Unit 2: We've got Potential

Unit 1 ended with drawing electric fields around charges. We reasoned through the rules of drawing them. I almost said "we learned," but we had gone through a lengthy discussion of gravitational fields, so by the time we got to charges, it was easy to come up with the "rules" of drawing field lines.
1. They ALWAYS point in the direction of force arrows.
2. The closer the field lines, the stronger the field.

Now, it's amusing that we came up with rules at all, because in hind-sight we often ignored that second rule in our own quest for representations that made sense to us. Sometime we drew them longer rather than denser, but the first rule did seem to hold for us!

At this point the idea of critical competitors came up- ideas that are similar but also different enough to make you wonder. We had been comparing the gravitational field of the earth to an electric field, and though there are many similarities, the differences began to emerge. And we hearkened back to other ideas on energy and magnets. This was a good review of energy and also a good connection to gravitational energy and electrical energy. We were reaching for this idea of Potential. Not potential energy, but the potential, which turns out to be a rather esoteric idea for gravity but much more useful for electricity. If you divide the mass out of gravitational potential energy, you get potential. Same goes if you divide the charge out of electrical potential energy. You are left with a potential at some point away from a charge. To further introduce this idea we stood on table and chairs to  make a model of a field with potential.

Energy levels! (I'm on the ground floor:)

Those of us on the table had more gravitational potential, etc. We then were able to make a connection between gravitation and electricity by drawing "topo" maps.

Just like a hiking map!

Once this connection was made, we had a way to visualize potential. We were ready for what I consider a watershed lab that served not only to help shape our ideas of potential, field and forces, but for the rest of the course I do believe it influenced how we thought about electric issues. Really, this lab was referred to for the rest of our time together.

It really was quite simple in execution. There were two bars wrapped in aluminum foil in a lasagna pyrex pan partially filled with water.  They were connected to a power source so that they had opposite net charge on them. We used the probes from an electric field detector (a voltmeter) to plot how the electric potential changed between them. We drew it on some quad ruled paper and we had a map of the electric potential around two lines of charge. Then we used Plot.ly to see a three dimensional representation of the field between the two lines of charge.

plot.ly'd

That was pretty cool! And we drew it on our whiteboards!

It's like a giant slide.

Colors help.

another depiction

I've just realized that I've been using the pronoun "we" in describing activities. Is it because I felt like it was always a group project? That we were all thinking together? I don't think I felt that way all the time. I personally am more of a loner. I also take time forming a big picture- making the connections I need to understand the big ideas. I'm not much for getting stuck in details, and I got impatient sometimes when folks hashed over what I considered trivial matters,which may or may not have been. I think most folks were struggling with their desire to tell. We changed groups often, so we did get to work with lots of different people. I guess what I'm trying to say is that I learned a lot about myself and other teachers, and a lot about how students may feel when they are doing these activities and interacting with each other. I do have a lot of food for thought about how I want to proceed with Modeling. Don gave us a lead on a great book called Mindset which I ordered, and in talking with others who have read it, it sounds like it could change my teaching. It's going to be my next read.

Back in the world of Physics, our lab led to much exploration of this idea of potential and how to imagine it, and how to depict it. I have many drawings in my notebook, and I even have a little cry-face drawn with the caption "wkst 3 is super confusing: using grav. equipotential to explain energy and potential."I must have hit some cognitive dissonance. Again.

But we soldiered on, through mini pep-talks about students having to get used to teachers not giving them an answer...whew that's a tough one. Especially for my AP students! I will be strong. I will let things hang in the air. I will let there be awkward silence. I will give pep talks about how important it is to hit upon ideas in your own context rather than being told by someone in their context.

There was a long discussion about the strength of the filed between two lines of charges connected to a potential difference (battery or other device) Laura, with the patience of a saint, took us through a quagmire of discussion about inverse square laws and how they may or may not apply to this situation. Turns out it didn't. Turns out that the electric filed remains constant no matter how far away the plates are from each other. Do they really? Yes they do. It was difficult to swallow until Laura played with geometry and math and we walked through the logic of it. Tough day!

Real learning: a permanent change in cognitive structures and procedures.

Next came the Genecon lab- fun city!

Geneconning

We explored energy transfer from the capacitor to the genecon by counting how many turns the handle made when connected to the "energized" capacitor. With this lab we were able to make some connections between energy and potential difference. It appeared to be a squared relationship, which our data supported. So we continued exploration with capacitors on the Phet lab. We learned that the slope of our graphs told us about the characteristics of the capacitor, and we refined our relationship between energy, potential difference and charge.

Discussing our board!

While we were doing these ongoing explorations, we constantly edited and morphed our representations so that they were understandable. I was often reminded of how much of a stickler I have been as a teacher about using correct units and labeling graphs, and having a consistent representation, regardless of any understanding about these tools. I am definitely of a different mind now! Work towards the understanding, and the details will follow.

I am going to teach for understanding, not for "the right answers!" We had an interesting discussion about how we were in an emotional and educational quandary; trying to understand with new and unknown representations while engaging this new material, even if it isn't totally new to us. Plus we all have "learning baggage" that we bring to the circle. I was very aware of my learning baggage, and my interaction baggage! So I can imagine how my students must feel. Discussions have been very eye and heart opening!

Meanwhile, the whiteboards are getting better- I think Don's example of well-drawn lab set ups and his perfect circles have inspires us to do better on our own whiteboards!

Capacitors

and more...

Capacitors are energy storing devices. I wrote that in my notes. But how much fun we had discharging them and finding out what happened to charge flow. We learned how the area and the distance between the plates changed the energy output. We did this with real capacitors, and also with a simulation which really helped see what was going on my manipulating the factors like area and separation. We found that capacitance was directly related to Area and inversely related to distance, as one might expect. But it was fun to see it.

Phet simulation

Cap happy.

Next chapter: on to Circuits.