Lately I’ve been flirting with the modeling approach to physics and it has done some wonderful things for my lessons. Last week I decided to teach induction this in mind: I got my students to try out moving a magnet through coils with different turns and record their results. This is what they tried out:

- Change the number of coils.
- Change the frequency.
- Change the strength of the magnet (for this, I used a stack of neodymium magnets that work as a “tower” taped to a popsicle stick. Adding them one by one creates a pretty consistent effect.)

After that, it was time to try to figure out what was going on. To my surprise, they were (with some prompting) able to come up with a definition of magnetic flux linkage. The easiest part was deciding that the EMF had to be proportional to the rate of change of the flux linkage.

The following day we worked on Lenz’s law. I gave students the following situation: a magnet falls through a loop of wire. I asked them to consider the energy changes being produced. I had a set of questions in the board which were meant to help them deduce the direction of the current. These were:

- Do the charges in the loop gain energy?
- Is energy conserved in the system?
- Taking into account (1) and (2), where is the energy gained by the charges coming from? Be specific: from which type of energy of which object?
- Therefore, should the magnet:
- Slow down?
- Speed up?

- Therefore, where does the force on the magnet point?
- Who is exerting this force?
- Hence, in what direction does current flow in the wire?

It took a while, but students got there. Then I did a bit of front loading, which I’m not proud of, but I can think of no way of organically going from the process above to Lenz’s law. I basically told the students they could go through the whole thing each time, but that there was a short cut to automatically decide the direction of the current. The reasoning to arrive at that short cut was ultimately also based on energy conservation.

Anyway, I presented Lenz’s law and realized that students struggled with the phrasing. So I came up with a new type of diagram to deal with it. According to my students, it helps quite a bit in dealing with problems. I call these “OO diagrams”, because there are two loops of wire. Here’s what they look like:

The basic idea is this: students consider the system at some point and then at some point immediately after. In the first part, they draw a loop of wire (representing the coil or whatever configuration of wire there actually is) and an arrow representing the magnetic flux. The direction matters, but not its length, since all we’re interested in is the change. They then draw a second diagram with a loop and a second arrow. This arrow should show whether the flux increased or decreased, which can be caused by the magnet getting closer (as in the image) or by the area getting larger, etc. Then they draw a final arrow in diagram two, which represents what the flux created by the coil should be in order to neutralize the change. That will give them the direction of the field created by the coil and therefore the direction of the current, which they can easily find using the right-hand rule.

The problem with this diagram is it doesn’t take into account the 3-d nature of the situation (the coil in the diagram should really be flat, perpendicular to the screen) but I find that students have no trouble imagining that. The beauty of this is it transforms a very abstract formulation into a very simple, tangible task: all you need to do is find the data that will allow you to draw a diagram, then find the little arrow and you’re done! If I compare my current students’ success at this with last years’ batch, I’d say it is much improved.

As always, any suggestions will be welcome. Especially if you know of some way of really getting students to organically come up with Lenz’s law.