Video: Understanding Electromagnetic Induction

The diagram shows a permanent magnet being moved through a loop of copper wire. This motion induces an electric current of 0.5 A 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?

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Video Transcript

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.

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