Unit: Potentials Due to Discrete Charges

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Potentials Due to Discrete Charges

1/6 Mon

Introduction to the Course

Introduction to Static Fields

Course Lecture Notes
Key Request Form
Research Consent Form

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

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

1/7 Tues

Electrostatic & Gravitational Potential

Electrostatic Potential Due to a Point Charge
The Functions $1/r$ and $1/r^2$

GSF: Electrostatic and Gravitational Potentials and Potential Energies
GEM 2.3.4
GSF: Dimensions

HW 01 Practice
HW 01

The Position Vector

Position Vector

GSF: The Position Vector
GEM 1.1.4

Dot Product

Dot Product Review

GSF: The Dot Product
GEM 1.1.1

Calculating the Distance Between Two Points

The Distance Formula (Star Trek)

GSF: The Distance Formula
GEM 1.1.2, 1.1.4

Visualizing Potentials

Drawing Equipotential Surfaces

GSF: Visualization of Potentials

1/8 Wed

Visualizing Potentials

Using Technology to Visualize Potentials

Visualizing Potentials Mathematica
GSF: Using Technology to Visualize Potentials

1/9 Thurs

Superposition

Adding Functions Pointwise
The Functions $1/r$ and $1/r^2$
Electrostatic Potential Due to a Pair of Charges (without Series)

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

Definition of Power Series
Calculating Power Series Coefficients

Adding Functions Pointwise
The Functions $1/r$ and $1/r^2$
Calculating Coefficients for a Power Series

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

More Power Series Information

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

Visualizing Power Series Approximations

Visualization of Power Series Approximations

GMM: Visualization of Power Series Approximations

Guessing Power Series

GMM: Guessing Power Series from Graphs

Series Approximations

Multipole Expansions
Using Technology to Explore Power Series Approximations

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

1/10 Fri

Potential Due to a Pair of Charges: Limiting Cases

Electrostatic Potential Due to a Pair of Charges (with Series)

GSF: Power Series for Two Point Charges

HW 02 Practice
HW 02

1/13 Mon

Power Series Sensemaking

Sensemaking from Graphs of Power Series I
Sensemaking from Graphs of Power Series II

Multipole Expansion

Linear Quadrupole Follow-up

Unit: Integration in Curvilinear Coordinates

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Integration in Curvilinear Coordinates

1/14 Tues

Densities

Acting Out Charge Densities

GSF: Densities
GEM 2.1.4

HW 03 Practice
HW 03

Modeling Nonuniform Densities

Modeling Nonuniform Density

Delta Functions

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

Step Functions

GMM: Step Functions
GEM 1.5.2
Video:
Step & Delta Functions

Definition of Gradient

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

Curvilinear Coordinates

Curvilinear Coordinates Introduction

GSF: Curvilinear Coordinates
GSF: Change of Coordinates
GEM 1.4

1/15 Wed

Scalar Line, Surface, Volume Elements

Scalar line elements
Pineapples and Pumpkins
Scalar Surface and Volume Elements
Total Charge of a Rod

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

1/16 Thurs

Total Charge: Spheres & Cylinders

Total Charge: Spheres \& Cylinders

GSF: Total Charge

Representations of Vectors

1/17 Fri

Curvilinear Basis Vectors

Curvilinear Basis Vectors
Representations for Finding Components

GSF: Orthonormal Basis Vectors
GEM 1.4

HW 04 Practice
HW 04

Use What You Know

Introduction to Use What You Know
Charge on a Parabola
Surface Area of a Paraboloid

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

1/20 Mon

MLK (No Class)

Unit: Fields from Continuous Sources

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Fields from Continuous Sources

1/21 Tues

Electrostatic Potential in Curvilinear Coordinates

Electrostatic Potential Due to a Ring of Charge
Ring Sequence Electric Potential

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

HW 05 Practice
HW 05

Limiting Cases

1/22 Wed

Other Continuous Sources

Potential from a Cone

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

Introduction to the Lorentz Force Law

Lorentz Force Law to Words

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

1/23 Thurs

Electric Field Due to a Point Charge

Electric Field of a Point Charge

GSF: Electric Field of a Point Charge

Vector Fields

Draw Vector Fields

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

Superposition for Electric Fields

Drawing Electric Field Vectors for Discrete Charges

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

Electric Field for Two Point Charges

Electric Field Due to a Pair of Charges (with Series)
Electric Field Due to a Pair of Charges (without Series)

Electric Field Lines

GSF: Electric Field Lines
GEM 2.2.1

1/24 Fri

Electric Fields from Continuous Charge Distributions

Electric Field Due to a Ring of Charge
Ring Sequence Electric Field

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

HW 06

Review of Derivatives

GSF: Leibniz vs. Newton

Partial Derivatives

Generalized Leibniz Notation
Partial Derivatives from a Contour Map

GEM 1.2.1

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

Introduction to the Unit
Learning Outcomes

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

1/27 Mon

Zapping with d

Differentials

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

The Multivariable Differential

GMM: The Multivariable Differential

Vector Differential

Vector Differential--Rectangular
Vector Differential--Polar
Vector Differential--Curvilinear

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

Unit: Gauss's Law (Integral)

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Gauss's Law (Integral Form)

1/28 Tues

Relationship of Fields

V, $\vec{E}$, U, $\vec{F}$

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

HW 07

Flux Calculation

Flux through a Paraboloid

GSF: Highly Symmetric Surfaces
GSF: Less Symmetric Surfaces

Visualizing Gradient

Acting Out the Gradient
Visualising the 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

Properties of Gradient

GSF: Properties of the Gradient

Gradient in Curvilinear Coordinates

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

Electric Field Due to a Point Charge as a Gradient

GEM 2.1.1-2.1.2

Directional Derivatives

GSF: Directional Derivatives

Products of Vectors: Cross Product
Triple Product

Cross Product Review

GMM: Cross Product
GEM 1.1.1-1.1.3

Vector Surface Elements

Vector Surface and Volume Elements

GSF: Vector Surface Elements
GEM 1.3.1

Flux Definition

Acting Out Flux

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

1/29 Wed

Visualizing Flux

Visualizing Flux through a Cube

GSF: Flux through a Cube

Unit: Divergence and Curl

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Divergence and Curl

1/30 Thurs

Gauss's Law in Integral Form

Gauss's Law in Symmetric Situations

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

1/31 Fri

Derivatives of Vector Fields

HW 08 Practice
HW 08

Definition of Divergence

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

2/3 Mon

Visualization of Divergence

GSF: Exploring the Divergence
GSF: Visualizing the Divergence

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

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

Circulation

Curl

Visualization of 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

Unit: Magnetic Fields

Introduction to the Unit
Learning Outcomes Learning Outcomes

Unit Learning Outcomes: Magnetostatic Fields

2/4 Tues

Lorentz Force Law

Lorentz Force and Work Done on a Rectangular Loop

HW 09 Practice
HW 09

Current Density
Total Current

Acting Out Current Density

GSF: Current
GEM 5.1.3, 5.2.2

Magnetic Vector Potential

Magnetic Vector Potential Due to a Spinning Charged Ring
Ring Sequence Magnetic Vector Potential

GSF: Magnetic Vector Potential
GEM 5.4.1

2/5 Wed

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

GEM 5.4.1

Biot Savart Law

Magnetic Field Due to a Spinning Ring of Charge
Ring Sequence Magnetic Field

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

2/6 Thurs

Ampère's Law in Integral Form

Amp\`ere's Law in Symmetric Situations

GSF: Ampère's Law
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

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

Electrostatic Energy Due to Discrete Charges

Electrostatic Energy of Discrete Charges

GSF: Electrostatic Energy from Discrete Charges
GEM 2.4.1-2.4.2

Electrostatic Energy from a Continuous Charge Distributions

GSF: Electrostatic Energy from Continuous Sources
GEM 2.4.3-2.4.4

2/7 Fri

Conductors

GSF: Conductors
GEM 2.5

HW 10 Practice
HW 10

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

Introduction to Static Fields
Static Fields Review

GSF: Learning Outcomes
GSF: The Relationship between $\vec{E}$, $V$, and $\rho$
GSF: The Relationship between $\vec{B}$, $\vec{A}$, and $\vec{J}$
GEM 2.3.5, 5.4.2
GEM 5.3.4

2/10, 7-9pm

FINAL EXAM

Static Fields Equation Sheet

Topic/Day

Activities

Resources

Homework Due