I had a great moment in my calculus-based introductory E&M course today. I had spent the last few minutes explaining with great enthusiasm and great clarity (according to all the nodding I was seeing) how the electric field due to an infinite sheet of charge does not depend on the distance from the sheet of charge. I pointed out the progression of the 1/r2 dependence for the point charge, the 1/r1 dependence for an infinite line of charge, and the 1/r0 = constant dependence for an infinite sheet of charge. I argued that you could easily see that it was constant because the electric field lines have a constant density (neither converge nor diverge) no matter how far you get away from the sheet of charge.
Then I asked them the following clicker question…
…and 2/3rds of them incorrectly chose option D which says that the electric field due to this sheet of charge changes with distance from the sheet.
And I was delighted! This created a great moment to generate some more buy-in for the methods I use in the course.
I will roughly paraphrase what I said to them. I’m pretty certain it was more enthusiastic and less coherent when I was saying it in class:
Before this clicker question, you all sat there nodding in agreement with me as I explained this idea to you. And then when I turned around and asked you to apply the concept on a fairly straight-forward question, 2/3rds of you did not answer the question correctly. This right here highlights exactly why I run this course in such an interactive way. Until you have had to wrestle with the concept and make the understanding your own, you can easily fool yourself into thinking that you have learned the idea.
Today was a great day.