# Day 52: Electric Potential Surfaces

Today, AP Physics 2 explored the resulting visual from yesterday’s mapping electric potential lab. We focused on visualizing the electric potential surface and continued to make an extended analogy between electric potential surfaces and equipotential lines and topographic maps and contour lines. Finally, we connected the magnitude of the electric field to the “steepness” (really gradient) of the electric potential surface.

I shared how an elevation plot of the electric potential surface can help visualize the electric potential and electric field. I shared xkcd’s Gravity Wells poster as an example of an elevation plot for gravitational potential.

The 3D electric potential plot of the conducting sheet with the closed conducting surface in the middle turned out fantastic. I nicely demonstrated that the electric potential within the closed conducting surface is constant and, therefore, the electric field is zero.

##electrostatics ##representations

## 3 thoughts on “Day 52: Electric Potential Surfaces”

1. Andy "SuperFly" Rundquist says:

That’s so cool about the closed conductor in the center! I have mixed feelings about this lab because the math is not the same as if you have free standing charges in the same shape (ie, the limit to the 2d page changes the math) but I do like how it helps develop intuition about potential, gradients, etc.

When I work with students on these ideas, I’ve noticed that they can follow along in a conversation pretty well as long as I don’t switch representations. In other words, if I’m talking about contour lines, they do great. Or if I talk about gradients, they do great. But if I switch back and forth talking about contour lines being close means high gradient, I lose some of them. It’s the mixing of models/representations where they struggle. Do you see the same? #NaBloCoMo

1. Andy, would you elaborate or point me towards a resource that explains what you mean by he limit to the 2D page changing the math compare to free-standing charges? I don’t think I appreciate how this lab may lead students astray…

Some students do struggle when switching between representations. Until the last couple of years, I didn’t have a lab that produced a clear potential surface plot that provide that particular representation. This additional representation, more than any other, seems to help students connect potential and field.

This year, students are discussing conceptual questions in class where I ask them to justify their answer using specific representations (mathematical model, conservation of energy, potential surface plot). While they are still struggling, many have a stronger understanding of the concept of field and potential. Regardless, this continues to be the concepts that students find most difficult in this course.

1. Andy "SuperFly" Rundquist says:

Sorry, just noticed your question (I didn’t get an email notification, weird). I was looking around for my old calculations but couldn’t find them. As I recall, assuming the paper acts as a 2D resistor is different than the 3D potential function around a charged particle