Student handout: Visualization of Curl

Static Fields
Students predict from graphs of simple 2-d 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
    • Dry-erasable plastic sleeves such as C-line CLI-40620.
    • 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
Learning Outcomes