Amperian loops

What are key challenges and opportunities when teaching this section?

• The Coulomb equivalent of Ampere's Law, i.e. Biot-Savart, is the most complicated equation that students will encounter since it's application involves vector integration over a cross-product.
• The non-physicality of breaking a current into separate chunks for analysis can be a source of fun, as illustrated for example in the Cleveland Wrecking Yard section of Richard Brautigan's Trout Fishing in America.

A field activity involving Amperian loops 

Here is an empirical observation challenge posed on the take home (open book) part of the physics 2112 evening exam 3 for WS2008.  I asked the students to make their case on a single page, even if they felt the need to attach supporting materials.  There were few complaints about usability, and my impression was that most of the students enjoyed it (some quite a bit).  What are some other ways to test a broader range of problem solving and communication skills in take home components of such assessments?

11.  This is the empirical observation exercise for part 2 (open book).

  Using the Mathematica notebook player (nbp) file here, take some data on the magnetic field perpendicular to a square pipe between two vertical walls*. Using that data show us what you can figure out about the distribution and magnitude of currents running through the pipe.  Supporting materials can be attached.  Use whole sentences and cite your sources.  

* Assume that the axis labels (see the screen capture above) indicate both displacement in meters, and magnetic field arrow components in Tesla. This file runs in Wolfram's free player as well as in Mathematica on UM-StL student computers.

11a.  Describe your method(s) for taking and presenting data here. Clarity is important.

11b.  Tabulate your data here, along with uncertainties if you estimate them.

11c.  Describe what your data tells you about the direction of the net current through the square pipe.  How certain are you as to this conclusion?

11d.  Describe what your data tells you about the magnitude of the net current through the square pipe, and your uncertainty in that value. Assume that the axis labels indicate both displacement in meters, and magnetic field arrow components in Tesla.

11e.  It is possible that the current through the pipe is not a single current.  Describe here, as clearly and originally as possible, how your data might be used to investigate this possibility.  How many currents can you prove are present?  What can you say about the location within the box, as well as the magnitude and direction of all currents?