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Comment from S. Pollock (CU Boulder, visiting OSU and teaching Paradigm “Vector Fields), Nov 2009: (Lecture 11) Only had about 10 minutes left in class to get this started, but they jumped in and made excellent progress. Little guidance was needed, they were much better/faster than in the similar Gauss' law activity. But, they didn't finish - so in the next lecture, I gave them another 20 minutes (30 total), and all groups sketched accurate graphs. What slowed them down in the end was me, I insisted that the groups articulate their “symmetry arguments” carefully, and they discovered that, for instance, the reason that B=0 in the interior is not “trivial” or “obvious” (just because a line integral of B vanishes doesn't mean that B vanishes). Students struggled when the reasoning was NOT symmetry (e.g, why is there no z-component of the B field inside this hollow wire? I believe the argument requires going back to Biot-Savart, it doesn't come in any obvious direct way from Ampere's law) The lack of a radial component can be argued from symmetry (with some care, and an invocation of Biot-Savart: when you reverse a current, you must reverse its B-field), or from “divergence of B=0”, and I tried to get them to make both arguments.

In the end, we discussed commonalities and differences of their plots, continuity of B, radial dependence, the “1/r” from all wires… Then I asked them to consider the limit that a→b, but keeping I fixed, and they sketched the resulting B field. (This was a lead-in to discussion of discontinuities in B caused by current sheets) They were fine with the sketch of B(r), but could not generate the mathematical formula for $\Vec J = K \delta(r-b) \hat z$ without help from me.