Student handout: Vector Integrals (Contour Map)
Students explore path integrals using a vector field map and thinking about integration as chop-multiply-add.
- group Small Group Activity 30 min. Dry-erase markers & erasers, Whiteboard for each group, Student handout for each student, Vector field with path Student handout (PDF)
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E&M Path integrals
What students learn
- Recall the relationship between the sign of the dot product and the orientation of the vectors.
- Use graphical methods to estimate the value of a vector line integral.
- Lay the groundwork for thinking about conservative and non-conservative vector fields.
The Sign of Work: For the force vector shown above, draw three paths such that the work done by \(\vec{F}\) is positive, zero, and negative for small displacements along each path.
Estimate Vector Line Integral: For each segment of the path on the vector field \(\vec{F}\) shown below, estimate the value of the integral:
\[ \int_{\textrm{path}} \vec{F} \cdot d\vec{r} \]
where the side of each square is 1 cm and the length of the longest arrow is 10 units (appropriate for the field \(\vec{F})\).
- Keywords
- E&M Path integrals
- Learning Outcomes
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