Table of Contents
Unit: Potentials from Discrete Sources
Potentials
- Reading: GVC § Idealizations and Symmetries
- Reading: GEM § ix-xv
- Introduction
- Electric Potential (SWBQ: 10 min)
- Fields concept (Lecture: ?? min)
Superposition
This section can follow “The Distance Between Two Points”
- Superposition (Lecture: ?? min)
- Visualizing Electrostatic Potentials (Maple/Mathematica: 20 min)
The Distance Between Two Points
- Reading: GEM § 1.1.1-1.1.2, 1.1.4
- Dot product review (SWBQ: 15 min)
- Magnitudes of vectors (Lecture: 5 min)
- The Distance Between Two Points: Star Trek (Kinesthetic Activity: 20-30 min)
Two Charges (without Power Series)
- Reading: GVC § Dipoles–More Dipoles
Unit: Power Series Approximations
Power Series Basics
- Reading: GVC § Power Series–Properties of Power Series
- Power Series (Lecture: 15 min)
- Approximating Functions with a Power Series (Maple/Mathematica) 30 min
- Properties of Power Series (Lecture: 15 min)
Two Charges with Power Series
- Reading: GVC § Dipoles–More Dipoles
Unit: Continuous Charge Distributions
dr(vector)
- Reading: GEM § 1.4
- Curvilinear Coordinates (lecture)
- Scalar Line Integral (lecture)
Integrating Charge Densities
- Reading: GEM § 1.1.2, 1.1.4, 1.3.1, 2.1.4
- Acting Out Charge Densities (kinesthetic)
- Defining the Cross Product (SWBQ)
- Cross products and scalar triple products (lecture)
Unit: Potentials Due to Continuous Distributions
Calculating Potentials
- Series expansion of potential due to a ring of charge (Extension of previous 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: The Electric Field as a Gradient
Derivatives of Scalar Fields
- Reading: GEM § 1.2.2
- Partial Derivatives (lecture)
- Curvilinear Basis Vectors (kinesthetic)
- Introducing $d\Vec{r}$ (lecture)
- Gradient (lecture)
- Visualizing Gradient (Maple/Mathematica)
- directional derivatives (lecture) (Optional)
Electric Field
- Electric Field - as gradient of the potential (lecture)
Unit: Superposition of Electric Fields
Unit: Electrostatic Energy
This unit could also be effectively placed in several locations in Paradigm: Vector Fields.
- Electrostatic Energy (kinesthetic)
- Vector line integrals (lecture)
