First, we discussed a question with which the student had been struggling about the meaning of the negative in Newton's gravitational law. We graphically addressed the basis of negative forces being attractive and how that would show up in the answer choices. Having discussed that, me moved on to our main topic of electrostatics. We began by discussing charge, its units, and current flow. Next, we analyzed Coulomb's law, comparing it to the universal gravitation law. We discussed the main metaphor of electrostatics. We defined electric fields and discussed their diagrams and summary points. We used an example problem in electrostatics to show how symmetry and logic can be used to solve them. We discussed electric dipoles, inducible dipoles (dielectrics), and how they react in external electric fields. We applied our perpendicular/parallel analysis to how electric fields modify the motion of charged particles, which started a discussion of what determines whether curved motion is parabolic or circular. We discussed electrostatic potential energy, comparing it to gravitational. We then moved on to voltage. We discussed how membrane potential is generated and analyzed the energetics of secondary active symporters, linking work and delta-g and bioenergetics. We then ran a few problems connecting voltage to energetics.
This was a big day for the student. She has been doing her assignments, going out of her way to do math review, and my mini-assignments to beef up her estimation ability, and it showed. She deals with math that previously stymied her quickly and with assurance. Her persistence in learning energetics in the way I presented allowed her to truly integrate the lessons on electrostatic potential energy and how that leads into a solid understanding of voltage. She is still a little cavalier with units, but I will continue to focus on that, especially with regards to how it helps with quantitative problems in energetics. I emphasized how important the progress she had made today was since she had grasped how to decide when a problem described parabolic vs. circular motion, and how fundamental electrostatics is to the understanding of biological membrane potentials, and will form the basis of bonds and protein folding. I mentioned briefly how many topics could be explained clearly and precisely now that she truly understood forces, energy, and voltage."