Navigate back to the activity.

Comment from S. Pollock (CU Boulder, visiting OSU and teaching Paradigm “Vector Fields), Nov 2009:

We started this activity immediately following the analogous Electrical discontinuity activity. I had  10 minutes left in class to get this started, and they made much better progress this time than on the previous (E) activity. The continuity stories were nicely explained in the last minute of class by several students, only the discontinuous story needs a little more fleshing out, but they had a pretty good idea of how to proceed and what the outcome was. What was missing here was any real discussion of the “choice of coordinate system” we are implicitly making, the naming (“parallel-perp”) was confusing to people, and needs a little more discussion tomorrow.

I started the next class by setting up the problem once more, again labeling the various components of B (this time clarifying the coordinate system), and I walked them through the “Gaussian box” story of why B_perp is continuous as you move across a current sheet. I then suggested they work in pairs (not groups) and decide which of the two “parallel” components was discontinuous, and find the formula for that discontinuity in terms of K. This took them 25 more minutes, and almost nobody was completely done. So I had *thought* that they were in good shape, but this is an abstract and challenging activity, and many issues arose that I hadn't seen. For instance, people wanted to use another “Gaussian box” to talk about the parallel/parallel component, by making the box shrink in such a way that the wall “poked” by the current stayed larger than the others. (So, they didn't realize that this was teaching about continuity parallel to the surface, not “above-below”, which was our task). Of those groups that were working with Amperian loops, most were not able to reconstruct the logic of “choose one side of the loop is negligibly small compared to the other, even though BOTH are infinitesimal”. In the end, students did manage to explain some of the story, and I fleshed it out with their help collectively, as well as talking them through Griffiths' “coordinate free” representation (e.g. the discontinuity in $\Vec E$ is $(\sigma/\epsilon_0) \hat n$. Asked them to come up with the harder B version ($\Vec K \times\hat n$) , one student did so…

In the end, this pair of activities is demanding, and needs a fair amount of time, broken up into pieces as you start to guide them. For students, the initial task is ambiguous, and I feel that even having gone through both activities, many of the subtleties of naming, coordinate choice, box or loop choice, size of box/loop sides, and the ultimate physical significance, are probably not completely settled by this activity.