Student handout: Number of Paths
Student discuss how many paths can be found on a map of the vector fields \(\vec{F}\) for which the integral \(\int \vec{F}\cdot d\vec{r}\) is positive, negative, or zero. \(\vec{F}\) is conservative. They do a similar activity for the vector field \(\vec{G}\) which is not conservative.
- group Small Group Activity 30 min. whiteboards/markers/erasers, vector maps (attachment provided), plastic sleeves, plastic graph models (Surfaces): Quadrupole z=0, a handout for each student Student handout (PDF)
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E&M Conservative Fields Surfaces
What students learn
- Various differences between conservative and non-conservative fields
- Line integrals on conservative fields are path independent.
- Conservative fields are gradients of a scalar potential that can be represented as a surface; non-conservative fields cannot.
Number of Paths: For each of the fields, mark two different points \(A\) and \(B\). Can you identify paths where the vector line integral has the indicated value (greater than, equal to, or less than zero)? In the table, enter the number of paths you can find for each condition (max 2 paths).
Match a Surface: One of the vector fields corresponds to (part of) your surface. Where does it match, and how do you know?
Extend to a New Surface: Could the other vector fields correspond to a surface? Explain why or why not.
- Author Information
- Liz Gire, Aaron Wangberg, Robyn Wangberg, and the Surfaces team
- Keywords
- E&M Conservative Fields Surfaces
- Learning Outcomes
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