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## Finding Potentials from Fields - The Murder Mystery Method: Instructor's Guide

### Main Ideas

- Relationship between electric field and electrostatic potential
- Determining whether a field is conservative

### Students' Task

*Estimated Time: 50 min*

Students are given several electric field functions. Students are then asked to find the potential function for each electric field. Finally, students are asked to determine if the electric field is physically reproducible with any kind of charge distribution.

### Prerequisite Knowledge

- $\vec{E}=-\vec{\nabla} V$

### Props/Equipment

- Tabletop Whiteboard with markers
- A handout for each student

### Activity: Introduction

Each group member will be asked to “interrogate” (read:integrate) each “witness” (read:component of electric field).

If a one component of the electric field is dependent on more than one spacial variable, the students should expect to see that dependence show up in the potential equation. Given $ V = - \int \Vec E \cdot d\Vec r$

### Activity: Student Conversations

- A conservative field in rectangular coordinates that has a potential with multiple terms
- This example is designed to emphasize the necessity of corroborating witness accounts with each other since each was looking in a different direction.

- A non-conservative field in rectangular coordinates
- The non-conservative example follows the conservative example so that students are already familiar with the process and do not simply assume they have done the differentiation incorrectly.

- The field of a point charge in cylindrical coordinates (no $\phi$ component)
- This example allows students to apply the process to cylindrical coordinates

- Same field as #2, but in cylindrical coordinates
- This example requires students to deal with the $\phi$ coordinate and allows for a comparison between the second and fourth problem.