30. Induction and Inductance

Lenz's Law

# Lenz's Law for a Long Straight Wire

Patrick Ford

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Alright, guys, let's work this one out together. We have a long straight wire on a horizontal surface in the X Y plane, and it carries a constantly increasing currents in the plus y direction. So now if the square loop when we need to figure out what the direction is off the induced currents. So that should automatically tell you this is gonna be a lenses law problem. So the first thing I like to do in these kinds of problems were given sort of like a three d perspective. It's just draw out sort of, what's going on here. So we have this access right here, which we're told is the plus y direction and we're told directly on the side of it on the right, that is the plus X direction. So in other words, sort if I have a straight line like this and this is gonna be my ex direction, all right, so it's kind of weird, So that means that this direction it was sort of like the Z axis. So I've got some three dimensional stuff going on here. So what I always like to do in these kinds of situations to see if I can change my perspective a little bit in sort of draw, like a parallel or a different diagram. So if I were to view this current from the side, then basically what that happened, what happens is if I were sort of view along the axis of the current, then that means that the current would be going away from me like this. And then that means that square loop would be sort of on the right like that. So I'm looking sort of, like, perfectly on the side on the access like that. Okay, so we need to find out what the direction of the induced current is. We need to use lenses law. But there's a couple things we need to figure out first. So we need to figure out what the direction is off the magnetic field to the square loop. And then we need to figure out how the the magnetic flux is changing. So in other words, well, it's Delta five B that will tell us what the direction is of the induced magnetic field. Okay, so we need to do is first we need to figure out the magnetic field is so for a straight current carrying wire. We know that there is some relationship between the current in that wire and the magnetic field that it generates. Now, you don't have to necessarily remember this, but remember that the the magnetic field for a straight carrying are straight current. Carrying wire is mu, not times I divided by two pi times are okay, so the direction of our magnetic field is gonna be given by our right hand rule. So now it happens is our thumb points in the direction of the straight thing. In this case, the currents and our fingers will curl in the direction of the magnetic field. All right, so get out your right hands on. What we're gonna dio is we're gonna point our thumbs in the direction of that current. So in other words, our thumbs are gonna point in this direction. But remember that were sort of viewing this from a weird perspective. So what I like to do in this situation is we're gonna use the side view. So in other words, we're gonna be looking at what's going on in this diagram right here. So what happens is we need to point our thumbs in the direction off the current in this case. And what you should see is that you should be pointing your thumb into the page away from you, and your fingers will be curling in the direction of the magnetic field from that wire. So what that means is that our magnetic field lines actually curl clockwise. So what that means in this sort of diagram is that in the first diagram on the rights, I have magnetic field lines that are going like this, but on the side view now, what happens is they have magnetic field lines that are sort of cooling around like this. And so we know that they're given by our right hand rule. They're gonna go clockwise or sorry, they're gonna go clockwise like Wait, no, that's right. Yeah. So clockwise like that. So what that means is that the magnetic field is gonna be pointing in this direction through the square loop. So, in other words, the magnetic field to the square loop is gonna be pointing downwards. So that is the direction of B. So that's our first question. The magnetic field through the square loop points downwards. So now What we need to do is figure out what the change of the magnetic flux is. So remember that the change of the magnetic flux is gonna be given by three variables B A and CO. Sign of theta. So what is changing as this current is constantly increasing in the wire? Well, remember that we said that the relationship between I and B is that as the current increases, the magnetic field also increases. So what happens is the changing variable in this case on our magnetic flux equation is going to be be right because the area of the square loop is not changing its always just constant right there and the direction of it. So there was the co sign of data is always going to be again straight and not changing. So what happens is RB Field is changing. So as the current increases, the magnetic field is gonna get stronger. So that means that the change in the magnetic flux is positive. So if we have a positive magnetic flux change and downward pointing, be, uh, magnetic field, then we can figure out the direction of the induced magnetic field using lenses, law lenses law says that it's going to do whatever the opposite is off that change in magnetic flux. So if it's downwards and it's increasing, then that means that lenses law wants to counter act that change by producing a magnetic field. That sort of fights that. So in other words, our magnetic field is going to point upwards like that. So now we find out what the direction is of the induced currents by using our right hand rule again. But in this case, we have to use a different right hand rule. So before we had our thumb pointing in our direction of the current because that was the straight thing. But now the straight thing here is our magnetic field. So now what happens is our right thumb is going to point in the direction of the magnetic field, and our fingers will give us the direction of the induced currents. So be careful when you're using these right hand rules, because sometimes in the same problem, you might be using two different right hand rules to solve it. Okay, so now what we're gonna do is on our page, right? So just follow exactly what we're doing. We're gonna take our right hands and we're gonna point in the direction off the magnetic field. So what happens is if we have a magnetic flux are sorry if we have an induced magnetic field that points upwards like this, then that means that our fingers will curl in the direction of that induced current. So if we're looking at it from the side view so we're still looking at the side view right here, then what happens is our induced currents is going to point sort of in the clockwise direction. So we're sorry that's gonna be counterclockwise. So in other words, if we're looking at it from this perspective in the first diagram like this, uh, it might be helpful to sort of visualize this as your thumb pointing so, like, quite a like upwards and are induced. Magnetic are sorry are induced. Current will point like this. So that means that in our first diagram are induced, current is gonna be pointing in this direction. So that's the direction of our induced current. And that actually happens to be the counter clockwise direction. So that's gonna be counterclockwise. Okay, so let me know if you guys have any questions with this and I'll see you guys the next one

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