Static Fields
Students predict from graphs of simple 2d vector fields whether the curl is positive, negative, or zero in various regions of the domain using the definition of the curl of a vector field at a point as the maximum circulation per unit area through an infinitesimal box surrounding that point. Optionally, students can use computer algebra to verify their predictions.

group Small Group Activity
schedule
30 min.
build
 Dryerasable plastic sleeves such as Cline CLI40620.
 Copies of vector fields for the plastic sleeves.
 (Optional) Computers with Mathematica
 (Optional) The Mathematical notebook: How do we reference this??
description Student handout (PDF)
What students learn
 A component of the curl of a vector field (at a point) is the circulation per unit area around an infinitesimal loop.
 How to predict the sign and relative magnitude of the curl from graphs of a vector field.
 (Optional) How to calculate the curl of a vector field using computer algebra.
For each of the vector fields below, decide whether the \(z\)component of the curl is postive, negative, or zero in each quadrant. Be prepared to defend your answers.
 Author Information
 Corinne Manogue
 Keywords
 Learning Outcomes
