 Hi, I'm Zor. Welcome to a user education. Before we were talking about how permanent magnetic field acts on the electric current. This lecture is about the magnetic field which is produced by electric current. Now this lecture is called magnetism of a straight line current. So we are talking only about straight line current. It's part of the course called physics 14 presented on Unisor.com. I suggest you to watch this lecture and every other lecture from the website because all lectures have very nice detail notes basically like a textbook. And there are exams if you want to. There is certain functionality of the website which you can definitely use as an educational process. The website has no advertisement and it's completely free. You don't even have to log in if you don't want to. So, okay, let's get back to the business. So, again, before we were talking about electric current in some kind of a magnetic field, usually uniform magnetic field. You remember the Lawrence force? Now, let's go back to the beginning of the origin of magnetism. In particular, I would like to remind you again, and we did talk about this before, the emperor model of magnetism. So if you remember, the magnetism is usually explained by electrons which are moving on an orbit around the nucleus. So this is an electron. This is a nucleus. And electrons are circling around the nucleus. Well, that's the model again. It doesn't really matter what's in the real life. We don't really know exactly what's there. But anyway, electrons are something which we consider in this model as rotating around the nucleus. They also have their own spin around their own axis. So all these movements actually are involved in producing the magnetic effect. So if you have two electrons, for instance, on the same axis, let's say, these are two different atoms, but they are on the same axis. And all these electrons are circulating in parallel planes in the same direction. That's what actually makes the magnetic properties of some kind of an object. If all these axes of rotation are not parallel to each other, then there is no magnetism. Well, that's the model. Now, in particular, let's consider electrons which are on the same plane and parallel axis of rotation. And again, it's the same rotation. Now, as you see, this is rotating, let's say, in this way. And this is rotating in this way. So here, where they are touching each other, they are rotating in opposite directions, right? This is this way and this is this way. This is the same rotation from the rotation perspective, but locally they are going into different directions, which makes this electrically neutral. There is no current, basically, in this particular area of the object. But where is the current? The current is only on the outer boundary of the object. So if this is a magnet, let's say, a natural permanent magnet, then only on the surface you have the real movement of electrons. Inside, the electrons are actually kind of neutralizing each other. It's a model. We're not talking about the reality. It's a model. But it's a good model because it corresponds experimentally to whatever we observe in the reality. Now, this is an ampere model and what it actually implies is that let's forget about inner structure of some kind of magnet. If you will just have a loop and put some kind of current in it, plus, minus. So this is a loop. That's basically equivalent to this flow of electrons on an outer perimeter of the permanent magnet. So it should have permanent magnet properties. It should be magnetic field. It should attract certain other objects, etc. So obviously experiments were conducted and Eric experiments confirmed that this actually is basically something which has the same properties as a permanent magnet. This is north. This is south. So this is north and this is south. And you remember about magnetic lines. Magnetic lines are going from north to the south and then inside the magnet they're going back. So it's this way and inside they go back this way. This is the permanent magnet. Exactly the same kind of magnetic lines, magnetic field lines are observed in the case of electric current in the loop. So the magnetic lines are going this way. This is north and this is south. Now, how did we confirm it? Well, very simply. What happens if you put the magnet flat on the surface and then you will put iron filings just drop on this surface? Well, they will actually line up in some kind of a form which basically resembles the magnetic lines because every particular fragment, every piece of this filing becomes a temporary magnet, polarized so north of one particle connects to the south of another particle and they are actually forming something which resembles the lines. It's really visible. Now, if instead of permanent magnet here we will have an electric current. Okay, this is the upper part and underneath there is a bottom part. So this is the current and obviously we can connect to plus and minus. So there is an electrical current in it. You will observe exactly the same kind of a picture with one from this to this. This type of a picture will be observed. I put the photographs of this experiment actually in the notes to my lecture, to this lecture. So if you will go to the website and read the notes, the notes contain really the photograph of all these filings around the electrical circuit in a loop. Okay, so we've done with the loop. The loop has again north and south poles. It behaves exactly like a permanent magnet. Let's say a bar magnet. The next thing which I would like to do is I would like to open up the loop. Let's just think about it. If this is a loop, this is plus and minus. And we were talking about that one side of this is basically north and now there is south and the magnetic field lines go around it. Okay? Now, what I would like to do is I would like to open this loop. Now, from just purely intuitive standpoint, there is nothing to change actually. The current is still running and the way how I shaped this loop shouldn't really matter for magnetic field which is produced by electric current. So it should still be the electric current. So if I will open it up this loop, I will have a current in the straight line and magnetic field would still exist around it and magnetic field lines would be around it like this. And again, experiment shows that this is true. If you will take a flat surface and put vertical electric current and put some kind of current plus or minus and then you will use the same iron filings and drop on this surface, they will form circular shapes around it and again they put the photograph of this in the nose for this lecture. So experiment confirms basically this model and now what we have to really do is to qualitatively and quantitatively evaluate the magnetic field around this type of thing. So, we are talking about magnetic field intensity B, which is a vector. Now, before when we were talking about magnetic field and electric current we usually used the uniform magnetic field when all magnetic lines are parallel to each other and the strength of the field is exactly the same. And that's how if you remember we have determined that if you have this magnetic field and you have some kind of a line with electric current and it's the line I is perpendicular to the vector of the magnetic field intensity, then there is kind of force also a vector which is proportional to I times L which is length of the conductor and vector product with B. Well, vector product just to make sure if it's perpendicular the vector product basically you can consider all of them as a scalars but if it's an angle let's say vertical magnetic field and this is not perpendicular to it but it's at some angle and the sign of angle between this direction and this direction it's supposed to be getting involved and that's what makes it a vector product and they put everything in my lecture for this particular thing. So, this is related but this is a uniform magnetic field in this case the field is not uniform. More than that in this case we have polarity in north and south lines go from north to south. In this case there is no polarity. That's interesting actually talking about magnetic field which does not have north and south poles because all directions are exactly equivalent. If you will put a compass on this top it will line up north-south direction along this and it will point this way but here under the wire the same compass will point north to this it will always be in sync with the magnetic line so there is no polarity so to speak. However, the vector does exist so this is the direction of the vector it's always tangential to the magnetic line so our purpose is to determine the magnitude so we know the direction so it's always perpendicular to the eye obviously to the current this is the current so this is in the plane perpendicular to the current so all magnetic lines are in corresponding planes perpendicular to the current and the vector of magnetic field intensity is in that plane tangential to the circle which magnetic lines actually make now magnetic lines exist on different radiuses so within the same plane if you will cut it with a plane like this you will have obviously magnetic lines on different circles on different radiuses all concentric obviously and the picture which I have showed to you when the vertical wire and the flat surface and iron filing it shows concentric circles around it so on every plane perpendicular to the eye you have obviously infinite number of magnetic lines but we are just drawing a certain number and they are all concentric circles so at any point from the consideration of symmetry it's kind of obvious that the magnitude should be the same if we are on the same radius because it's all kind of cylindrically symmetrical we can always turn the wire without basically changing anything because we are considering this is a thin wire and it should not really change any kind of distribution of the forces in the magnetic field so that's why this magnetic field intensity depends basically only on the radius it's perpendicular to the radius it's tangential to the circle of this radius and the magnitude we have to determine that's a very interesting consideration right now what I'm going to talk about this magnitude it generally comes from just a general concept of the field we have gravitational field we have electrostatic field etc let's just think about the field as certain form of energy which is emitted from the source in this case the source is this line straight line with an electric current in case of electrostatic it can be a point charge in the case of gravitation it's a planet and the gravitational force around it so in all those cases we have certain source of this I would call it energy it's reasonable to call the field a form of energy so there is a source of this energy and energy is emitted so at any moment of time let's say it's emitted not in a constant flow for instance like from the gravitation gravitation just exists but let's just imagine for a second that we have an impulse an impulse of gravitation it goes all around the source of this gravitation now at certain time it reaches certain frontier this impulse so if you have this impulse of let's say gravity or electrostatic at certain speed actually the speed of light it goes to a new frontier and this energy is spread around this frontier at certain other moment it goes a little bit further and again it reaches certain new frontier and it's spread around it now the density of this energy per unit of area of that surface so we're talking about a surface of equal timing so to speak so whenever this energy is reaching a new surface of equal timing it's basically spread around and if you remember in case for instance of gravitational field it's inversely proportional to square of the distance why? well because it's spherical right? so if you have a point charge let's say gravity charge or electrostatic charge doesn't really matter then the surface of equal timing is a sphere around it the greater the timing the greater the radius because it reaches the new frontier every new moment of time and the area of a surface of a sphere is 4 pi r square so it's proportional to r square that's why we are spreading this energy to a bigger and bigger surface of equal timing and the area of the surface is proportional to square of a distance and that's why the intensity of the field on that area of that surface of the equal timing is inversely proportional because we are spreading to a bigger area same thing here the only thing, the area is not spherical now what area of surface of equal timing in this particular case well it's a cylinder obviously if this is a source of magnetic field then we have at equal time the surface reached by these impulses of energy if you wish is a cylinder now if you have let's say finite lengths L of this of this wire then the surface of a cylinder the side surface of a cylinder is 2 pi r that's the lengths of the circle of the radius r times L, right? so let's forget about L for a second what's important is this r so if I double let's say the distance my circle will have twice as big the lengths and the area of the cylinder will be also twice as big so for every L is inversely so the intensity should be inversely proportional to to the radius actually to the 2 pi r that's more convenient kind of a thing because we are dividing by this lengths of this curve well 2 pi is obviously just a multiplier so it's just for convenience purpose what's important is it should be inversely proportional to r so as radius is increasing the surface of the equal timing is increasing proportionally to r so the intensity should decrease by the factor of r so that's one thing another thing is magnetic field is related to movement of electrons as we know I mean unless we have the current there is no magnetic field well obviously it's not like 0 and 0 and some particular finite number obviously depends on movements of electrons and the more electrons are moved per unit of time the greater magnetic field should be because every electron by its movement produce certain magnetic effect so the more electrons the more magnetic effect it should be proportional so but we have come up with this is supposed to be the current which is basically number of electrons per unit of time q divided by coulombs divided by seconds and it should be inversely proportional to 2 pi r with a fixed length okay so this is this is it I mean this is a final kind of formula for intensity all we need right now is some kind of a this is proportionality now for equal sign we need some kind of a coefficient which depends on the units of measurement and obviously this coefficient exists it's something it's whatever the number is doesn't really matter right now what is important is that it's proportional to I to the current to amperage basically and it's inversely proportional to the distance from this and this is the most important part of this lecture so doesn't really matter I wouldn't pay too much attention to mu zero which is actually some kind of a permeability of the space magnetic properties maybe in vacuum it's one thing in some other area around this current it will be something else you can probably shield from the magnetic field by using some kind of a metal around it I mean this is physics which are related to very very practical aspects of this the theory is this proportional to the amperage inversely proportional to the distance from this wire and that's what makes actually the whole magnetic property from the qualitative standpoint important and that would probably be it for today so this is it this is magnetic properties of a straight line current depending on the amperage and distance from this current and don't forget that this is circular magnetic lines around this straight line current these circles are each one is in the plane perpendicular to the current and obviously in each plane we have many this is stronger because this particular force this energy is spread only to a circle lower radius and the lower radius means less length of this circle so the energy is spread to a smaller smaller area and that's why the intensity of this energy the intensity of this energy is greater the closer you are to the wire the greater the magnetic properties you can observe well that's it for today I do recommend you to read the notes for this lecture so you go to unisor.com to electromagnetism that's among the physics 14th course of course and in the electrical magnetism you will find magnetic properties of the electric current and that's one of the lectures there I think it's the first lecture of that topic ok thank you very much and good luck