Lenz's Law

Hey guys, in this video we're going to talk about LenzÕs law. Faraday's law was the quantitative law that described electromagnetic induction, it told us how to find the induced EMFÕs and the induced currents, but it didn't tell us anything about qualitative information such as the direction of the current, that's induced on a loop, LenzÕs law is going to tell us that. So let's get to it, right? Faraday's law tells us the magnitude of the induced EMF, which gives us the magnitude of induced current to find the direction of the induced current, we want to use Lenz's law. What Lenz's law states it's a qualitative law, states that a conductor will induce the magnetic field on itself to oppose any changes in this magnetic flux, okay? So, the conductor is going to have an initial magnetic flux, and then once that starts changing, it's going to want to oppose the change. So, it will induce a magnetic field on itself to change that, sorry, to oppose that change in magnetic flux. Remember, that a magnetic field can only be produced by a current, so in order to induce a magnetic field on itself, it has to induce a current on itself, okay? So, this is the concept behind Faraday's law. Where does that current come from? Where does that induce the EMF come from? It comes from the fact that conductor's want to resist changes to the magnetic flux passing through them. So, if we look at these two scenarios here, starting on the left. We have a bar magnet, which is initially some distance away, right? So, the magnetic fields coming out of it, is some strength, if I were to bring that bar magnet closer, what's going to happen is the magnetic field strength is going to increase downward, right? Magnetic field lines come out of the North Pole and the closer that magnetic, sorry, the closer of that bar magnet gets, the larger the magnetic field. So, you have it increasing magnetic field downwards, okay? This was your initial, this is your final, this is your change. The conductors want to induce a magnetic field on itself to oppose that change, okay? So, it induces the magnetic field upwards. Now, IÕm going to minimize myself. Remember, it's going to induce a magnetic field to oppose changes in the magnetic flux, not just changes in the magnetic field. So, let's look at this ring, this ring starts here, where it's only partially embedded in this magnetic field. So, you see there's a very small area here, that is feeling that magnetic field, but as it moves inwards, that area experiencing magnetic field gets larger and larger and larger. Remember, the flux doesn't only depend upon magnetic field strengths, it also depends upon how much area that magnetic field is passing through, okay? Because the magnetic flux downwards is increasing, the coil responds by inducing a magnetic field upwards to oppose that increasing downward magnetic flux, okay? This is the deal with Lenz's law, how does this tell us the direction of the current, though? Well, once the direction of the induced magnetic field is known, the right hand rule just tells us the direction of the current, okay? For example, what we just looked at, we have an initially small amount of area, so we have a small magnetic flux downwards through this loop, that area increases, so the magnetic flux downwards through the loop increases, which causes the loop to induce some magnetic field upwards, all we have to do is then use the right hand rule upwards and we see, it's hard for you guys to see because of the camera, but if you do it yourself, point your right thumb in the direction the induced magnetic field, okay? And you'll see that your finger should be curling towards you, curling towards you means that this current should be curling towards you, just like that, right? Coming around towards you, okay? This is exactly how you use Lenz's law to find the direction of the induced current. LetÕs do an example. In the following scenarios, find the direction of the current induced on the following conductors, okay? So, let's say we have a magnet with a North Pole into downwards moving up. So, what we have, is we have a magnetic field pointing downwards, that's decreasing, so it starts out downwards and large and then it becomes smaller and smaller and smaller pointing downwards, meaning the induced magnetic field has to be downwards, it wants to bring it back to what it originally was. Now, once again, if you put your thumb down, you'll see that the current is moving away from you, meaning that the current is going like this, this is the induced current, okay? Now, what about a magnet with it South Pole into downwards? With a South Pole into downwards the magnetic field is pointing upwards, right? It's still moving away though, so that upwards magnetic field it's still getting smaller and smaller and smaller, it wants to return to the larger upward magnetic field, so it induces a magnetic field on itself upwards. So, we have to do this right hand rule upwards, this current is coming towards us, okay? So, this induced current is coming towards us, and once again, you guys need to do the right hand rule on your own, it's kind of hard to see it on camera here. Lastly, we have the South Pole oriented down and this time it's moving downwards. So, we have an upward oriented magnetic field, that's getting larger, right? It continues to get larger in order to oppose that increase in heights, we need to induce a magnetic field downwards, pointing your thumb downwards once again, you have the current, that's going away from you, okay? So, this current starts here, and it is going away from you, okay? That wraps up our conceptual discussion on Lenz's law. Thank you for watching guys.

Hey guys, let's do an example. A bar magnet moves relative to a coil of wire as indicated in the figure below and induces a current in the coil. A current carrying wire carries a current relative to a coil as shown in the second figure, which we can't see yet but I'll scroll down when I'm done reading the question. So, this current carrying wire carries a current relative to a coil shown in the figure. Would you need to increase or decrease, right? Increase or decrease the magnitude of the current in this wire to induce a current in the coil, that is in the same direction as the current induced by the bar magnet, okay? So, this problem sounds convoluted but is very straightforward. The bar magnet in the top figure induces a current on a coil in a certain direction, either clockwise or counterclockwise. Does the current in the wire indicated right next to me, have to increase or decrease, so that the current induced on the coil goes in the same direction, either clockwise or counterclockwise, we don't know yet. So, first, let's figure out, what direction that current induced current is supposed to go. If we have the North Pole coming in, then the magnetic field is pointing into the page, right? If the North Pole is coming at the magnet, then the magnetic field is pointing into the page, okay? Now, because it's getting closer that magnetic field is increasing, okay? This is increasing, that means, according to Lenz's law that the opposing magnetic field needs points in the opposite direction, okay? That way subtracts back to its original size. So, the induced magnetic field is coming out of the page, now right hand rule says if it comes out of the page, right towards me, it curls counterclockwise, okay? Once again, I'm sorry about how the right hand roll looks, but coming towards me is coming out of the page and you can clearly see, that's counterclockwise, okay? So, in scenario 2, we need a counter clockwise current. The question is: Does our current and the current carrying wire have to increase or decrease? Well, just like above, in order for the current, that's induced on the coil to go counterclockwise, the induced magnetic field has to be out of the page, that means that whatever the magnetic field is doing, it has to do it, so that its change is into the page. First, let's use right hand rule on this wire, if I stick my thumb in the direction of the current on the wire, then my fingers are going towards you guys into the page, okay? So, our indu-, sorry, our magnetic field produced by the wire is into the page, exactly like it is in the above scenario. How did the above scenario produce a magnetic field and induced magnetic fields out of page? Because the magnetic field produced by the bar magnet into the page increased, we need this to increase in magnitude, how do we get increase in magnitude? We just need the current to be increasing. So, our answer is current needs to be increasing, okay? Thanks for watching guys.