Now we're going to change gears and talk about Inductors for a few moments. Now, inductors are devices that store Magnetic Flux. And the first thing we have to do is define what we mean by Magnetic Flux. Now, let's assume that we have a coil of wire like this, and it has an area A, we'll call A the variable for the area. And let's assume that we're running a current through this coil of wire, that comes back out the other side. Well, that current is going to give you a magnetic field. That's going through the center of loop and it also goes around the outside and back through, so it sort of loops around the wire. But, there's a certain amount of magnetic field penetrating the area, the fields cutting through the, the, the surface of the loop. Now, the magnetic flux is defined to be the magnetic field strength times the area. And so, that's the total magnetic field multiplied by the area of the loop gives you the total magnetic flux linking that loop. Now, the other thing that we need to introduce here is Faraday's Law. So, this is kind of a crash course of half a semester of electricity magnetism. But, we're going to just hit the high points here that we need for this course. Now, Faraday's Law says that for this configuration, this loop over here. If the magnetic flux changes over time, then a voltage is going to appear across these terminals. And so, you only get a voltage here if the magnetic flux is changing over time. If you just, if there's a steady current and an unchanging magnetic flux, then there will be no voltage appearing here. Now, the the other thing that note here is that the, the voltage is increased if I add more turns. So, imagine I made a coil that had ten turns of wire. And I had a certain magnetic flux linking all ten turns than the, if phi is the flux through one turn, then if I have n turns or say, n equals 10. Then, I'll have ten times the voltage. And so, I have to multiply this by the number of terms. Now, the other thing to notice is that minus sign. And that minus sign comes about, from something called Lenz's law. And Lenz's law just says that a change in magnetic flux generates a voltage that tries to drive a current that's going to produce a magnetic field that opposes the change. So, in other words, the, this coil doesn't want to change the magnetic flux inside. And if I try to change the magnetic flux, then there's going to be a voltage induced by that change. Such that its going to try to drive a current that's going to oppose the change. And so in a sense, coil kind of light the way it is, it doesn't want to make magnetic flux to change. That's where the minus sign comes from. So these, this is I realize I'm just kind of pulling this out of a hat but this is the some of the essential pieces from a, an electricity and magnetism course. That we need to really intelligently discuss inductors. And I just have to ask you to take my word for this, or go look it up on pick up a book on electricity and magnetism. Now, an inductor is nothing more than a coil of wire. And let's say this coil of wire has n turns, and the inductor is defined by it's inductance, L. And let's say I run a current through this. What's going to happen is there's going to be a magnetic field set up from each loop. And the magnetic fields from all of these loops adds up And it produces this magnetic field with this sort of configuration. It's going through the core of the set of coils, and then returns back around from the outside. So, it's kind of like a, like a little bar magnet in a sense. Where this would be like the north pole and that would be like the south pole. Now, this is not something we're going to use again. but just for your interest I wanted to show you the formula for the inductants of this coil wire. This is called a solenoid and the inductants. There's some constant times n squared times the area of one loop divided by the length of the entire coil. And this constant here, mu, is 4 pi times 10 to the minus 7 Henry's per meter, and I'll tell you what a Henry is right now. Now, the just finishing this up, if I have this inductor and I run a current I, through it, then I get a magnetic flux phi, which is L times I. So, this defines the inductance of this coil, it tells you how much magnetic flux you get for a given amount of current. Now, putting this into Faraday's Law, I get the voltage across this inductor, is equal to the inductance times the time rate of change of the current. So the magnetic flux here, I need to take the derivative with respect to time, I want to say how fast it's changing over time. Now, L, I'm going to assume is not changing this is just a fixed geometry set of coils here so d phi sub b dt appear it's just going to be L dI/dt. And the minus sign disappeared because of the way we defined the voltage across the inductor, we just kind of sweep that under the rug. Let's not don't worry about that, just remember this formula. This is the one that is the main formula that tells you what the, what the behavior of an inductor is. Now, this then is, the units on this, 1 volt is 1 Henry times 1 Amp per second. So if I have a, 1 Amp per second time rate of change of the current, and 1 Henry inductor would give you a voltage of one volt. Now, just to kind of draw the parallel to capacitors and inductors, energy is stored by the magnetic field inside the coil and around the coil. in capacitors, energy is stored by the electric field. So, inductors and capacitors are both energy storage devices. Capacitors store energy in the form of an electric field which comes about from segregating charge on two plates, a plus and a minus plate. So, you get an e field inside a capacitor that stores the energy. An inductor is something that has a current running through it, and the magnetic field set up by that current then is the, the medium by which the energy is stored.