Magnetic field due to current carrying loop

- [Narrator] In a previous video, we saw that a straight wire carrying an electric current produces magnetic fields which are in concentric circles. In this video, we will explore what do the magnetic fields lines look like for a circular loop of wire carrying an electric current. And a small spoiler alert, you may be familiar with these field patterns. So to figure out the field pattern experimentally, all we need to do is sprinkle some iron filings on top of it. And that's what we'll do first. In this clip, we have copper wires which are in a circle. And notice that these are made to pass through a glass lab. Inside this glass lab we have iron filings, and so when we pass electric current through this it goes through the loop, generates a magnetic field and then the iron filings will arrange themselves and they will reveal the pattern to us. So here it is, we have done the connection. And now once we click on, once we close the circuit, electric current will run through and we'll see a pattern forming. And there it is! You can already see a pretty good pattern formed over there. Wow! That's beautiful, isn't it? Look at that! All right. So we can see that close to the wire the field is in circles. But as you go farther away from the wire, as you move towards the center, notice the circle tends to become larger, you tend to get a bigger curve. Look at the curve, it tends to get bigger. It tends to get flatter. And then as we move towards the center of the loop, notice it's pretty straight over here. Pretty straight. So now, let's try and figure out why the field looks like this. And we'll see that this is actually a familiar field line. We've seen this before. So here's our copper ring. It's a circle but we are looking at it from an angle like this. And so it looks oval to us. And let's say we put a current through it in this particular direction. So the current is flowing this way, into the board, goes from the back, outside the board, comes out from the front, and so on. Just like this, goes here into the screen, comes out from the back, comes out, and then goes on in circles. How do we now figure out the direction of the magnetic field everywhere is the question? Well in a previous video we have seen, that if we have straight wires, then we can use the right-hand thumb rule. Basically take your right hand, clasp the conductor, so that the thumb points in the direction of the current. Then four encircling fingers will give us the direction of the magnetic field. Encircling that straight wire. And if you need more clarity on this, we've discussed this in great deal in previous videos so feel free to go back and watch that video. But here we don't have a straight wire. We have a circle. What do we do then? How do we use our right-hand thumb rule over here? Well, all we have to do is clasp each section of the wire separately and figure out what the magnetic field looks like around that section. So, let's take an example. Imagine I want to know what the magnetic field looks like somewhere over here. And I'm choosing this section of the wire because it's easier to draw the magnetic field on the screen as you will see. So let's say this section, I want to know what the magnetic field looks like around that section. And, how do I do this? Well, I have to clasp my right hand through this section so that the thumb points in the direction of the current. But what direction is the current over here? Well, since the current is moving to the right here, it enters into the screen over here and so my thumb should point into the screen. So let's see what it looks like if I were to clasp over there, that's what it would look like. You can't see my thumb because my thumb is pointing into the screen. And now the four encircling fingers give me the direction of the magnetic field around that section. And notice the encircling fingers are running clockwise. And so I know that around that section, the magnetic field is going to be clockwise. Similarly, if I consider now this section, again, I am choosing that section because it's easier to draw the magnetic field over there. You'll see that the current is coming out of the screen over here, it comes out and then goes to the right. So if you're to clasp this section of the wire, can you imagine what it will look like? Well, this time with my right hand, it should always be right hand, my thumb should now point outwards, outside the screen. So if you clasp it with my right hand, this is what it would look like. And now notice the four encircling fingers are going anti-clockwise so I know the magnetic field around that section is going to be anti-clockwise. So this explains the circular fields over here. Now, to figure out the magnetic field everywhere else, we don't have to keep doing this over and over again and make our job tedious. Instead there is an easier way to guess what the field might look like. Here's how I like to do it. If you look over here, it's telling us that the field inside the loop is pointing upwards. Outside, downwards. Same thing over here. Even the field this way is telling us inside the loop is upwards, outside the loop is downwards. In fact, regardless of which section you clasp, you will find the field inside will be up, and outside will be down. So to convince you, let me show you two more sections that we have clasped. Here they are. Use the same right-hand thumb rule, thumb points in the direction of the current. You can clearly see the four fingers are telling us inside the field is upwards, outside downwards. Inside, upwards. Outside, downwards. And so from this, we know the fields should start over inside should be up, outside should be down, and they should be closed loops, we have studied that. Therefore, all the field lines should go like this. Should go like this. Can you guess that? Can you see that now? Can you imagine it? And so, if we were to draw the complete picture, let me get rid of these additional hands so that we can look at these field lines properly now. If we look at all these field lines, this is what it would look like. So notice all of them, the field is inside is up, and they will tend to go down outside. And this is exactly what we got in our experiment. The last thing I want to discuss is, is this field look familiar to you? And for that, let me zoom out a little bit. All right, here it is. Look at this beautiful field pattern. What does this resemble? Well, this field looks very similar to that created by a tiny bar magnet. We've seen what the field carried by a bar magnet looks like, it looks somewhat like this. And look at these two field patterns. Don't they look very similar to each other? Here also the field lines start from here, and they continuously keep looping back like this. Here also the field lines start from here, and they continuously keep looping back. Small difference you might see is over here, the field is a little flatter, and over here, the field is more round. But if this bar magnet was very small, if this bar magnet was very tiny, then notice we would get a very, very, similar field like this. So this means, a current carrying loop resembles a tiny bar magnet. And we can now say that this side represents the north pole of that bar magnet, and this side over here represents the south pole. The poles are not really there, but if you think of it as a bar magnet we can treat it this way. And this is pretty awesome because now we've learned how to create our own artificial bar magnets! Well, tiny bar magnets. And so in this video, we learned how to figure out the magnetic field around a current carrying loop using the same right-hand thumb rule. And eventually we saw that a current carrying loop is equivalent to a tiny bar magnet.