged objects, which means in both you have a deficiency of electrons, they will repel each other with certain force. Or negatively charged both, which is excess of electrons in both objects. They're also repelling. If you, however, have one object with positive charge and another with negative charge, so one has deficiency and another has excess of electrons, they do have the certain attracting force. Now, so numerous experiments were conducted to measure this force and today I'm going about numerical representation of this force. But before going to this, I would like to talk about the electrical field. Now, so far we have been familiar with one particular kind of field, which is gravitational field. So what is the field? Field is basically certain area of space where certain forces exist without basically physical contact. So the gravity exists on the height of 100 kilometers from the surface of the Earth. Earth still gravitates the objects which are 100 kilometers from its surface. That's basically what we call the field. Again, this is just a terminology. Now the same thing with electrical charges. They are on the distance from each other and still they experience the force. One experiences the force of another, attracting or repelling force. Which means that electric charge has certain electrical force around it. Let's call it the force field. So this electrical field or electrical force field, if you wish, is certain area of space where attracting or repelling electrical forces exist. Okay. Now, I think it's basically it's time to go into the measurement of these forces. Let's think about it this way. If you have, let's say, two electrons, one electron and another electron, now both are just electrons by themselves. There are no protons. Which means this has a negative charge and this has a negative charge. Which is equal to the charge of one electron, which is certain amount of certain units called Coulons, by the way, which we were talking about before. So anyway, two negatively charged electrons. Let's put them at a certain distance from each other. Well, they will repel each other, right? Okay. Now, what if I will get two electrons here and still one electron there? The repelling force of which we can measure actually, which is this particular electron is experiencing would be double the one which was before, right? So we can say that the force between these two objects, one object containing two electrons and another containing only one. It's twice as strong. The repelling force is twice as strong, right? Well, obviously, we will take n electrons here. It will be n times as strong because the forces as vectors are adding to each other. This is one object. We are considering the small object, obviously, a point object. So this is the point object with n electrons and this is the point object with one electron and the force between them, a repelling force, will be n times greater than one of them. Now, if I have objects with m electrons here, it will again increase in m times. Again, obviously, because each one of them has all these. So if I will just add them up, it will be m times greater. So obviously, if we are talking about two objects, one has certain, like, n-axis electrons and another has m-axis electrons, the force should be proportional to m times m, correct? It seems to be natural because, again, the forces are adding together and there is one particular value of force at this distance between two electrons and then if I have m electrons here, here and n electrons there, it's supposed to be multiplied by m and by n. So the force is proportional to the number of axis electrons in these two objects. Now, axis of electrons is basically a measure of electrical charge. Now, we measure electrical charge in coulons. This is, again, the same guy who invented this law, obviously. So, and there is a definition of what is the charge of one coulon. That's such a unit, which for electron, I think it's 1.6 times 10 to the minus 19 coulon, if I'm not mistaken. So, this is the definition of coulon, because electrons charge is very small. It's very difficult to measure anything. So, they have invented another unit, coulon, defined it completely differently, but, again, later on, they have decided that the most convenient way to define this unit of electrical charge, coulon, in terms of electrons. So, one electron has so much coulons in it, and that's the definition of the coulon. If you wish, you can say that one coulon is one electron charge, whatever one electron is, divided by 1.6 times 10 to the minus 19. It doesn't really matter. All right, so, number of electrons, therefore, is proportional to the electrical charge measured in coulons. Because one electron has charge proportional to one coulon. So, it's all matter of coefficient, right? So, number of electrons here, and number of electrons here, are basically proportional to the charge of one object and electrical charge of another object. So, instead of proportionality to number of electrons, we can say that it's proportional to charges, where q1 is electrical charge of one object proportional to the number of excess electrons, and this is the coefficient of proportionality, and q2 is the electrical charge of another. Okay. So, we've got this particular proportionality purely, logically. We never measure anything. Now, another thing. You understand that, intuitively obvious, that if you will put these electrons at a further distance, well, the force must be weaker between them. Attracting force or repelling force doesn't really matter. It must be weaker. By how much? Well, here we will use the same logic, which I was using when I was explaining the gravitational field. Consider the following model. If you have two electrons, or two objects, doesn't really matter. This is one, and this is another. Now, what is electrical force look like? Well, I can compare it to a little spring, which goes between them. And the springs are emitted to all the direction from this object, and obviously from this object also. These are little springs. So, every spring is some kind of a model of a force. So, there is a spring between these two. All right. Now, how many springs? Let's say there is a certain finite number of springs, which are originated in this particular thing. Now, this is an object. Now, the further I go, you see these springs and these springs. These are actually going and don't touch this object. So, only these objects, these springs, are touching these objects. So, there is some kind of a cone, if you wish, which is reaching this particular object. I'm not talking about point object, by the way. There are certain dimensions, if you wish. Now, what is the dependency between force and the distance? Well, obviously, if you will take further, then you will have a little narrower cone, right? So, the number of springs, which actually hit this particular object, is proportional to the density of these springs, right? How many per square inch or square meter or whatever? Square something, square linear unit. How many springs are falling into unit of area? Now, what is the area around this particular object? Well, it's 4 pi r square, where r is the radius, right? So, all these finite number of springs are, well, basically are spread around the spherical surface around this object. We are talking about three-dimensional world, right? And so, in three-dimensional world, all these springs are basically somehow reaching the whole surface. But the density would be obviously inversely proportional to the area of the entire surface. And the entire surface is proportional to r square, so the density would be inversely proportional to r square. Where r is the distance. So, that's why I put r square here. So, if my force acts like these springs, then the number of these springs, which are falling on the unit of area, is inversely proportional to r square. Now, obviously, all these logical statements are good, but it's necessary to confirm it with practical experiment. And this person probably was one of the first, but anyway, he was the one who formulated this type of a law. And, well, he basically measured the force, measured the charges, measured the distance, measured the force, and came up with this law, which right now can be equal sign, where k is certain coefficient of proportionality, which definitely depends on the unit we are measuring this thing. So, this is a cologne, and this is a cologne, this is a square meter, this is newton. Then, the k has certain number, which is 9 to 10 to the 9th degree. And they mentioned would be newton divided by cologne square multiplied by meter square. Cologne square would be in the numerator, and here it's denominator, so they cancel, meter square, meter square, so we will have only newtons, which is the unit of measurement of the force. Okay, now if this is positive and this is negative, the force will be attracting. If this is negative and negative or positive and positive, the force will be repelling. And what's interesting is that since we are associating the sign, negative or positive, you can see that if two are positive or two are negative, then this product will be positive. So, the force is positive for repelling and negative for attracting, when these are different signs, plus, minus, or minus, plus. Basically, that's all about this Cologne's law. What is interesting is not only to understand this formula, but also kind of feel how it is numerically, how big it is. And for this, I did some little calculations. I took two particular objects, one electron and another electron, on the distance of one millimeter from each other. And using this formula, I have calculated the force of repelling force. And the repelling force was 2.31 times 10 to the minus 22 Newton. Very small, right? Well, but look, electrons are too small. One electron has so much Cologne's, you see, 10 to the minus 19. So, that's why the force is small. But now it's interesting to compare this force with the gravitational force between the same two electrons positioned at the same distance of one millimeter. And for this, we will use Newton's universal law of gravity, right? And that shows the result is 5.53 times 10 to the, well, brace yourself. Minus 65 Newton. You see how much smaller this is? It's like 43, 10 to the 43rd degree difference, all right? So on the subatomic level of electrons, we can definitely ignore the gravitational force altogether. Now, when we are talking about planetary movements, well, the electrical charge in this case would probably be negligible because usually planets are electrically neutral. Number of protons and number of electrons are the same. And I don't know, maybe as a result of historical, whatever, the world creation, I don't know. It was basically neutral. But the masses are significant. And in these cases, in case of planets, it's the gravitational force which plays extremely important role. But on a level of elementary particles, atoms and subatomic particles, it's the electrical forces which are predominant, where we just completely ignore the gravitational effects, or we can't ignore. Because the difference is so much on this particular magnitude. Okay, that's it. I just wanted to introduce you to basically the main thing is this formula. And I was trying to present some kind of justification for this, not only the practical result, because if you're given just the formula, you might say, okay, why? I mean, yes, experiments really kind of confirms it, but how did people come up with it? Well, these are the logic which I was just trying to convey to you behind this formula. Okay, that's it. Thanks very much and good luck.