 Hi, I'm Zor. Welcome to a new Zor education. I would like to talk today about electromagnetic field created by a moving charge, moving particle, which is charge, like a proton or electron, for example. So it's magnetism of moving charge. That's what this lecture is about. Now, in the same chapter of this course, we were talking about magnetic field created by a current. So if you have some kind of a very long wire with certain current running in it in amperes, the moving electrons create a magnetic field which has the circular magnetic field blinds. So the magnetic field intensity vector is tangential to these circles. Well, it's supposed to be a different direction. So it's basically circles around the wire. So every circle, every magnetic line makes a circle in the plane which is perpendicular to the wire. And the center of this circle is in the plane, the center where the wire actually is going through all these planes. And we have come up with a formula about intensity of the field. We nu i divided by 2 pi r, where i is the electric current, the amperes. r is the distance from the wire. So basically, if you have a wire and you have this concentric circles of magnetic field blinds, around the same line, the magnetic field intensity is the same. It depends on the distance from the wire, basically. And nu is a permeability constant for particular media where we are. In case of the vacuum, it's nu with index zero usually is used. So that's basically how well magnetic field penetrates the media. And vacuum is the media as well. Okay, so we came up with this formula kind of logically and obviously experimentally as well. And what I would like to do is to do something similar to come up with some kind of a meaningful formula, in case not a wire where electrons are moving all the time with certain constant speed. But if you have one particular point charge, basically, moving, in theory it's supposed to be creating a magnetic field as well. Because if many electrons moving in one direction create magnetic field, one electron should actually do the same. The question is what exactly kind of magnetic field, what's intensity of this magnetic field is created by a moving particle. Okay, so let's just think about this. And again, we will try to come up with certain formula using logic. And then, obviously, I will mention that it's supported by experiment. And here it is. So let's consider we have an observer at the origin of coordinate. And somewhere there is a moving electrically charged particle. So there is an electric charge Coulomb. And there is some kind of a velocity vector V. Now, my question is what exactly this observer observes as far as magnetic field at this particular point. So let's say this is vector R, which points to the charged particle. And obviously it's changing. V is constant. That's easier for us right now. So the particle is moving with a constant speed. But position vector, which points to a position, is obviously the variable depending on the time. And well, actually vector is equal to dr by dt. Because speed is the first derivative of the position. You remember that from the mechanics. And this is a vector actually, which means on every component, x component, y component and z component is exactly like this. So let me just think about what... Now in this particular case, we came up with what exactly the dependency between the electric charge which is moving along the wire and the magnetic field intensity. Well, obviously it should depend on the intensity of the current itself, which is amperage, right? The greater it is, the more electrons actually are going through the higher the magnetic field intensity is supposed to be. That's kind of natural. Now, the fact that it's inversely proportional to the distance is also kind of understandable. Because the magnetic field actually is like a cylinder, right? So the farther it is, obviously the weaker magnetic field is supposed to be. Why is it proportional to the first degree of r, not the second degree? Well, it's kind of obvious because every little detail of this particular wire creates magnetic field very narrow. It's supposed to be kind of symmetrical. So it's a cylindrical surface. And if it's a cylindrical surface around the wire, I mean one particular layer of magnetic field, if you wish, then the energy is distributed towards the whole cylinder. And the radius is basically the greater area is, because this is infinite or very long time, very long lengths. But as far as the area where energy is distributed is distributed proportionally to the circumference of this circle, which is 2 pi r. We will do basically the same thing here. But instead of infinite line, we have just a point. Now, in case of infinite line, you know, magnetic field, the same layer of magnetic field, which means the same parts of magnetic field which have exactly the same magnitude of intensity. Because all these are of the same magnetic field intensity. Now, here, magnetic field intensity will be spherical, obviously, around the point. So it's supposed to be inversely proportional to the area of the sphere in this case, right? So that should be in denominator. Now, that's kind of understandable. What also is understandable? Well, it's obviously understandable that it should be proportional to charge itself. The greater the charge, well, if you double the charge, it's supposed to double the magnetic field. It's also kind of natural. What else? Now, magnetic field is created by movements of the charge, right? In this case. So I would not have any kind of, you know, problem to say that it's supposed to be proportional to V. Yes, sometimes you might consider that maybe it's supposed to be like V-square or V-cube or something like this. But it's not really very kind of counter-intuitive to consider it's proportional to V. And obviously, experiments support it. What else? And then there is a very important thing, which is not as obvious, quite frankly. And I would like to talk about it a little bit longer. Let's consider you have two different situations. This is one, and this is another. The same speed, the same queue, but position is here. What's the difference between these two things? Well, let me go to analogy. If you are on the Earth's surface and the Sun is here, it emits certain amount of heat, which is by the way electromagnetic way it says well. And now you have Sun here. The same Sun, and obviously the distance, this is around the noon, let's say, and this is in the evening. The distance to the Sun is basically the same. There is no difference. But the angle it falls on Earth is different. And obviously this is much hotter than this one. Why? Well, explanation is actually very simple. Well, consider if this is the Sun, and this is a very narrow amount of heat which goes here. It falls from A to B. Okay, perpendicularly. Now here, the same amount of heat goes at the angle. So let me go into a bigger picture. This is A, this is B, and this is an angle. So what goes to the same segment of A, B? This is the right angle. And this is, let's say, alpha here. So this is alpha here, right? So the same, and this is alpha. So the same amount of heat which comes from the Sun now goes against longer area. So if this is distance D, so this is distance D, this is distance D, then this would be D divided by sine of alpha, right? So if this is a greater area onto which the same amount of heat falls, well, that means that the intensity of the energy which is falling from the unit area, which is basically intensity of the heat we feel, would be by this factor less. So the area is greater, so the intensity should be less. So that's why if certain amount of energy or whatever is here, here it will be e times sine of alpha where alpha is this angle at which we see. Exactly the same thing happens in this case. Amount of magnetic field energy which comes from here, well, in case of magnetic field energy is cold actually, the magnetic field flux. So the same basically amount of magnetism comes from this and from this. Now, we have here some kind of a device. Well, device is what this device. I don't know, but there is some kind of an area which feels magnetic field. And if the angle is less, then the amount of magnetism falling onto this sensitive device which we are using to measure magnetism would be proportionally smaller. And what is the coefficient of proportionality? The same sign. Now what is this sign? It's a sign basically between the angle of between R and V or V and R, whatever. It's more traditional. So, by the way, it's supposed to be lowercase R. So lowercase R is the length and the lowercase R with an error on the top is a vector. So basically this is the formula we are looking for. Now, in addition to this, I obviously should put some kind of permeability coefficient and experiments show it's exactly the same permeability because it's a property of the space, not property of the charges or device which we are using to measure it. And that would be my intensity of the magnetic field. Now, all we need now is just a little bit of mass to come up with something which is more traditional. Now, let's just think about what is the times sign of the angle between V and R. Well, if you remember the vector product of two vectors is, as far as the magnitude, it's a vector, but as far as the magnitude is what? The magnitude of this is equal to V times R times sign of the angle between V and R, right? That's basically the magnitude of vector product and direction is perpendicular to both of these. Well, again, if you remember, the direction of the magnetic field intensity is always perpendicular to magnetic field lines. Now, what is magnetic field lines here? In this case, if it's moving this way, it's at this every moment is something like this. And at this particular point, it should be perpendicular to both of them, which means it goes into the board, into my white board, right? So it's perpendicular, which is good. Now, as far as this formula is concerned, it's almost like this except we have R. So what we can do instead of this, we can put vector V times vector product with R divided by R. So this will be a unit vector. So that would be V, the magnitude of this, times magnitude of this vector, which is one, times the sign, and the sign would be the one which we actually need. In other words, it can be new Q vector product with R divided by 4 by R cubed. Sometimes, instead of this, they put square here, and instead of arrow here, they put this sign, M%, I think it's called, which means this is a unit vector in the same direction as the R vector is. Well, it's just a different... Oh, sorry, I forgot V. So this is the vector product of V and a unit vector of R. So this is the same thing, basically, and yet another way you can put... It's new Q... Now, what is V? V is actually derivative of R. So you can put R. I use R prime, which is also a vector, times R, divided by 4 pi R cubed. So there are many ways of basically expressing this formula, but it's exactly the same formula. And again, my probably a little bit more difficult part was to explain why we need this type of sign of this angle, and in addition to whatever was before with Q and V and the sign, that was only the magnitude. In the vector form, it shows also a direction of the intensity vector. It's perpendicular to direction to the charge and the vector of speed. So in this particular case, as I was saying, it's just perpendicularly to both these vectors, which is going into the board. Now, depending on the charge, positive or negative, it will be either into the board or out of the board into space. So basically, it all depends, but there are some rules which we talked about this. If charge goes this way and magnetic lines, magnetic field lines are that way, then the intensity, the magnetic field intensity will be perpendicular to this and that. So that's not really as important right now. I mean, it's important for certain practical tasks, but my purpose was just to explain why we have something like this, a formula which looks not exactly as natural as something, let's say, the gravitation law, where we had mass times mass times square distance. That's kind of, with some kind of a coefficient. So that was kind of obvious, again, r squared because the gravitation energy is distributed throughout the whole sphere. Same thing as Coulomb's law, q1, q2 divided by r squared with some kind of coefficient again. Well, again, it's kind of 4 pi and then it was epsilon here. It doesn't really matter how we express this constant with this permittivity. The matter is it's always proportional to two kind of things and inversely proportional to either radius squared. Now, if it's a line with everything, it was current, it would be inversely proportional to radius because we are talking about cylinder of magnetic field lines in the same radius. So in any case, it's all kind of natural. This doesn't really look as natural from the first glance, at least. But again, if you think about it, it's just a convenient representation of both the magnitude and direction of the intensity vector. And that's all about magnetism of moving electric charge. Okay, so I suggest you to look at the Unisor at Physics 14's course and read the notes for this lecture. It's within the electromagnetism part of the course where we're talking about magnetism of electric current. That's it. Thank you very much and good luck.