 Hi, I'm Zor. Welcome to Unizor education. Today I will talk about something which I can probably classify as a theory behind transformers of electricity. So we know about transformers. They all exist around us. They increase the voltage, decrease the voltage. So right now I'm not talking about transformers, but the theory behind these transformers. Now this lecture is called induced variable EMF. EMF stands for electromotive force, as you know, which is basically a voltage. Now this lecture is part of the course called physics for team presented on Unizor.com. This is a free website. You can find mass for teams course on that website, which is I considered to be a prerequisite for physics because you really have to know your mass. Something like derivative is everywhere in physics, in integrals, in many cases, vectors everywhere. Okay, so I do recommend you to watch this lecture from the Unizor.com because you will see that this lecture is just part of the course. So you will have the whole curriculum of this course, what topics are covered, etc. And you can basically go logically from one lecture to another. They are in sequence and obviously the subsequent material is based on the previous one. So okay, let's go. Now by now we know what induction is. Induction is the generating the electromotive power in some conductor, wire or something, which doesn't have its own source of electricity like a battery. Nevertheless, the electric current can be generated, the electromotive force and electric current can be generated by this process of induction. And induction is always related to a variable magnetic field. Now let's just recall the most important formula for induction. This is the Faraday's law, basically. That if you have some kind of electromotive force generated by induction, then it's basically a rate of change of electromagnetic flux, phi. This is a Greek letter phi. So phi is the electromagnetic or magnetic flux going through some kind of a loop or whatever. So if you have, let's say a loop, wire loop and you have variable magnetic field which goes through this, then the magnetic flux, if it's variable, which means in this case its derivative is not equal to zero. If it's a constant derivative is equal to zero and there is no voltage generated, here there is no EMF, there is no electric current in this loop. But if it's variable then the electricity is basically generated. The electromotive force is generated and the electric current appears in this loop. Now what is the magnetic flux? Well, magnetic flux is basically a result of, in the very simple case, result of multiplication of the electromagnetic field intensity, magnetic field intensity and the area of this contour. So if we are talking about constant various, let's say you have contour which stands still and you have a uniform magnetic field with intensity be perpendicular to this plane of this wire loop, then you just multiply basically. If there is some angle between them, so let's say this is the loop and magnetic field is not perpendicular but at the angle, then you have to multiply it by corresponding like sine or cosine depending on which angle you're talking about. So we're all, this is all covered in in the previous lectures where I explained everything about magnetic field induction. So this is given. Okay, now, now we will talk about a series of three different experiments which will lead us to this functionality of transformers, which I just started the lecture with. Okay, now my experiment number one is again, a pure demonstration of electromagnetic induction. So let's consider that you have a permanent magnet north-south. Now, let's also consider you have a wire loop and you're inserting the magnet inside the wire loop. Now, let's think about what happens in this particular case. The magnetic field lines for permanent magnet are like this, right? Now, inside obviously they continue because magnetic lines are always closed. Now, what happens if this permanent magnet stands still and my wire loop also in a stationary position, well, nothing happens. As soon as we start moving, you see magnetic field lines are different. When this loop is very far, the only thing basically it does, the magnetic field lines are almost parallel. Let's say it's a small one here. All right, it's parallel. So there is no change in the magnetic flux because the area stays the same and the magnetic field intensity is also the same. We are not crossing magnetic field lines. So if you're not crossing, it's exactly the same magnetic field lines we are crossing. We are actually going through this loop, whether it's in this position or where it's in this position. Now, let's consider it's a little bit closer. So my loop is greater. So now this is a magnet. Now, let's think about this way. You see at this position we are actually crossing these lines more and more intensely. Now the next position when it's a little bit closer, it's this one, right? See now we are crossing all these lines here and here and here. So my point is that the closer we are to the edge, let's say north edge of the magnet, the more intense obviously the more intense the magnetic field is, but also we are crossing more magnetic field lines because we are getting closer and closer. And at this position we are actually actually all the magnetic field lines which are coming from this edge of the magnet going through our loop. At this position only these which are here are going through the loop, but at this position all of them are going through this loop. So that's very important. Now, what's the consequence of this? Well, the B in this formula is basically increasing. The more magnetic lines it means more intense magnetic field actually is. And since it's changing, B is changing, so B times S is changing, where S is the area of the loop and if it's changing then the derivative is not equal to zero and we have electromotive force generated. So what happens further? Well, next position, let's just wipe out this one. My next position is in the middle. Now, what happens in the middle? You see in the middle when we are moving in the middle here, it's basically exactly the same magnetic field lines are going through this loop. It's basically parallel to these lines. So only these and these and only these lines are actually going through this. No more. All these guys are outside and they stay outside. If it's right near the edge, sorry, right near the middle, these lines are almost parallel, right? So only these lines, there is no change in intensity. It's exactly the same. If intensity is the same, my flux is the same and at this time my derivative is equal to zero, no EMF. So there is very small EMF in the far distance. Then it's increasing. It reaches its maximum at this point when basically all the lines which are coming from here have to go through the loop, right? But as soon as we move to the middle, only certain part of these lines go through the loop and no more and no less, which means B stays the same in this case and flux stays the same, basically. Now, what's next? Well, let's move forward. We move our magnet forward and our next position, let's say this near this edge. Now, at this edge again, all the lines are going through. So again, the flux is increasing from this position of the loop to this position of the loop. Flux is again increasing and if it's increasing, then again, my derivative is not equal to zero. The only little problem is that in this case my magnetic field lines which are going from north to south are going from inside to the outside of the loop, right? If loop is here, it goes, first it goes to the inside and then to outside. In this case, the direction is opposite from outside into inside. If direction is opposite, my generated EMF would have a different sign, right? So, I mean, you consider this flux as increasing in absolute value but changing the sign. So first it's positive here, here it's negative because B changed. The B is a vector, actually. So B is changing the direction and that's why phi is changing the sign. So absolute value is growing again to the maximum when it's at the edge but it's in different direction. So my EMF is small, then it's very large at this point, then it goes to zero, then it goes to, let's say, negative large, an absolute value of large but negative. And then as we move forward, as we move magnet forward and our loop goes there, it's again decreasing for obvious reasons. So the bottom line is, as I'm moving the magnet through the wire link, the magnetic field induction is working, it's demonstrated and basically it's changing according to this Faraday's law. Now, my next experiment is very much like this. However, I will change something. Now, instead of a permanent magnet, I will have some kind of a wire loop with electric current, direct electric current from the battery going through it. Now, we spoke many times that the properties of the wire loop with the direct current in it are very much like that of the magnet. It's one of the lectures dedicated to what exactly the magnetism is, etc. So it acts like a magnet, which means there are magnetic lines which are going around it and basically it's equivalent to a north-south permanent magnet. All right? So what I will do, let me just do a little better picture. Okay, so it's about like this. Now, here is my same loop wire loop as before. Just a wire loop without any kind of source of electricity like this one. So all I did is I have replaced my permanent magnet with a wire loop with a direct current in it, which has exactly the same properties as permanent magnet. And what happens if I will do exactly the same? I will move this wire loop with electric current through this, the bigger one, apparently. So what happens in this case? Exactly the same as before. If I am far, there is basically no noticeable electric current. But as I'm moving closer and closer, the magnetic field lines are going through this ring and I'm crossing these magnetic lines. My number of magnetic lines, if you wish, is which goes through this loop is increasing. By the time I'm completely around my this wire loop is around this one, all magnetic lines go through this. So I have the biggest EMF. And then, again, as soon as I'm crossing this, it goes to a different direction and basically it's exactly the same as with with a permanent magnet. So at some point we are reaching maximum and maximum. And on this side it will be positive obviously, on that side it will be negative. In the middle it will be it will be zero because I will move parallel to my lines. If I'm completely around this loop is around this one, I'm moving parallel to magnetic field lines. So the flux is not increasing, but on a certain rate, on a certain distance, it becomes the biggest and on this distance it will become the biggest in absolute value, but negative. So exactly the same thing. Now what actually causes the change of the flux in the first and the second experiment? Movement. Mechanical movement. So as I'm moving my geometry is changing basically and number of magnetic field lines which are going through this loop is changing just because we're changing their mutual position. What's most important is that flux is changing. Yes, the reason is mechanical movement, but the result is that the flux is changing and that's why EMF is generated. Okay, but why don't we do it differently? Why don't you keep these two loop stationary and instead of changing the whole geometry, the mutual position, we will do it differently. We will change the current inside this loop. Now you remember there is a formula for the magnetic field intensity B which is in the center of a of a circular loop, we did calculate it. It was mu zero which is permeability of the space times current divided by 2r where r is the radius. Now this formula was derived in one of the previous lectures and that means that if I will change my current, if it's not a direct current like here, what if it's source of some kind of a variable current? It doesn't matter how we achieve it. Maybe we have some kind of variable resistor here. So we are changing resistance and even if it's a battery which has constant voltage by changing the resistance, I'm changing the current. So as soon as current is changing, it becomes function of time. My intensity becomes a function of time. It's changing. If intensity is changing, my flux is changing. If it's changing, my derivative physical is not equal to zero and my electromode force is generated and there is some kind of a current running in this particular loop. So my last experiment is keep these two wire loops stationary, but instead somehow change the current in this loop instead of just constant direct current, change it in some way. It doesn't matter how. As long as it's changing my magnetic field intensity is changing, my flux therefore is changing and my EMF is generated. Basically this is the theoretical basis for transformers. We have basically two loops. One is with some kind of a voltage and another has a generated, inducted electricity in it and now we can actually change the voltage using certain technique, which I'm going to discuss right now. Now, what if instead of one loop you have a spiral? This spiral tightly positioned loops basically one one near another, but it's one piece of wire actually. So you have source of electricity and you have many loops here. Well, each loop creates its own intensity, magnetic field intensity vector, right? Now, since these loops are very close to each other, we can consider basically that each one of them creates exactly the same magnetic field with exactly the same intensity and since intensity is something which is basically supposed to be added together. It's a vector algebra, but all the Bs, all the intensity vectors are identical. So we just multiply it by the number of loops. So if you have n loops here, the intensity of the n loops is n times greater. Fine. Now, how about this one? What if instead of one loop I also have spiral? Now my spiral has maybe some kind of consumer like a lamp or whatever. Now, each loop basically feels the change of the field, magnetic field, change of the flux. Flux is the same through each loop, which means in each loop there is a generated EMF and all these generated EMFs are added together and we have basically, this is multiplication by n, this is multiplication by m, where m is number of loops. So the result in resulting EMF depends on number of loops and number of loops here. So by changing these two numbers, we can play with how big electromotive powers generated on this side and how big how strong electromagnetic field is generated on this side. So this is how transformers are working. They're playing with these two numbers and playing with these two numbers, we can actually do whatever we need to do with the voltage. And again, details of this I will discuss when I'll talk about transformers. Right now, it's just the theory behind. We start with one permanent magnet. We replaced it with one loop with a direct current moving. Then instead of moving, we are changing the current and then we're just adding a certain number of loops in a spiral instead of one single loop. And that basically leads us to to a transformer. Okay, now I suggest you to read the notes for this lecture because the notes are accompanied every lecture on Unisor.com. Starting from math 14, now it's physics 14, all notes are there. Also, the website has problems which I solve. Then there are exams for you to solve. The site is completely free. No financial strings attached. You don't even have to sign in if you don't want to. Basically, that's all I wanted to talk about today. So good luck. Thank you very much.