Motional EMF

by Patrick Ford
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Hey, guys, over this video, we're gonna be taking a look at a special kind of MF called emotional MF. Let's check it out. So remember the theme of these last couple videos have been about Is that the changing magnetic flux through a loop or something like that produces an induced E M F. That's what Faraday's Law tells us. Well, sometimes what happens is that this change in magnetic flux can happen through something moving. So it happens through motion. And when that happens, we call it emotional e M f. So what I want you guys to take away from this video Is that really emotional? E m f is just a special case of Faraday's law. All right, so let's go ahead and check it out. So we have this bar or this conducting rod that is moving through a magnetic field. We have the velocity to the right magnetic field that points into the page so away from you. And what happens is as this conducting rod moves through a magnetic field with some velocity. The charges on this magnetic rods So if I have a charge like this, they feel a magnetic force, remember that charges inside of a moving inside of a magnetic field will produce will feel a magnetic force if they have some velocity. And to sort of figure out what the direction is, we have to fuse our right hand rule. So remember, what we're gonna do is we're gonna take our fingers and we're gonna point their fingers in the direction of the magnetic field, which points into the page. We also want our thumb to be pointing off towards the right. And what happens is that the palm of your hand should face in the direction of the magnetic force. So what I've drawn here on the diagram above is that the magnetic force actually points upwards like this. And so what ends up happening is that positive charge will end up moving to the top of the rod like this, so positive charges will feel a force upwards. And what that means is that negative charges will feel a force in the opposite direction. So negative charges like this. So I have a negative charge over here. Those will actually start moving in the opposite direction so you'll start to get negative charges that buildup on the bottom. Now what happens here is we've actually separated these charges because we have a magnetic force. F B is equal to Q V b sign of data, and it depends on the Q that's involved. So what ends up happening is these charges that have now separated to the ends of the Rod have now actually produced an electric field. So he have an electric field. That point sort of through this conductor like this. And when is it happening is that these charges will eventually sort of work themselves out to balance the magnetic field. So what that means is that the force that is that that they experienced due to this magnetic field is actually perfectly balanced with the magnetic with a magnetic force. So these things will feel a sort of electric force in this direction. That's gonna be F E. But that's gonna be perfectly balanced with the magnetic force that's keeping them upwards. Now all that's really happening here is if we sort of write out some equations for this, remember that the electric force on a charge Q is Q times the electric field, and that's gonna be equal to Q times. VB we could sort of drop this sign of fate a term because we know theta is equal to 90 degrees for this particular example. The velocity goes to the right and the magnetic field points sort of straight out towards your story straight into the page. So that means that the angle is equal to 90 there. So what that means is that so you can cancel out the charges involved And that means we have a relationship between the electric field, he and the velocity with the magnetic field so easy equal to V B. Now what that basically means is that we have now have an e m f that is induced on the charges or in this conducting rod, the E M f is just equal to V b times L. So what do we actually come up with? This equation will remember way back from a couple of chapters ago that the voltage which is really just a which is really what the IMF is, is equal to the electric field times a distance. This is an equation that we used a few chapters ago. Well, the electric field Would you have a relationship with the velocity and the magnetic field. That's just VB and the distance is actually just equal to L. The length of the conducting rod. So, really, this is the equation. We're gonna have to use its like a special kind of IMF that's due to motion. So you might be wondering what this has to do with Faraday's law or what happens is now Things get interesting if we if we attach this conducting rod here to a conducting wire like this and make a loop. Because now what happens is we've created a circuit in this little region right here. So we have a circuit of charges that's moving through either this way or this way. We have no idea. But as this bar is moving through in this direction, what happens is that the magnetic flux through that the circus throughout the circuit is constantly changing. So we have to use Faraday's law on the circuit that this thing creates. Remember, when we're using Faraday's law, we're gonna be looking at the change in the magnetic flux. So let's think for a second as this rod is moving to the right sort of outside of this circuit, which of the three variables is changing. Is that the magnetic field? Is that the area or is it the angle? We'll see? The magnetic field is uniformed. It points into the page and it never changes the angle. This thing makes right there. Velocities to the right magnetic field is out there is into the page, never changes. So what's really going on is that the area is changing. That's are changing variable. So we can write our Delta Phi over Delta T as b times Delta a times cosine of fada over Delta T Now what happens is the art. Sorry that Z that's cosine theta where the cosine of the angle here is remember gonna have to take the normal of this sort of surface that we've made and the normal points in the same direction as the magnetic field. So this is the normal, or this is the area sort of vector like this, and these things points in the same exact direction. So that means that the coastline of the angles equals zero. Right? So that means that we can write this Delta A. So let's see what happens here. The rod is gonna be moving to the right, and in some time it's gonna go from here and it's gonna end up over here. So it's changed a distance of Delta X. So if we have the length, which is L and the width of this rectangle, which is little X, then the new area that we've made as this rod has been moving. So in other words, we've made a new area as this thing is moving the length or the area of this sort of new Breck tangle that we've made is actually equal to L. A times Delta X And that's gonna be over Delta T. So remember, we've gotten rid of that coastline of term here. Okay, so we have two constants over here, the magnetic field and the length of the rod. And we have two variables Delta X over Delta T. But if you remember back from way back in like early physics one this Delta X over Delta T the change in the position and the change in time is really just the velocity. So this velocity here is that the velocity which they're conducting Rod is moving through the field. So what basically happens is that the induced E M f. Which remember, is equal to Delta. Fire of a Delta T is just equal to V B l, which is the exact same equation that we got from before. It's no coincidence that we got the same exact equation because remember, emotional MF is just an applied Faraday's law. So, really, this is the equation that we're gonna be using to solve these problems. All right, so let's get to it. So we have a circuit that's below here, and the wire has a resistance of 10 Mila homes, and we have to do is figure out what the induced current is. If the length of the bar is 10 centimeters were given some other conditions right here. So let's write. Our variables were supposed to be figuring out what the strength of the induced current Sorry, that's gonna be the induced current. So they are induced currents is always gonna be related to our induced e M F. That's absolute induced, divided by the resistance that's just owns law. Now remember, what happens is that this induced e m f. When we're talking about emotional E. M f is actually given a special form that's gonna bvb times l. That's the new equation that we have divided by our. So let's take a look here. I've got my eye induced is gonna be the magnetic field or some of the velocity. First, the velocity is 25 m per second, which is 0.25. Now we have the strength of the magnetic field, which is 0.2 Tesla. And now we have the length of the bar, which is 10 centimeters. So it's gonna be 0.1. Now we have the resistance is equal to 10 million homes, which is actually point. This is 0.10 Right? So if you work all this out, you're gonna get an induced current that's equal to 05 amps, and that's actually the answer. So that's the induced current as a result of this bar moving through this field. And that's again just using Faraday's law. So how about the power? Let's see, How do we get power? Remember, that power actually has three equations again, this sort of an equation that we use a little while ago, so we have three forms of it. We have the voltage times, the currents We also have the current squared times, the resistance, and we have the voltage squared, divided by the resistance. Now, remember, in these equations you can always replace a V with an epsilon. So we have excellent. I equals I squared. R equals Epsilon squared over r, remember that these EP salons and voltages are the exact same thing. So let's see, which one of these things do we have? Well, I just figured out what my current is, and I know what the resistance of the wire is. So that means that I'm gonna be using not this equation, Not this equation. But I have the equation that relates the current and the resistance. So what I have is that the power is gonna be equal to 0. squared times the resistance, which is 0.10 So what I get when I plug that in is I get 2.5 times 10 to the minus three, and that's in Watts. So that's gonna be my power output. This is actually equal to 2.5 million watts as my final answer. All right, guys. So that's it. We're gonna get a couple more practice problems, and I'll see you guys the next one