Video: Magnetic Fields

In this lesson, we will learn how to correctly draw the field lines of the magnetic field created by a magnet and how to relate field lines to the force experienced by two magnets.

12:35

Video Transcript

In this video, we’re learning about magnetic fields. Magnetic fields are enablers of cool things, such as levitating objects, and also very useful things, such as very fast magnetic trains.

To start off talking about these fields, let’s begin with a bar magnet. This is a permanent magnet shaped like a, you guessed it, a bar. Now let’s say we put this bar magnet so it was sitting flat on a table top, stationary. In this situation, we certainly can’t see any field created by this magnet. But just like electric fields need a charged object in order to show their presence, so magnetic fields need a magnetizable object around them in order to show that they exist.

One great example of objects which can be magnetized are called iron filings. These are very small rod-shaped bits of iron. If we were to pick up a small pile of these filings, which would amount to hundreds and hundreds of them, and then drop that pile bit by bit around the magnet on our table top, as we did that, we would see that the filings don’t just fall in a random distribution on the table top. What we would see instead is that the filings, these tiny little iron rods, start to organize according to a pattern.

This is an experiment you can try out yourself. And it’s because of this, because the filings don’t just fall down in clumps but actually arrange according to a pattern that looks something like this, that we say that this bar magnet, this permanent magnet, produces a magnetic field around itself. And not only does this experiment show that some sort of field is being produced by the magnet, but it also gives a good idea of what that field looks like.

We can see that there are lots of iron filings bunched to the ends of the bar magnet, which seems to indicate maybe that the field is strongest in magnitude there. And we also notice this general pattern of arcing from one end of the magnet to the other on both sides of the magnet. That also gives us a sense for what the field created by this magnet looks like.

This whole idea of magnetic fields raises a question though. Remember when we talked about electric fields, we said that these fields are created by electric charge. So anytime you have a charge, either positive or negative, that charge creates a field around itself. But then what would be the source of the magnetic field? Is there such a thing as magnetic charge?

It turns out that the physical origin of magnetic fields is electric charge, electric charge in motion. Simply put, the way you get a magnetic field is to take an electric charge and to move it. This idea of moving charge can remind us of the structure of an atom, comprised of a nucleus surrounded by orbiting electrons. These electrons are charged particles in motion. Therefore, each one creates its own magnetic field. And the atom overall has a combined or effective magnetic field. It’s all the net magnetic fields from all of the atoms in this bar magnet which combine to give it an overall magnetic field.

To understand magnetic fields better, it’s worth talking about the two parts — we can almost call them the two halves — of a magnet. The part of the magnet that we’ve colored blue we’ll refer to as the north pole. And the other half we’ll refer to as the south pole. These names, north pole and south pole, come from the fact that one of the earliest uses of magnets was to help people navigate to find their way.

When magnetic materials were first discovered, it was found that one end of the material always wanted to point towards the north pole of the Earth. The other end pointed the opposite way towards the south pole, hence their names, north and south pole.

Now we saw from our iron filing experiment that more filings seem to gather at the poles than anywhere else. That’s where they clumped together. And if you recall, we saw that the filings organize themselves into roughly shaped arcs from one pole to the other.

Based on what we saw in that experiment, we can draw in what are called magnetic field lines. Magnetic field lines are representations. They’re a way we have of showing what a magnetic field is like. We’ll find that magnetic field lines indicate two things. They show us magnetic field direction, which way it points, as well as its strength.

Before we draw in the field lines on this bar magnet, notice that these two points, taken together, indicate that magnetic fields themselves are vector quantities. And here’s how magnetic field lines show us this. Looking at the field lines for this bar magnet, we can notice a couple of things. First, each one of the lines has a direction associated with it. They all have an arrowhead, which shows which way it points. We can look at any one of these field lines. And we see that, by their direction, they’re pointing from the north pole of the magnet towards the south pole.

For example, if we pick this line right here, we can see that it seems to start at the north pole of the magnet and then moves towards the south pole, in that direction. We can see then how these field lines indicate magnetic field direction. But what about magnetic field strength?

It turns out that this strength is indicated by what we could call the magnetic field line density. Think of it this way. Say that we had a square of a set size, this one right here. And let’s say that we could move this square from one spot to another in this diagram. Right now, we can see that the square has no field lines moving through it. There are zero field lines passing through this square. But if we were to move this square over here, say, then that would change.

Now there are two magnetic field lines passing through the square. And then if we were to move it down here, we see that even more field lines are passing through this space. This gets at what we mean by the magnetic field line density, how many field lines there are in a certain volume of space. The higher that density, the stronger the magnetic field it indicates.

Based on that, we can say that, for a bar magnet like the one we have here, the place of strongest magnetic field is near the poles. That’s where the field lines are most concentrated. And we further notice that as we move out from the poles, the field line density gets less, indicating a weaker field.

Beyond this, there are a couple of things about magnetic field lines which are not easy to see from the sketch but are nonetheless true. First, magnetic field lines form closed loops. In other words, a magnetic field line would never be part of a broken loop such as this. Our diagram seems to contradict this claim since the field lines appear to start at the north pole and end at the south pole.

Really though, what’s going on that we haven’t drawn here and often doesn’t get drawn in diagrams is that there’s a portion of the magnetic field line, the loop, that travels through the magnet. If we included all these parts of all the loops that we’ve drawn, then indeed we would see that they all do form closed loops.

A second important fact about magnetic field lines is that they do not cross one another. That is, we would never see a physical situation where a magnetic field line went like this and another one went, say, like this. The reason this can never happen is if we did have crossing magnetic field lines, that would mean that, at the intersection point, the magnetic field points in two different directions at the same time. That’s not possible. And that’s why magnetic field lines never cross. Now that we know a bit about magnetic fields and the lines that represent them, let’s get some practice with a couple of examples.

Which of the four diagrams correctly shows the field lines of the magnetic field produced by two very wide flat magnets that are placed near to each other but are aligned in opposite directions? Red represents the north pole of the magnets and blue the south pole.

Looking at the diagrams, we see these four options — a), b), c), and d) — for the correct representation of the field lines of the magnetic field between these two magnets. We may be used to seeing magnets constructed differently than the ones in these diagrams.

We’re told they’re very wide and flat. So whereas we might typically see a magnet that looks like this, these magnets look like a smushed version of that, more like this. We’re told that, with these magnets in the diagram, the red side represents the north pole and the blue side the south pole. We’re also told that these two magnets are aligned in opposite directions, meaning their north poles don’t point the same way but actually point the opposite ways. That fact of being pointed in opposite directions lets us cancel out a few of our answer options.

For example, notice in answer option c) that the north pole, the red part of each of the two magnets, points upward. But since the magnets point in opposite directions, that means this diagram doesn’t represent our scenario. Same thing with answer option b), in this case, the north pole of each of the two magnets points up. So that’s not our answer choice either. That leaves answer options a and d remaining.

If we look more closely at option a, we see that, in this case, we have magnetic field lines which are directed towards the north pole of the two magnets. We can see that from the little arrowheads that are on the field lines, indicating that the field lines go towards the north pole. We can recall that, in reality though, this is opposite the direction that magnetic field lines point. Magnetic field lines always point from the north pole of the magnet to the south pole. That’s true whether we just had one magnet — so the field lines might look like this — or if we had multiple magnets, as we do in this case. So that means option a isn’t our choice either. The field lines in this case point opposite the way they do in real life.

Taking a look at our last option, choice d, we see that, in this case, the south pole of each magnet, indicated in blue, has the field lines pointing toward it. That is an accurate way to represent magnetic field lines pointing from north pole to south pole. Option d shows us two magnets pointed in opposite directions and the field lines are drawn in correctly. So this is our choice for the correct representation of the magnetic field created by these two magnets. Let’s look now at a second magnetic field example.

The diagram shows a bar magnet. The bar magnet creates a magnetic field around it. At which point marked on the diagram is the magnetic field strongest? At which point marked on the diagram is the magnetic field weakest?

Taking a look at our diagram, we see this bar magnet with north and south poles and the four points — A, B, C, and D — marked out around it. We’re told that this bar magnet creates a magnetic field around it. And in representing that magnetic field using magnetic field lines, we’ll find the answer to our question of where that field is strongest and where it’s weakest.

We can start out by sketching in the magnetic field lines representing the field created by this magnet. We can recall that, in general, these field lines move from the north pole of the magnet to the south pole. With these example field lines drawn in, notice that each one has a direction associated with it and has an arrowhead on the field line telling which way the magnetic field points.

However, it’s not the magnetic field direction we’re interested in, but rather its strength. We want to know where the field is strongest as well as weakest. To find this out, we can recall that magnetic field line density, that is, how many magnetic field lines pass through a given space, is an indication of magnetic field strength. The more field lines within a certain fixed volume, the greater the strength of the magnetic field.

This means we can look at the field lines we’ve drawn in on this diagram and scan for regions of high concentration as well as low concentration. The places where field lines are spaced more closely together, say around here, indicate a stronger magnetic field. On the other hand, places where there aren’t many magnetic field lines in a given space, say out here, indicate a weaker field.

Knowing this, we want to evaluate our four locations — A, B, C, and D — on this diagram. To start out, let’s look for the point where the field lines are densest, most closely together. That will be where the field is strongest. Comparing the four points, we see that it’s point A that exists where there are more field lines per unit space than any other. That indicates a relatively stronger magnetic field. So we’ll say that this point is the one at which the field is strongest.

Now what about the point at which the field is weakest? If we consider the space around points B, C, and D, we see that it’s point D which has the fewest field lines nearby. The lowest magnetic field line density indicates the smallest magnetic field strength. Therefore, of the four points, the magnetic field is weakest at point D.

Okay, as we wrap up our lesson, let’s summarize what we’ve seen about magnetic fields. For starters, we saw that magnetic fields are created by electric charge that’s put in motion. And we noted that, at the atomic level, those electric charges in motion are electrons orbiting the nucleus.

Additionally, we saw how magnetic fields have magnitude as well as direction. That is, they’re vector quantities. Magnetic fields are represented by magnetic field lines, which themselves have a number of properties. Magnetic field lines point from the north pole of a magnet to the south pole. They form closed loops. And they do not intersect with one another.

Finally, we learned that magnetic field direction is indicated by the arrowheads on magnetic field lines and that magnetic field magnitude or strength is indicated by the density of the magnetic field lines.

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