Embedded Files
Amperian loops offer a very concrete opportunity for students even in a non-calculus introductory physics class to explore uses for Ampere's Law in the study of electrical currents "from a distance".
For example, the "magnetic mystery" empirical-observation-exercise illustration at right shows a 6-segment Amperian-loop (dashed in green, with mid-segment measurement arrows) for help in analysis of the vertical electric-currents through an "inaccessible region", which looks like a black square in this top-down view.
The black-arrow "streamlines" show this illustration's magnetic field directions, while the field-amplitude (as also shown for individual points by the green-arrow lengths) is indicated by the local color on a scale of reddish (low) to bluish (high).
By comparison, we make available below a file for use with Mathematica's free notebook player, which allows students to quantitatively investigate the current(s) through a similarly "impenetrable square-pipe" e.g. between two floors in a building, via measurements of the (horizontal) magnetic field components perpendicular to that pipe.
Can your students form a Riemann sum to accurately estimate the net current through the pipe? Can they further gain insight into the possible existence of more than one current at different locations within the square?
* Mathematica notebook player nbp file.
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