Question Video: Determining Whether a Potential Difference Is Induced in a Wire in a Uniform Magnetic Field Physics

Video Transcript

Parts (a), (b), (c), and (d) in the diagram show a straight piece of copper wire moving through a magnetic field. The magnetic field is uniform, and in each part the wire is moving in a different direction through the magnetic field. Which of (a), (b), (c), and (d) show a motion of the wire that would lead to an electric potential difference being induced in it?

To answer this question, we need to work out how the direction of the copper wire’s motion will affect the magnitude of the potential difference that’s induced in the wire. Let’s start by clearing some room on screen and thinking about how a potential difference can be induced across the wire.

Imagine we have a straight piece of copper wire. We can look at the wire from a different angle, like this, so that the length of the wire is pointing into the screen. Currently, there is no potential difference between the two ends of the wire. The wire is not connected to a circuit, and there’s nothing else near the wire that could create a potential difference.

Now, let’s think about what would happen if the wire was then placed into a uniform magnetic field. When the wire is stationary in the magnetic field, there’s still no potential difference between its two ends. But if the wire then started to move through the magnetic field, it is possible that a potential difference could be created across the wire. Imagine that the wire begins to move in this direction. We can see that as the wire moves, it will cross these magnetic field lines. When the wire moves in such a way that it crosses magnetic field lines, a potential difference will be induced across it. This is electromagnetic induction.

This question is asking us to work out which parts of the diagram show the wire moving in such a way that a potential difference will be induced across the wire. To do this, we simply need to recognize which of the parts show the wire moving so that it will cross magnetic field lines. Let’s take a closer look then.

In part (a), the wire is moving diagonally, up and to the right. If we extend the arrow to show the path that the wire will take, we see that the wire will cross several of the magnetic field lines. So we know that a potential difference will be induced across the wire.

Next, in part (b), the wire is moving antiparallel to the magnetic field lines, following this path. This means that the wire will never cross any of the field lines, and therefore no potential difference will be induced across the wire.

Similarly, part (c) shows the wire moving parallel to the field lines, along this path. Here, like we saw with part (b), the wire can never actually cross the field lines. So no potential difference will be induced.

Finally, part (d) shows the wire moving perpendicular to the magnetic field lines, following this path. This means that as the wire moves, it will cross magnetic field lines at a great rate. And because the wire is crossing the field lines, a potential difference will be induced across the wire.

Thus, we’ve seen that only parts (a) and (d) show the wire moving in such a way that it will cross magnetic field lines. So we know that for (a) and (d), a potential difference will be induced across the wire. In parts (b) and (c), the wire never crosses any field lines. So no potential difference would be induced. Therefore, parts (a) and (d) show a motion of the wire that would lead to an electric potential difference being induced in it.