Unit: Potentials Due to Discrete Charges

Introduction to the Unit
Learning Outcomes

1 1/9 Mon

IRB intake

Qualtrics Version of Consent Form

Review on your own
(as necessary):
  Basic Calculus
  Exponentials & Logarithms
  Vectors

Review Reading
GSF: Review of Single Variable Differentiation
GSF: Vectors
GSF: Bases
GSF: Unit Vectors
GEM 1.1.1-1.1.2
Taylor 1.2

The Distance Formula

GSF: The Distance Formula
GEM 1.1.2, 1.1.4

Position Vector

GSF: The Position Vector
GEM 1.1.4

2 1/10 Tues

Dot Product

GSF: The Dot Product
GEM 1.1.1

Introduction to the Course

Rules for Differentials

Dimensions

GSF: Dimensions

Electrostatic & Gravitational Potential

GSF: Electrostatic and Gravitational Potentials and Potential Energies
GEM 2.3.4

Visualization of Potentials

GSF: Visualization of Potentials
GSF: Using Technology to Visualize Potentials

Superposition

GSF: Superpositions from Discrete Sources
GSF: Two Point Charges
GEM 2.3.4

3 1/11 Wed

Definition of Power Series
Derive Power Series Coefficients

GMM: Definition of Power Series
GMM: Calculating Power Series Coefficients

Calculating Coefficients of Power Series

GMM: Calculating Power Series Coefficients

Power Series Approximations

GMM: Visualization of Power Series Approximations

Power Series Notation

Guessing Power Series

GMM: Guessing Power Series from Graphs

Power Series Approximations

GMM: Discussion of Approximations Using Power Series
GMM: Using Technology to Explore Power Series Approximations

More Power Series Information

GMM: Common Power Series
GMM: Dimensions in Power Series
GMM: Convergence of Power Series
GMM: Theorems about Power Series

Power Series Sensemaking

4 1/12 Thurs

Potential Due to a Pair of Charges: Limiting Cases

GSF: Power Series for Two Point Charges

Compare Series and Visualization

Unit: Integration in Curvilinear Coordinates

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Integration and Differentiation in Curvilinear Coordinates

5 1/13 Fri

Zapping with d

Prep Review how to find total differentials
Watch some short video:
Rules for Differentials
Product Rule
Chain Rule
and/or Read:
GSF: Leibniz vs. Newton
GSF: Differentials
GSF: Rules for Differentials
GSF: Properties of Differentials
GSF: The Multivariable Differential
GSF: Differentials: Summary

6 1/16 Mon

MLK (No Class)

7 1/17 Tues

Curvilinear Coordinates

GSF: Curvilinear Coordinates
GSF: Change of Coordinates
GEM 1.4

Curvilinear Basis Vectors

GSF: Orthonormal Basis Vectors
GEM 1.4

Representations of Vectors

Vector Differential

GSF: The Vector Differential
GSF: Finding $d\vec{r}$ on Rectangular Paths
GSF: Other Coordinate Systems
GSF: Calculating $d\vec{r}$ in Curvilinear Coordinates

Scalar Line, Surface, Volume Elements

GSF: Scalar Surface Elements
GSF: Triple Integrals in Cylindrical and Spherical Coordinates
GEM 1.3.1, 1.4

8 1/18 Wed

Step Functions

GMM: Step Functions
GEM 1.5.2

Delta Functions

GMM: The Dirac Delta Function
GMM: Properties of the Dirac Delta Function
GMM: Representations of the Dirac Delta Function
GEM 1.5

9 1/19 Thurs

Densities

GSF: Densities
GEM 2.1.4

Total Charge

GSF: Total Charge

Proportional Reasoning

Use What You Know

GSF: Using $d\vec{r}$ on More General Paths
GSF: Use What You Know

Unit: Fields from Continuous Sources

Introduction to the Unit
Learning Outcomes

10 1/20 Fri

Introduction to the Lorentz Force Law

GSF: The Lorentz Force Law
GEM 5.1, 5.3.4
Taylor 2.5

Vector Fields

GVC: Vector Fields for Mathematicians
GSF: Vector Fields for Physicists

Electric Field Due to a Point Charge

GSF: Electric Field of a Point Charge

Superposition for Electric Fields

GSF: Superposition for the Electric Field
GSF: The Geometry of Electric Fields
GEM 2.2.1

Electric Field for Two Point Charges

11 1/23 Mon

Multipole Expansion

Electrostatic Potential in Curvilinear Coordinates

GSF: Potentials from Continuous Charge Distributions
GSF: Potential Due to a Uniformly Charged Ring
GEM 2.3.4

12 1/24 Tues

Electric Fields from Continuous Charge Distributions

GSF: Electric Field from Continuous Charge Distributions
GSF: Electric Field Due to a Uniformly Charged Ring
GEM 2.1

Limiting Cases

Other Continuous Sources

GSF: Potential Due to a Finite Line of Charge
GSF: Potential Due to an Infinite Line of Charge
GEM 2.3.2
GSF: The Electric Field of a Uniform Disk

Unit: $\vec{E}$ as a Gradient

Introduction to the Unit
Learning Outcomes

13 1/25 Wed

Review of Derivatives

GSF: Leibniz vs. Newton

Partial Derivatives

GEM 1.2.1

The Multivariable Differential

GMM: The Multivariable Differential

Definition of Gradient

GSF: The Geometry of the Gradient
GSF: The Gradient in Rectangular Coordinates
GEM 1.2.2-1.2.3

Properties of Gradient

GSF: Properties of the Gradient

Visualizing Gradient

GSF: Visualizing the Geometry of the Gradient
GSF: Using Technology to Visualize the Gradient
GEM 1.2.2-1.2.3
Taylor 4.3, 4.8

Directional Derivatives

GSF: Directional Derivatives

Gradient in Curvilinear Coordinates

GSF: The Gradient in Curvilinear Coordinates
GSF: Formulas for Div, Grad, Curl

Navigating the Hill

Electric Field Due to a Point Charge as a Gradient

GEM 2.1.1-2.1.2

Unit: Gauss's Law (Integral)

Introduction to the Unit
Learning Outcomes

14 1/26 Thurs

Products of Vectors
Cross Product
Triple Product

GMM: Cross Product
GEM 1.1.1-1.1.3

Vector Surface Elements

GSF: Vector Surface Elements
GEM 1.3.1

Flux Definition

GSF: Flux
GSF: Flux of the Electric Field
GEM 1.3.1, 2.2.1

Flux Calculation

GSF: Highly Symmetric Surfaces
GSF: Less Symmetric Surfaces

15 1/27 Fri

Visualizing Flux

GSF: Flux through a Cube

16 1/30 Mon

Gauss's Law in Integral Form

GSF: Gauss's Law
GSF: Gauss's Law and Symmetry
GSF: Gauss's Law for High Symmetry
GEM 2.2.3

Electric Field Lines

GSF: Electric Field Lines
GEM 2.2.1

Big Quiz Opens

Unit: Divergence and Curl

Introduction to the Unit
Learning Outcomes

17 1/31 Tues

Derivatives of Vector Fields

Definition of Divergence

GSF: The Definition of Divergence
GSF: The Divergence in Curvilinear Coordinates
GEM 1.2.4

Visualization of Divergence

GSF: Exploring the Divergence
GSF: Visualizing the Divergence

18 2/1 Wed

Divergence Theorem

GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7

Differential Form of Gauss's Law

GSF: Differential Form of Gauss's Law
GSF: The Divergence of a Coulomb Field
GEM 2.2.1-2.2.2

19 2/2 Thurs

Circulation

Curl

GSF: The Geometry of Curl
GSF: The Definition of Curl
GSF: The Curl in Curvilinear Coordinates
GSF: Exploring the Curl II
GSF: Visualizing the Curl
GEM 1.2.5

Work

GSF: Conservative Vector Fields
GSF: Independence of Path
GSF: Visualizing Conservative Vector Fields
GSF: Finding Potential Functions
GSF: Finding the Potential from the Electric Field
GEM 1.3.2-1.3.3
GEM 2.4.1
Taylor 4.2

Curl-Free Vector Fields

GSF: Curl-Free Vector Fields
GEM 1.6.2
Taylor 4.4

20 2/3 Fri

Electrostatic Energy Due to Discrete Charges

GSF: Electrostatic Energy from Discrete Charges
GEM 2.4.1-2.4.2

Relationship of Fields

GSF: The Relationship between $V$, $\vec{E}$, $U$, and $\vec{F}$
GEM 2.3.1-2.3.2
Taylor 4.2

Electrostatic Energy from a Continuous Charge Distributions

GSF: Electrostatic Energy from Continuous Sources
GEM 2.4.3-2.4.4

Unit: Magnetic Fields

Introduction to the Unit
Learning Outcomes Learning Outcomes

21 2/6 Mon

Current Density
Total Current

GSF: Current
GEM 5.1.3, 5.2.2

Lorentz Force Law

22 2/7 Tues

Ampère's Law

GSF: Ampère's Law

Ampère's Law in Integral Form

GSF: Current in a Wire
GSF: Ampère's Law and Symmetry
GSF: Ampère's Law on Cylinders
GEM 5.3.3

Stokes' Theorem

GSF: Stokes' Theorem
GEM 1.3.5

Differential Form of Ampère's Law

GSF: Differential Form of Ampère's Law
GEM 5.3.3

23 2/8 Wed

Magnetic Vector Potential

GSF: Magnetic Vector Potential
GEM 5.4.1

Product Rule
Integration by Parts
Second Derivatives
Laplace's Equation

GSF: Product Rules
GSF: Integration by Parts
GSF: Second Derivatives
GSF: Second Derivatives and Maxwell's Equations
GSF: The Laplacian
GEM 1.2.6-1.2.7, 1.3.6
GEM 2.3.3

Magnetic Field $\vec{B}$ from Magnetic Vector Potential $\vec{A}$

GEM 5.4.1

24 2/9 Thurs

Biot Savart Law

GSF: The Biot-Savart Law
GSF: The Magnetic Field of a Straight Wire
GSF: The Magnetic Field of a Spinning Ring
GSF: Comparing $\vec{B}$ and $\vec{A}$ for a Spinning Ring
GEM 5.2.2

25 2/10 Fri

Conductors

GSF: Conductors
GEM 2.5

Boundary Conditions

GSF: Dot Products and Components
GSF: Boundary Conditions on Electric Fields
GSF: Boundary Conditions on Magnetic Fields
GEM 2.3.5, 5.4.2

Review

GSF: Review
GEM 2.3.5, 5.4.2
GEM 5.3.4

26 ??

FINAL EXAM 7 PM

Static Fields Equation Sheet

Exam Equation Sheet

Topic/Day

Activities

Resources

Homework Due