Student handout: Visualization of Curl
Static Fields 2023
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.
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group Small Group Activity
30 min.
- 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??
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
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