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# Lenz's Law

## Video transcript

- So, right over here depicted a square loop of a conductor. Let's say it's a wire and it's stationary and it's sitting in a magnetic field. And I've drawn a few vectors that represent the magnetic field and you can see at least on the surface that is defined or that is contoured by the wire that the magnetic field looks constant. So, if we just had this scenario nothing too special going on but it becomes interesting if I were to actually change the flux going through the surface. So, both of these pictures right over here they actually show the same scenario where we have increased the flux. We have increased the flux at these points on the surface defined by the wire at every point the magnetic field has now gotten stronger. So, we have increased the flux. So, let me write that, the flux. We use the Greek letter phi used to denote flux. The flux of the magnetic field. The flux of the magnetic field has gone up. And we know from Faraday's law that when you have a change in your flux that that's going to induce a current in the loop. And so an interesting question is what direction is that current actually going to go in? We have two options. The current could go. The current... Let me find a nice color for the current. The current could go in the clockwise direction or it could go in the counter clockwise direction. So, which of these two do you think the current will actually go with? Well, let's think a little bit about it. We know that a current flowing through a wire actually on it's own will induce a magnetic field above and beyond a magnet field that's already there. So, let's think about the type of magnetic field that this orange current would actually induce. So, if it's going in the counter clockwise direction remember we use the right hand rule. I can take my right hand point my thumb in the direction of the current. So, let me see if I can do that. So, my thumb in the direction of the current and then my hands are going to loop or I should say my fingers are going to loop in the direction of the magnetic field. So, when I do that with my right hand, so my right hand looks something like that thumb in the direction of the current right over here we see that it shows the magnetic field being induced that would wrap around like that. Or if we were to show it, if we were to sample it points right on the surface the magnetic field that would be induced would look something like this and I'm just doing it at some sample points. So, notice it would be additive to the existing magnetic field. In fact, it would increase the flux even more. In fact, at these points these vectors would increase even more. These vectors, let me see if I can draw that. These vectors would increase even more. Well, what would that do? If the flux increases even more then the current is going to increase. The current is going to increase even more which is going to make the flux increase even more and which makes the current increase even more and you would have this never ending cycle where the current keeps increasing, the flux keeps increasing and you would have this energy that's appearing out of nowhere which would violate the law of conservation of energy. And so that's a pretty good argument for why you would not... That's a pretty good argument for why we would not expect the counter clockwise scenario. We would not want the current that's been induced to induce a magnetic field that goes in the same direction as our increase in flux. So, just by deductive reasoning we know that this is going to be the scenario and let's see if we think about what happens here. We can do the right hand rule again. We take our right hand point our thumb in the direction of the current point our thumb in the direction of the current and we see if we do that with our right hand. Well, now this would induce a magnetic field that would decrease the flux. So, it would produce a magnetic field. The current right over here would produce a magnetic field that's going downward. The current in that direction would also when you take your right hand and you were to put it along here. Once again if you're going in the counter clockwise, or sorry if you're going in the clockwise direction over here that too when you do your right hand rule right over here your fingers would coil around that way. And so once again when you look at the surface it would produce, it would induce a magnetic field that is going in that direction. And so it would have the induced magnetic field from the induced current will go against the change in flux. And this makes sense because we won't go into this never ending positive feedback loop where the current keeps getting strong and stronger and the flux keeps increasing and increasing and increasing. And this idea that the orientation of the current that is induced will produce a magnetic field that counter acts the change in flux. This is Lenz's law. Lenz's Law. And once again if that wasn't true then you would have a violation of the conservation of energy. So, in general if someone says okay well, this is the change in flux is happening in a certain direction. Well, to think about which way the current would flow you just have to say well what type of a magnetic field would each direction of the current produce? And that magnetic field should go in a direction that goes against your change in flux. So, if the flux is increasing the magnetic field that's induced by the induced current should make the flux decrease. If the flux was decreasing then the induced magnetic field by the induced current should make the flux decrease less or should be additive to the flux.