I'm not going to bury the lede. The blog post below describes my experience programming; a later post will explain how I'm going to use the program next year. The program shows the flux as brighter or dimmer shades of red (flux out of the surface) and blue (flux into the surface). Play with it. Zoom in and out. Rotate the sphere. Edit and break the program. (I tried to write a lot in the comments, so hopefully you can change a number or two and see what happens.) Give me suggestions. (My students like running it in fullscreen. Find that in the menu at the upper left of the screen.) Here you go:
Finding electric potential seems easy. Once we understand that we can add the contributions to the change in electric potential energy for our test charge like numbers since voltage is a scalar, it became easier to see. But electric field is much more difficult. How do we add all the contributions to the electric field. We had to spend some time with that one.
We also got into a long discussion about how the electric field from a long plate of charge could end up being constant, no matter how far away you were from the plate. That was a difficult one, and I don't feel my answer was the best. I have a great answer, but it uses calculus. In fact, I have more than one good answer that uses calculus.
We finished the day talking about electrostatics and conductors, which sounds boring until you google things like Faraday cage video or lightning scars on body.
We went over our results from lab. Everyone seemed to notice that the equipotential lines between parallel plates were parallel and straight in the middle but curved towards the ends. Fringing was easy to teach because of that. We then talked about the power of voltage. Energy is easier than forces, and one student, who used forces and acceleration to solve a problem when energy made it so easy, made the point clear.
We finished our equipotential line drawings. We also talked about how to calculate electric potential energy and electric potential.
Most of the day, though, was spent with various teachers talking to us about the science classes we could take next year.
We should have done this lab yesterday. Today started with a struggle to understand how to draw equipotential lines and how equipotential lines and electric field lines interrelate. (We quickly understood that the unit for electric field strength, newtons per coulomb, were equivalent to volts per meter, but we had no idea why that was important.) It was tough. But, once we got to lab, the equipotential lines made a lot more sense.
We have a good idea of what electric field is. We've drawn a lot of pictures; we've made a mathematical model and applied it to some situations. But we don't have a good picture of electric potential energy. So we started by drawing an analogy to gravitational potential energy. We defined gravitational potential as the amount of gravitational potential energy per kilogram. We got out the contour maps and saw how these contour lines are isolines—lines of equal gravitational potential. We talked about it as a class and then in groups. We're starting to see a connection between these equipotential lines and electric field lines.