Video: Electromagnetic Induction

In this lesson, we will learn how to describe the electric current induced in a wire that is placed in a changing magnetic field.


Video Transcript

In this lesson, we get to learn about one of the most important and useful discoveries in history of physics. This is the discovery of the phenomenon of electromagnetic induction. Electromagnetic induction is useful in cell phone chargers, laptops, headphones, CD players, cooking, guitar pickups, heating, welding, energy generating, transformers, graphics tablets, flow metres on pipes, and electrocranial stimulation. Electromagnetic induction is just about anywhere you look in any field or any industry.

And yet the idea behind electromagnetic induction is really pretty simple. Say that we had a loop of wire and a permanent magnet. At the moment, there’s no current running through this loop of wire. That’s because there is no electromotive force that could push charge around the loop. But let’s say that anyway we put a device for measuring current called an ammeter into the loop just to see when current is running through it.

Our ammeter — our current measurement device — has a scale. And we see that at the moment the needle on the scale is pointed to zero, no current flowing through the loop. That’s not too surprising of course because we don’t have a cell or a battery or anything else to power current in our loop. Let’s say though that we then take our permanent magnet and we move it through the loop of the wire. If we did that, we might notice very briefly a flicker in our ammeter. But then with the magnet at rest, we see the ammeter needle is at zero. We do almost start to doubt ourselves. Did we actually see the ammeter reading change? Let’s try that again.

This time we move the magnet through the loop in the opposite direction. This time ever so briefly we see the needle deflect again, but in the opposite direction. Once more, when the magnet comes to rest, the needle goes to zero. At this point, maybe, we can explain what’s going on. But it definitely seems like something is happening in terms of the current in this loop of wire when the magnet passes through it. So we keep trying passing the magnet back and forth through the loop one way and the other way and seeing how the ammeter responds. Each time we do it, we notice the needle on the ammeter flicker then come back to zero. Eventually, we’re able to make a couple of conclusions which we can jot down in our lab notebook.

Our first observation is that when the magnet moves through the loop, current flows in the loop. That seems completely odd. But it is what we’re seeing over and over. The second thing we’ve noticed is that when the magnet is not moving, no current flows to the loop. And lastly, we notice that when the magnet moves in the opposite direction through the loop, so does the current in the loop. What we’re uncovering here through these three observations is that when our magnet moves through this loop, it induces a current. And apparently, there’s something about the motion of the magnet that’s very important. It’s only when the magnet is moving, we’ve noticed that current is actually induced in the loop.

Let’s think for a moment about our magnet. The way we’ve drawn it, we just see the north and south pole of this permanent magnet. But we know that there’s more to the story. In particular, that every magnet creates a magnetic field around itself. That magnetic field looks something like this. We show it using field lines that point from the north pole to the south pole. We can recall from earlier that this magnetic field is strongest where the field lines are most dense; that is, where they’re closest together. That would be near the poles, here and here. And then, as the field lines become less dense, that indicates a weaker overall field strength.

So every time that we move our magnet through this loop of wire, it’s not just the magnet that moving through, but it’s also the field. And since the field of the magnet has a different strength here as compared to here or here or here or farther out on this line, we can say that as the magnet moves through the loop, the loop experiences a changing magnetic field. Another way to say this is that if we were to look at the cross-sectional area of our loop of wire, then as the magnet moved through the loop, the magnetic field across that area would be changing. And apparently, based on our observation, when that happens current flows through the loop. That is current is induced in the loop of wire.

Here is one way we could write out a concluding thought on this experiment then. We can say that when the magnetic field through a loop of wire changes, current flows; that is, is induced in the loop. This statement we’ve developed here it turns out is a great summary of what electromagnetic induction means. It says that when we have a closed loop of wire when the magnetic field through that loop of wire is changing, then current is created or induced in the wire.

Now, this is really interesting. And there are a lot of ways to explore this idea further. There are plenty of changes that we could make to our experimental setup to see what effect those changes have. For example, so far, we’ve just used a single loop of wire. But what if we used lots of loops of wire and pass the magnet through those? Or what if we used a stronger magnet and passed that back and forth through the loops? Or what if we made the size of the loops in our wire bigger or smaller? All these changes we’re talking about will create changes in the amount of current that’s induced in our loop.

We can summarise those changes by expanding a bit on what we’ve said here about electromagnetic induction. We find that the greater the change in magnetic field through the total loop area, the more current is induced. So for example, when we talked about adding more loops to our single loop of wire, whereas with a single loop, our total loop area would be this area, when we add more loops, our total loop area will go up because now all this area is included in our loop calculation. Or consider the question of using a stronger magnet. In that case, we have a stronger magnetic field.

And therefore, the change in the magnetic field through the loop area — whatever that loop area is — would be greater overall and therefore more current would be induced. And we can see that when it comes to changing the loop size, either making them bigger or smaller, making them bigger would increase the total loop area, therefore inducing more current. And making them smaller would decrease that area, decreasing the current induced.

One last thing about this experimental setup, we saw that when we have the magnet oriented the way it is with the north pole to the right, then when we pass this magnet through the loops, the needle on our ammeter move to the right. That movement in the direction of what’s called positive current indicates a certain direction of the current as it flows around the loop, either clockwise or counterclockwise. If we then flip the magnet around so that now the north pole points to the left and passed it in this orientation through the loops of wire, then we would see the needle deflect in the opposite direction. In other words, current is induced in the loops running the opposite way as before. We could say that this change in the magnet orientation implies a change in the magnetic field through the total loop area. In that sense, this statement here really does summarise what we’ve seen in terms of the phenomena of this experiment.

Now, so far, we’ve had a stationary coil of wire and a magnet and therefore a magnetic field which is in motion through it. That’s been the way that we generated a change in the magnetic field through a total loop area. But there’s another way to create this type of change. Let’s say we had this. What this is is a magnetic field — we’ll call it B — that’s pointed out of the screen straight at us. We’ll say that this field has a constant strength, that it has the same magnitude everywhere. Imagine then that into this field, we place this U-shaped track. And we’ll say that this track is made of a conductive material. It could be a wire.

We can see that as it is there’s no way for current to flow along this track because it’s not a closed loop. But what if we take a straight wire and we lay it across the track like this? In this case, thanks to this wire across the track, we now do have a closed loop. It’s right here that current could flow. But of course, in order for current to flow, we need something to push it along, some electromotive force. Okay, let’s think creatively here.

Electromagnetic induction tells us that a change in the total magnetic field through a conducting loop induces a current. We don’t have here a changing magnetic field. The magnetic field in this case is constant. But we could still change the overall magnetic field experienced by this loop. How could we do that? We could do it by changing the area of the loop. And we’ll do that by putting our wire in motion along the track. Think about it. At first, this is the area of the loop that we’re working with. But then as our wire moves along, we’re adding area to our conducting loop.

So whereas before, the total magnetic field passing through our loop was contained within this area, now since our loop is bigger we’re enclosing more total magnetic field. In essence, the magnetic field is changing through our loop. That’s because the loop area is changing. Described in other way, we could say that this magnetic field has a certain strength per unit area. As the area we’re considering grows then, we’re adding more and more magnetic field strength together for the total field strength. That means the total field strength is changing as area grows.

What all this means is that if we really did have this uniform magnetic field — this conducting track and the wire across it in motion along the track — then as the wire moved, electrical current would actually be induced around this closed loop. And here’s something interesting: the faster that our wire moved along, the more current would be induced in the loop. What we’re seeing overall is that there are two important components to inducing current in a loop of wire. One is the magnetic field going through the loop and the other is the area of the loop. What we’ve seen is that if either one of these two things is changing, that’s enough to induce a current in the loop.

Like we said, it’s a change in the total magnetic field through a conducting loop that induces a current. And it doesn’t matter how that change occurs whether by altering the field or altering the loop area. Now, let’s get a bit of practice with electromagnetic induction through an example.

The diagram shows a permanent magnet being moved through a loop of copper wire. This motion induces an electric current of 0.5 amperes in the wire. If the magnet is moved through the loop at half the speed, what will the current in the loop be? If the permanent magnet is changed for one that is twice as strong and moves through the loop at the original speed, what will the current in the loop be?

Alright, looking over our diagram, we see our loop of copper wire, a conducting material, and the permanent magnet which is moving through it. We’re told that when this happens, when the wire moves through the loop, it induces a current of 0.5 amperes in the wire. This motion of the magnet moving through the loop occurs at some speed. We can call it 𝑆, even though it’s not labelled in our diagram.

Our first question asks if we change nothing about our setup, except the speed with which we move the magnet; we make it half as big as it was before, then what will happen to the current induced in the loop? To start figuring this out, it will be helpful to draw in the magnetic field lines that show the magnetic field created by this magnet. That field and the field lines representing it look something like this. So initially, we move this magnet and its magnetic field through the loop at the speed we’re calling 𝑆.

That means that the total magnetic field through this loop is changing while the magnet moves. And the rate of that change — the speed with which it occurs—has to do with the speed 𝑆. The higher 𝑆 is, the faster the magnet is moving and therefore the faster the magnetic field through the loop is changing. And this change is the mechanism that induces current in the wire. The rate at which that change occurs directly corresponds with the amount of current induced. In other words, the faster the magnetic field through the loop is changing, the more current will be induced in the loop.

That bit is important because we’re told that the modification in this first question is that we no longer move the magnet with our speed 𝑆. The original speed will be moving at half that speed. Since we’re moving the magnet relatively more slowly, that means the magnetic field experienced by the loop will change more slowly. When that rate of change of magnetic field through the loop goes down, so will be induced current.

We don’t know exactly what the current will be when we move our magnet at half the original speed. But we just know that it will be less than the original amount of 0.5 amperes. We’ll write that down as our answer. And the explanation for it like we saw is that the rate of change of the magnetic field through our conducting loop is decreasing relative to what it was originally. Less change means less induced current, which means that whatever the current is will be less than 0.5 amperes.

In part two of our question, we asked if the permanent magnet is changed out for one that’s twice as strong, but moves through the loop at the original speed — what we’re calling 𝑆 — what will the current in the loop be. If we were to double the strength of this magnet and therefore the strength of its magnetic field, while keeping the motion of the magnet the same, then the question is what effect will that have on the rate of change of the magnetic field through this loop.

With the field of the magnet being stronger overall, that means we could expect the change in magnetic field strength from moving from one pole of the magnet to the other to be greater than it was before. That means if we pass this magnet entirely through the loop, the change in magnetic field experienced by the loop would increase. That increase will lead to an increase in induced electric current.

Just like before, we can’t say exactly what the current will be in this modified case. But we do expect that it will be greater than what it was before, greater than 0.5 amperes. And we write that down as our answer because we’ve seen that the rate at which the magnetic field through the loop changes is increased in this case. And we expect that increase to increase the current induced.

Let’s take a moment now to summarise what we learnt about electromagnetic induction.

In this lesson, we saw what this big long term electromagnetic induction means. Electromagnetic induction occurs when a changing magnetic field through a conducting loop creates or induces current in the loop. We saw there are different ways this can happen. One is by taking a permanent magnet and moving it through a stationary loop of wire. Another way is to set up a constant magnetic field and then set up a conducting loop whose area changes over time. In both of these scenarios, we saw that overall there is a change in the magnetic field through the area of the loop and therefore an induced current in it.

Additionally, we saw that the greater the rate of change of total magnetic field strength through a loop, the more current is induced. And we saw this worked the opposite way as well. The smaller that rate of change, the less current is induced. These are the basic ideas behind electromagnetic induction, a phenomenon so useful and so widespread we see it all over in our everyday life.

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