Table of Contents

### Unit: Electrostatic Potential of Point Charges

#### Potentials

Prerequisite Ideas Introduction

- GEM § ix-xv

"Write down the electrostatic potential due to a point charge"; write down the gravitational potential due to the earth. *10 min*

Fields concept (Lecture)

- scalar fields are a number at every point in space
- GVC § Scalar Fields

- think of temperature as an example
- electrostatic and gravitational potential are other examples
- GEM § 2.3.2

- we bring in a voltmeter with attached wires and actually point to various points in space stating that it would measure a value at every point in space. We return to this visual aid often, but at some stage (perhaps this first day) it is important to point out two things:
- How a voltmeter actually works and that you have to set the zero of potential somewhere.
- The fact that voltmeters do NOT work the way you theoretically want them to may be an issue, especially for experimentalists. Nevertheless, we have found that STUDENTS often miss the fact that what a voltmeter measures and what you mean by electrostatic potential have anything to do with each other, even in principle.
- GVC § Voltmeters

#### Superposition

* This section can follow “The Distance Between Two Points”*

- Lecture
- electrostatic potentials and gravitational potentials satisfy the superposition principle. It would have been very difficult for us ever to have developed the field of physics if this were not the case.

- GVC § Superposition

- Visualizing Electrostatic Potentials (Maple)
*20 min*

#### The Distance Between Two Points

- Dot product review SWBQ: "Write down something you know about the dot product."
*15 min* - Finding magnitudes of vectors - dot product with itself, then sqrt (lecture)
*5 min*- GVC § Vectors and § Dot products
- GEM § 1.1.1-1.1.2

- GEM § 1.1.4

#### Two Charges (without Power Series)

- If you feel like your students need some physics right away, part 1 of the next activity now. You can then come back and do part 2 of the activity after you have covered power series (or skip it if you are not covering power series). Alternatively, skip this whole activity now and cover it immediately after power series.
- GVC § Dipoles
- GVC § More Dipoles

#### Power Series

- Intro lecture
*15 min*- introduce especially language for coefficients, order of term, etc.
- derive derivative formula for coefficients (most students know this formula, but they don't remember the derivation).

- GVC § Power Series

- Approximating Functions with a Power Series (Maple)
*30 min* - Properties of Power Series (Lecture)
*15 min*- GVC § Common Power Series

#### Two Charges

- Superposition (Cover this section if you have not already done so.)
- GVC § Superposition

- Start Electrostatic Potential Due to Two Point Charges (You may have covered part 1 of this activity earlier.)
- GVC § Dipoles
- GVC § More Dipoles

### Unit: Potential Due to Continuous Distributions

#### dr(vector)

- Curvilinear Coordinates
- Lecture Intro with “overheads” (lecture)
- Discussion of math vs. physics conventions (switch $\theta$ and $\phi$) (lecture)

- GEM § 1.4
- GVC § Curvilinear Coordinates

- Curvilinear Basis Vectors (kinesthetic)
- GVC § Basis Vectors
- GVC § More Basis Vectors

- $d\Vec{r}$ intro lecture
- Draw pictures of $\Vec{r}$ and $\Vec{r}$ + $d\Vec{r}$. Find $d\Vec r$ in rectangular coords
*5 min*

- GVC § The Vector Differential
- GVC § Other Coordinate Systems
- GVC § Coordinate Expressions

- scalar line integral (lecture)
- do an example or two. Use $ds = |d\Vec r|$

- GVC § Scalar Line Integrals

#### Integrating Charge Densities

- Acting Out Charge Densities (kinesthetic)
- GVC § Densities
- GEM § 2.1.4

- cross product (SWBQ)
- GEM § 1.1.2
- GVC § Cross Products

- Cross products and scalar triple products (lecture)
- GEM § 1.1.4
- GVC § Scalar Triple Products

- GVC § Surface Elements
- GEM 1.3.1

- GVC § Scalar Surface Integrals
- GVC § Volume Integrals
- GVC § Total Charge of a Shell
- GVC § Total Charge of a Cube

#### Calculating Potentials

- GVC § A Uniformly Charged Ring

- Series expansion of potential due to a ring (Extension of SGA)
- Potential due to a finite line (lecture)
- Potential due to infinite line (lecture) (This is a longish lecture and a bit more sophisticated than much of the other material. It is an excellent opportunity to do lots of series expansions and review logarithm rules. Alternatively, it can be left out to save time.)

### Unit: Electric Field

#### Derivatives of Scalar Fields

- Partial Derivatives (lecture)
- Gradient (lecture)
- GEM § 1.2.2

- Visualizing Gradient (Maple)
- directional derivatives (lecture)

#### Electric Field

- Electric Field - as gradient of the potential (lecture)

### Unit: Electrostatic Energy

- Electrostatic Energy (kinesthetic)
- Vector line integrals (lecture)