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Visualizing Curl: Instructor's Guide

Main Ideas

Students' Task

Estimated Time: 20 min

Students view several vector fields and calculate their curl in order to get a sense of what a field with a non-zero curl looks like.

This worksheet is designed to be an instructor-led activity. You would need to add appropriate instructions and questions to use this as an independent student activity. The activity can be used quite effectively with the instructor projecting the worksheet at the front of the room if students do not have access to a computer for each small group.

Prerequisite Knowledge

Props/Equipment

Activity: Introduction

We precede this activity with a derivation of the rectangular expression for curl from the definition that (the magnitude of a particular component of) curl is the circulation per unit area around an appropriately chosen planar loop. Our derivation follows the one in “Div, grad, curl and all that”, Schey, 2nd edition, Norton, 1973, p. 74.

This worksheet shows a number of different vector fields. Most vector fields are shown as a cross-section of the field and it is assumed the the vector field is independent of the third (unshown) dimension. Students are asked to use the definition of curl as the circulation per unit area around an infinitesimal loop to predict the direction and relative magnitude of the curl at various points in the vector field. The worksheet then calculates the curl, so students can check their predictions.

Activity: Student Conversations

Activity: Wrap-up

No particular wrap-up is needed.

Extensions

This activity pairs nicely with the Visualizing Divergence activity.

This activity is part of a sequence of activities which address the Geometry of Vector Fields. The following activities are included in this sequence.