You are here: start » courses » order20 » vforder20 » vfconservative

Table of Contents

# Conservative Fields

## Prerequisites

Students should be able to:

- Find $d\vec{r}$ for a straight or curved path.
- Evaluate the dot product between two vectors qualitatively.
- Read vector field maps.
- Use chop-multiply-add ideas to construct an integral.
- Estimate integrals by approximation.

Reading: GVC § Independence of Path–Finding potential Functions

## In-class Content

- Counting Paths (SGA - 30 min)
- Lecture - 20 min
- What is the difference between the line integral and the flux integral (given that both use the dot product)?
- What does it mean for a field to be conservative?
- Path independent
- Corresponds to a surface (scalar field) that it is the gradient of
*Is curl free***Note:**Curl is needed for 3 different ideas in this class: Conservative Work, Going from $\vec A$ to $\vec B$, and getting from $\vec B$ to $\vec J$.

- QUIZ
- Lecture - 10 min

## Optional In-class Content

- Murder Mystery Method (SGA - 50 min) (alternatively a homework problem - see below)
- Conservative Fields (lecture) (
*Math 3.5: Independence of Path*,*Math 3.6: Conservative Vector Fields*,*Math 3.7: Finding Potential Functions*) - Equivalent Statements (lecture)

## Homework for Static Fields

- (PathIndependence)
*Students explicitly compute the work required to bring a charge from infinity using two different paths. Include part (e) as an additional path that cannot be solved by integration. (You must invoke path-independence of conservative fields.)* - (MurderMystery)
*This question is adapted from the in-class activity*