 Hi, I'm Zor. Welcome to Unizor education. I would like to talk about magnetic induction, continue to talk about magnetic induction. In this case, we will talk about self-induction. It's a very important topic actually, especially for practical implications. Now, this lecture is part of the course Physics 14 presented on Unizor.com. By the way, this course has a prerequisite on the same website. It's called mass proteins and I do consider mass to be really very very important for physics course because there are lots and lots of mass in everything we're talking about, especially vector algebra and calculus. So, let's talk about induction. Let's consider a very simple experiment which we were actually doing before, we were talking about, we didn't do any experiments, we talked about experiments. So, let's say you have a loop, wire loop. So, you have a source of electricity, a battery. So, there is a direct current in it. Okay, now let's assume that our direct current is changing. Now, why it can change? For example, if you have something like a resistor here in this circuit and you are changing, it's a resistor which can actually change its own resistance. Then, obviously, since you have certain primary source of voltage and you have certain resistance here R, which is a function of time, you're changing it. So, that's why your primary current using the Ohm's law would change, right? Well, right, but not exactly. Now, another example is when you have a switch here and that's what actually makes some practical implication. So, if you have a switch here and you are turning the electricity on basically, like for instance, you have a lamp and you just turn the switch on to turn the lamp on. What happens? Well, in this particular case, right now, if the switch is off, you have absolutely no electric current, right? So, you can consider that the resistance of this is equal to, well, infinity, almost infinity. Now, when it's closed, when your switch is on, obviously, you expect that you have certain current. Now, switch is turning on and off, not instantaneously. There is certain very small period of time during which this switch is, first it just touches the contact, then it goes really firmly onto the contact. So, there is a tiny interval of time during which your electric current in this loop should grow from zero to some substantial value, whatever the value is supposed to be. So, there is a growth from zero to certain maximum. It doesn't grow in just a jump. Things in nature don't really jump. They really do things slowly with whatever the pace is. In this case, pace is very fast, but it's still not a jump from zero to max. So, there is a change of current. In some way it happens, whether it's a switch or a resistor, a changing resistance, etc. And that's what's very important to basically analyze what's happening in this particular case. Now, we do know that whenever you have direct current in a loop, let's say it's a circular loop for simplicity. Now, what happens is around this there is a magnetic field. Around every wire, if there is a direct current around it, you have magnetic field generated by moving electrons. Now, in this case, it happens exactly the same thing. So, you have magnetic field around this. So, it goes through the wire loop and then comes around, and that's how magnetic lines are arranged. So, in the center of this loop, the direction of all magnetic lines is perpendicular to the board, right? And we actually did some calculations and we have determined the intensity of the magnetic field as being equal to mu i divided by 2r, where r is the radius of the loop. So, in a different lecture dedicated to magnetic field generated by direct current, in this case, current in a loop, we did derive this formula for a center. Now, if it's not a center, it's something else. You will still have proportionality to i. Now, why? Very simple reason because basically like every electron creates by its moving certain field. So, i is a measure of basically a number of electrons per unit of time which travels through this wire. So, it's additive function. That's why you increase, you double number of electrons, you double the intensity of the field. So, at every point in this particular loop, intensity of the magnetic field would be proportional. Now, this is the formula for a center. Not in the center, it would be some other parameters like how far from the center you are located and stuff like this. A little bit more complicated formula. But doesn't matter. What matters is it's proportional to i. Okay, that's the second observation. So, the first is that we have the magnetic field. The second one is it's changing. If i is changing, if i is a function of time, then intensity is a function of time. Okay, now in one of the previous lectures we have learned about the Faraday's law. Now Faraday's law basically is related to induced electricity. Do you remember when the frame is rotating in the magnetic field? It generates magnetic field because of its changing, generates electricity inside. So, what happens is magnetic flux which goes through the frame is changing and that's what actually generates the electromotive force and additional current in this wire frame. Okay, so what's important is magnetic flux. But look, if my intensity of the field is changing, my loop stays as it is. So, magnetic flux is basically amount of magnetic intensity going through the area of this loop. So, at any point flux, differential of flux is equal to b times differential of area. So, somewhere here. For instance, this is my little area differential of the area. There is some magnetic flux here which is proportional to changing electric current. So, you have certain amount of flux. So, that's why flux is also, the whole flux is sum of these and again every one of these is proportional to i. So, the whole flux as a function of t would be proportional to i. But now what's happening? The flux generates electricity if it's changing, right? Remember, the Faraday's law, the electricity generated, this is electric electromotive force basically EMF. It's actually equal to a rate of change. Now, let me put absolute value here. So, we're not talking about signs right now. But anyway, whenever my flux, which magnetic flux which goes through this loop is changing, it generates electromotive force. Now, this electromotive force, I should say it's a secondary one. See, this is the primary. It exists by itself. But because I have changed the resistance of this loop by switching some kind of a switch on and off or changing the resistance using rail start or whatever, we are changing the current. Now, since we are changing the current, we are changing the intensity of the magnetic field at any point inside the loop. Changing the magnetic field intensity results in changing of my magnetic flux which goes through this loop and changing of magnetic flux causing generation of secondary EMF, secondary electromotive force. And that's what's very important. And that's what actually self-induction means. We are generating additional electromotive force by changing the current in this circuit. Now, obviously, we understand that the circular loop in this case, it doesn't really matter what's the shape of it. It's just different calculations of dependency of magnetic field intensity at every point inside the loop, inside the circuit. But whatever it is, it's still proportional to I. And since it's proportional to I, if we are changing the electric current, the magnetic field intensity is changing. And from magnetic field intensity, my flux will be changing again, proportional to change to I. And that's why we have generation of the secondary induced EMF, induced electromagnetic force. So there is a primary one which is here and there is an induced one. Now, what does it mean that we generate induced electromotive force? Well, it means we are actually adding, we have two different electromotive forces. And each one of them contributes our results in certain electric current. So this one also generates certain electric current inside the loop. So there is a secondary, this is primary, and this is secondary. Also, the bending continues. And now my total current in the loop will be some of these. Let's check the signs. For instance, we are increasing my current. So whenever we are switching on, for instance, or we are reducing the resistance of rail step, which is part of this circuit. So what happens if we are increasing IP primary? Now, whenever we are increasing primary current, my primary intensity is increasing, my flux is increasing, and derivative is positive, right? When the function is increasing, you remember from calculus, its derivative is positive. Okay. Now, derivative is positive. Let's just think about this one. If this one, if this generated electromotive force generates it in such a way that this sign of this secondary electric current is exactly the same as sign of the primary, we are increasing our electric current even more. Right? So increasing of the primary if, now this thing is positive, okay? So if we are increasing primary current, my flux is positive, my derivative of the flux by time, rate of change of flux is positive. Now, if this is also positive and correspondingly my current is positive, adding to this one, it would probably be growing even faster, right? So my primary is growing, but we are adding something, which means it's growing even faster during the same amount of time. Now, the faster it grows, now my intensity would grow even faster. That's the secondary intensity, because the primary intensity is produced by primary current, secondary intensity produced by additional secondary intensity. Now, if it has the same sign as the primary, my total intensity would be even greater, my flux would be even greater, so it grows faster. If it grows faster, my derivative would be greater, you remember? The derivative is basically a rate of growth, and we will generate even more, and that would generate even more current, secondary current, it would add up into the primary, etc., etc., it looks like we will very easily grow to an infinite amount of electricity produced right from basically nothing. Unfortunately, the law of conservation of energy doesn't allow us to do this. So from this, you can just logically derive the conclusion that this should be an opposite sign. So whenever my current is increasing, primary current is increasing, my total current should decrease, otherwise we would have infinite amount of energy. So that's why I put this minus when generated the secondary EMF. Okay, now what happens if we are decreasing the current? Okay, if we are decreasing the current, our intensity is decreasing, our flux is decreasing, our flux is decreasing, and that's why its derivative, the rate of change is negative, when the function is decreasing, rate of change is negative. Now if we are changing the sign of this, obviously the generated electricity would change the sign, generated EMF, induced EMF secondary one would also change the sign. So in this particular case, if increasing gives us the current which goes against, then decreasing, since we are changing the sign, should really increase, and that's actually what's happening. So whenever you are decreasing the primary current, the secondary current would work opposite to it, which means it will try to increase it. So if this one goes down, this one would help you, it would add something into the current, more electrons will go. So in both cases, this minus sign is valid. Whenever you're increasing the current, the induced current would be working against it. Whenever you're decreasing the primary current, the induced one, the secondary current would try to support it. It would add something into the current. And that's what's very important for practical application. You see, whenever you're switching something on and off, since during a very, very short time, we have a significant change in the current, either from zero to some value, or if we are switching off from zero down to, from something down to zero. Now, since the time is very short, my flux is changing from whatever the value is. Let's talk about the decreasing. So it will go down to zero during a very, very short amount of time. Well, which means that the rate of change is great. It doesn't really matter how big it was in the beginning, but since we are changing the time during which it goes down to zero, if this time is significantly small, my rate, my first derivative by time would be really large, which means that whenever you're switching off the electricity from the circuit, if this switching off is really instantaneous, we should expect the secondary current to grow very, very fast and very significantly. That's why it's very dangerous, especially for high voltage circuits, to abruptly switch it, switch the whole thing off and on as well, because we will have these plus or minus positive and negative flows of electricity. If the time is up switching on and off is very short, then these secondary currents might be really, really significant and they might actually blow some fuses or do something else. That's why it's recommended, especially again in high voltage circuits, to switch them off using some rail start, which means it's a device which will either increase or decrease the resistance gradually during a certain amount of time, not instantaneously, because again, there is no such thing as instantaneous in nature. It's still very short amount of time and we don't want the derivative to be very fast, function to be very fast growing the flux. Now, the situation is actually much more complex, because whenever we're adding something or subtracting something from the current, we are adding more change. We are adding more change, which means it also should be involved in this. Now it should be primary plus secondary, but that will be the tertiary, etc. It really grows. The only thing is every next piece of that thing is smaller than the previous one, so we usually are ending on a secondary one. But in theory, it's a very complicated process, which happens in the circuit whenever your switching is on or off. Excuse me. Okay, that's all I wanted to talk about. So why don't you just take a look at the Unisor.com. This particular lecture has notes as every other lecture. It has very detailed notes, which can be used basically like a textbook. And then there are some problems which are solved. There are exams for people, so I do recommend you to take the whole course on Unisor.com. That's for those who just found this lecture by accident or by searching the YouTube channel or something like that. The website is much more comprehensive, and it also has very important functionality. Okay, thanks very much. That's it for today, and good luck.