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## Electrostatic Energy of Discrete Charges: Instructor's Guide

### Main Ideas

### Students' Task

*Estimated Time: 20 minutes*

A group of students are asked to represent point charges. As a calculation demonstration, the instructor calculates the amount of work needed to bring the students in from infinity and assemble them into their seats.

### Prerequisite Knowledge

- Line integrals
- Electric Field/Forces
- Electrostatic Potential

### Props/Equipment

None

### Activity: Introduction

We begin this activity with a reminder that electric fields store energy (remind them of the VEUF square and capacitors from their intro courses).

### Activity: Student Conversations

This activity is really more of a lecture with a kinesthetic components - there are not many conversations among students.

The instructor selects a handful of students to pretend to be “charges”. The charges start at r=infinity (outside the doorway of the classroom), and the instructor will bring them in from infinity and assemble them into the configuration of the students sitting at their seats. Each time a charge/student is brought in, the instructor calculates the work done by doing writing down the integral of the force dotted with dr.

- Students find this activity particularly memorable when the subscripts used in the calculation are the names of the individual students.
- It is nice to have a conversation about how it takes energy to bring like charges together - where does that energy go?
- Students in the middle division do not have much experience or comfort in using summation notation. This is a nice opportunity to remind students about the notation and how to expand the notation into a long sum.
- This is one of the first topics where students see a “double counting” simplification using summation notation. It is worth spending some time explaining how this simplification works.

### Activity: Wrap-up

We conclude this activity with a discussion of how the elecrostatic potential can be used to calculate the energy stored in the field. We follow the standard Griffiths treatment (p. 90 of the 3rd edition of Introduction to Electrodynamics).