A month ago or so I took to the net to ask for help modeling the electric field and potential. Many people came to the rescue. I’d like to especially thank Frank Noschesche (@fnoschese) and Dany Doucette (@danny_doucette) for their help and to apologise for the late reply: I got commissioned a new book that I had to finish in three weeks, so I barely did anything but write for that time.

Frank suggested using Scotch tape as a model for the electric charge. Unfortunately, Germany’s equivalent to it (“Tesa” tape, they call it) does not seem to work as well. The tape kept curling on itself and its electric repulsion and attraction were not enough to be noticeable. I had to get creative.

Finally I ended up using two methods suggested in Greg Jacobs’s blog: oil and seeds to observe the electric field lines, as well as water and electrodes for the potential. I only recently got into modeling, so my students already had some knowledge of the electric field and potential, though they really seem to struggle to understand both.

Without further ado, here’s what I ended up doing.

**The metal sphere**

I started the lesson using a Vernier metallic sphere and a generator. I attached some strings to the sphere and I connected it to a potential of around 3,000 V. I then asked students to model the situation in their mini-whiteboards. Most of them decided that the strings were getting charged and were thus repelled by the sphere. They were pointing perpendicularly because that was the way the electric field decreased the fastest. I asked them to depict that field and they did.

**The oil and seed experiment**

For the next part, I first asked them to guess what the field lines would look like between two equal and opposite spherical charges. They drew their guess in their mini-whiteboards. Then I proceeded to show them the set-up in the picture below. In the petri dish there was vegetable oil; then I had two styrofoam cups with a hard wire through them. Each wire was connected to one end of my voltage supply. In the oil there were seeds (lettuce seeds to the trick; in general, anything elongated enough will work) which aligned with the electric field.

I asked students to show me a model of the seeds that would explain why they pointed in the direction of the electric field. To my surprise, most of them deduced that there had to be an induced dipole in the seeds.

Then I asked students to predict what would happen if I replaced the spherical charges by straight wires (mimicking a capacitor). Most of them came up with the right idea, some with bending at the edges and some without it. I bent my wires to achieve the desired shapes and turned on the voltage again. Then we spent some time discussing why the lines don’t bend in the middle but do at the edges. They came up with the explanation that, at the edges, there is no positive charge to the sides to “balance” the force.

**The water experiment**

For the next part, I used a transparent plastic box with around 2 cm. of water in it. On each end there was a flat wire connected to each end of my voltage source, again mimicking the plates in a capacitor. The voltage source and the voltmeter were both set to AC, to around 25 V. The water is needed so that it will conduct electricity, making it possible to observe the potential changes in it. I then gave my students voltmeters and asked them to keep the ground on one end. They then had to move the other end to find regions of equal potential. They quickly concluded that the regions of equal potential were parallel to the plates and that the potential only changed perpendicularly to these.

I then asked the students to draw the lines of equal potential in millimeter paper and to compare them to the electric field lines they found before. They quickly concluded they were perpendicular.

Then came the fun part of the experiment: students were asked to place their fingers in the water, next to each other. They were then asked to separate the fingers parallel to the plates. Did they feel anything? (No). What can we say about the current between your fingers? (It’s zero) And the field? (Zero too.)

Then I asked them to separate their fingers perpendicularly to the plates. Students started feeling a tingling that got stronger the more they separated them. I asked them: if you had to associate a physical quantity to the tingling, what would it be? (The field). So what can we say about the relationship between the potential and the tingling? (More difference → more tingling). So what can we conclude then about the relationship between the potential and the field? (More potential *difference* → more field).

**Wrapping up**

The rest of the lesson was more conventional. I tried to get them to come up with some sort of visual metaphor they could use to picture the potential and the field: they came up with the idea of height as the potential, whereas the push down the slope would be the field. In the case of a negative particle, you have a hole. Then I did a quick *corner quiz* (I use corners to quickly ask multiple choice questions to the class and get an instant feel for the answer) the aim of which was to get students to realise the field has to be proportional to the *rate of change* of the potential, which lead us to the mathematical relationship between field and potential.

I ended up by using the PHET charges and fields simulation. The idea was the following: first, I asked students to predict what the equipotential lines would look like for a given situation. Then, I asked them to use those lines to generate the field lines. Finally, we would check with the simulation. The idea is that by doing this prediction-correction cycle they would start to get a feel for what potential and electric field lines look like.

**What I would change**

Even though this lesson worked well (much better than anything I’ve previously done) there are several aspects I’d like to improve on in the future.

- Less guidance: I felt that I guided my students too much in their inquiry. In the future, I would like to start this kinds of activities earlier to get my students to be much more independent in how they investigate, with me only presenting the situation and letting them decide what to change and how to model it.
- More quantitative treatment: the models in this lesson were qualitative in nature. I would have liked things to be more quantitative, but I am unsure of how to do this with something as hard to measure and manipulate as the electric field. Would it be possible to get students to discover Coulomb’s law? If so, how? Any ideas would be welcome.
- Focusing on less: next year I will introduce one concept at a time, making students play with it enough so that they get a better grasp.
- Doing this without previous knowledge: I’d like to introduce the ideas of field and potential from scratch, getting students to come up with them through experiment. This is my goal for my next batch of students and I should be doing this some time this year. I am not sure how yet, so suggestions will be appreciated.