 Hi, I'm Zor. Welcome to Unisor Education. Continue talking about different units in physics. Today we will talk about units in magnetism. Derived units of magnetism. Derived from the base units which we have already covered in previous lectures. Now this lecture is part of the course called Physics 14's presented on Unisor.com. The website is totally free. I suggest you to use it. There are no advertisements, by the way. No strings attached. You don't even have to login if you don't want to. In any case, the website contains prerequisite course, mass 14's. You do have to know mass if you study physics. Now this part of the course, units in physics, is just some kind of a recap, because I'm talking only about units. But I do touch base with certain concepts in physics, because to talk about unix in, let's say magnetism, I have to talk about certain concepts related to magnetism. Not in all the details, but just some of them as a recap. The most important part is in corresponding lectures, in this case for electromagnetism and in some other cases. Ok, so let's go to magnetism. Well, magnetism is related to the concept of a field, as you know, magnetic field in this case. More precisely, it's electromagnetic field, but this was covered in corresponding lectures about electromagnetism. Right now, we're talking only about certain characteristics, and more precisely, magnetic characteristics of the field, and how they can be measured. Now, well, the field implies that there is some kind of a force under certain circumstances. Now, you recall that there is a concept called Lorentz force. So what is Lorentz force? Now, I will use only the simplest magnetic field, which is totally uniform. So there are magnetic field lines, and if you can imagine, let's say, a very large magnet of this type. This is north, this is south. Then in this particular part of the magnet, the lines, magnetic lines, are practically parallel. And you know what magnetic lines is. We covered this topic, how to basically display them using some kind of shavings, metal shavings. Okay, so that's done. So I'm assuming that we have a uniform magnetic field, and these are the lines, lines of magnetic field. So it's totally parallel lines, and the vectors associated are of the same magnitude. Now, what about the force? And how can this force be actually demonstrated? Well, the force can be demonstrated if you put some kind of a conductor with electric current. Now, you remember that electrostatic field manifests itself as a force if you put a static electric charge in it. There will be attraction or repelling. In case of magnetic field, you need a moving electric charge to demonstrate that there is some kind of a force. So let's say that perpendicularly to these lines, perpendicular is very important, it would be actually perpendicular to the surface of the board. So I'll put it this way. There is an electric current. It's a conductor of lengths L. Now, electric current is basically a flow of electrons and there is certain amperage associated with it. And the length has a fixed length. Now, if you do this, then the force will be perpendicular to both the magnetic field lines and the line of electric current. So if electric current is perpendicularly to this board, then the direction of the force which is perpendicular to both, to this and to this, will be this. So this will be my force. So that was experimentally basically confirmed. And the Lorentz force basically says that the force in its magnitude, so direction became already determined. So force in its magnitude is proportional to both the amperage and the lengths of the conductor. Okay, now what is proportional means that there is some kind of coefficient of proportionality, which in this case, use the letter B. And this is a characteristic of the field itself. So regardless of what kind of a conductor, lengths or amperage which is going along the conductor is, the formula will be the same. So you will have twice as much amperage, you will have twice as much force. You will have twice as much lengths, you will have twice as much force. But the coefficient will be exactly the same because it's a characteristic of the field. And this characteristic is called either intensity, which I prefer as a term. Or there is another term, length here, but more precise I would say. It's called magnetic flux density. So magnetic flux density, why is it flux density? I will talk just a little bit later. But meanwhile, let's call it density for now. So intensity is a characteristic of the field. At any point of the field, it's directed along the magnetic field lines from north to south, usually. I mean, if it's magnet like this, for example, this is north and this is south, then magnetic field lines are like this, right? And the direction of the B vector would be tangential to every line. So this is direction and the magnitude is basically a coefficient of proportionality. Now obviously at any point of space, it can be different because maybe it will be further from the magnet or it will be closer to the north pole and then to the south. It's not uniform field, generally speaking. I have defined it for uniform field, which means that we can always define it locally. So for every locality, very small one, infinitesimally small one, obviously it will be a concrete vector. So it's a vector field, basically. When the vector is defined at every point of space around the magnet, it constitutes the vector field. It's a vector at each point. This point vector, this point vector, etc. Okay, now let's talk about measuring intensity. Measuring this magnetic flux density. Well, from this formula it's very easy. We can measure it using, we have already defined units for force, units for electric current and units for lengths, right? So if B in this case is equal to F over I times L, so we can say that one unit of measurement of magnetic field intensity is one Newton divided by ampere lengths. So it can be one Newton force, which is produced by the field, in case one ampere of electricity is going through the conductor of one meter lengths. Now, if this condition, then whatever the magnetic field which delivers this one Newton, in case you put one ampere and one along the one meter, that's the unit of intensity. And it's called Tesla. Well, almost almost almost all units in physics. I'm not talking about early units like kilogram. I'm talking about a little bit more advanced units, which were basically established, discovered much later. They're all in honor of some physicists. In this case it's Tesla. So Tesla is a unit of magnetic flux density or intensity of the magnetic field. So magnetic field intensity is a vector. This is a unit of measurement of magnitude of this vector. And the direction, as I was saying, is along the magnetic field lines. So this is a unit. Let me just repeat again. If one amperage exists in lengths of a conductor of one meter, and if the field is uniform and this conductor is perpendicular to the magnetic field lines, and if the resulting force is one Newton, it means that the field, magnetic field in this particular point, where this particular conductor is located, is one Tesla. Okay, now the second thing is related to magnetic flux. That's where you will see why intensity is called magnetic field flux. First of all, what is flux? Flux is basically a, well, half mathematical, half physical concept, which basically means that if you have certain vector field, and right now I draw a uniform vector field, if you put some kind of an area perpendicularly to this particular vector field, so let's say vector field has magnitude V, and the area is S. Then V times S basically is a flux. It's amount of something which goes through this surface, basically. That's what it is. Now, if situation is much more complex, for example, the source is a point and the vector field goes this way, and the area which you would like to basically find the flux through is some kind of ellipsoid or whatever around this point. So it goes through this surface. All the vectors go eventually through the surface. How can we calculate the flux? Well, it's an integration. You take one small piece, one piece has a concrete vector which goes through it, and since it's infinitesimal piece, we can consider that vectors which are coming through this infinitesimal piece are all the same, and it has certain area. You multiply these vectors by this infinitesimal area and integrate along the whole surface. It's mathematically involved, but physically it's much simpler. So let's say some source of energy. Let's say a heater, and you have a heater inside the room, and you would like to know how much energy is consumed by all walls of the room, including ceiling and floor. Well, that's basically the calculation of the flux. In this case, flux of the heat energy. Now, in case of magnetic field, we have exactly the same story. We have a vector field of intensity, right? Let's B. And if we put any kind of a surface through which magnetic field lines are going through, you can always calculate the product. Well, if this surface, let's say, is flat and perpendicular to magnetic field lines, well, you will just multiply by area. So this is area, and this is intensity. So this is Tesla. This is meter square. So the unit of magnetic flux is Tesla times square meter, which is called Weber, WB, capital W, lowercase b. So one Weber is one Tesla times meter square. So this is basically how, sorry, this is how the magnetic flux actually is calculated. Well, magnetic and electricity and magnetism are very complex. And I have this whole part of the course called electromagnetism, which explains the details. This is just a recap to talk about units of measurement of electricity, magnetism and some other things. So that's why it's very brief. My purpose was to introduce basically two units of measurements related to magnetism, which is Tesla. That's a characteristic of the field at each point. It's a vector, which is called intensity or magnetic flux density. And magnetic field is another concept which is integrated kind of a flow of whatever, magnetic field energy, if you wish. This measured in Weber's. And by the way, Weber is just yet another physicist. Everything is by name of somebody. I suggested to read the notes for this lecture. Notes are on this website just parallel to the lecture itself. So if you go to the website, you choose physics for a team's course, units in physics, that's the chapter or part of the course. And then you go to derived units, derived C units. And I'm talking about C only because there are many other units and there are conversions, etc., which I'm not getting involved in. So it's a derived C units and among the derived C units, you have units of magnetism. So notes basically are more or less the same thing as I'm talking about right now. But it's always good not only to listen, but also to read. You have different kind of parts of the brain involved in this. All right, that's it for today. Thanks very much and good luck.