W1 D1: Math Bits

Introduction to the Static Fields (Math Bits)

Course Lecture Notes
Key Request Form
Research Consent Form

Introduction to Static Fields (Physics)

Introduction to Static Fields
Static Fields Equation Sheet

Unit: Integration in Curvilinear Coordinates

Unit Learning Outcomes: Integration and Differentiation in Curvilinear Coordinates
Charge on a Parabola
Acting Out the Gradient

Vector Fields

Scalar and Vector Fields Intro
Draw Vector Fields

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

Review: 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

W1 D2: Math Bits

Components of Vectors with the Dot Product

Representations for Finding Components

Review: GSF: Curvilinear Coordinates
Review: GSF: Change of Coordinates
GSF: Orthonormal Basis Vectors
GEM 1.4

Work and Vector Line Integrals

Vector Line Integrals (Contour Map)

Use What You Know

Introduction to Use What You Know
Work from Wind on a Hamster Ball

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

W1 D3: Math Bits

Densities

Acting Out Charge Densities
Modeling Nonuniform Density

GSF: Densities
GEM 2.1.4

HW 01 Practice w/Solution
HW 01 w/Solution

Total Charge

Total Charge of a Rod
Charge on a Parabola
Charge on a Spiral

GSF: Total Charge

W1 D4: Math Bits

Vector Cross Product

Cross Product Review
Cross Product

Triple Product

Vector Differential Area and Volume Elements

Vector Surface and Volume Elements
Pineapples and Pumpkins
Surface Area of a Paraboloid (Vector)

GSF: Vector Surface Elements
GEM 1.3.1, 1.4

Total Charge

Total Charge: Spheres \& Cylinders

W1 D5: Math Bits

Delta Functions

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

HW 02 Practice w/Solution
HW 02 w/Solution

Step Functions

Read After Class:
GMM: Step Functions
GEM 1.5.2
Video:
Step & Delta Functions

W2 D1

Unit: Potential Due to Discrete Charges

Unit Learning Outcomes: Potentials Due to Discrete Charges
Drawing Equipotential Surfaces
Electrostatic Potential Due to a Pair of Charges (with Series)
Linear Quadrupole (w/ series)

Quiz 1

Electrostatic & Gravitational Potential

Electrostatic Potential Due to a Point Charge

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

$1/r$ vs. $1/r^2$

Review Distance Formula

Visualizing Potentials I

Drawing Equipotential Surfaces

Read After Class:
GSF: Visualization of Potentials

W2 D2

Superposition of Discrete Charges

Electrostatic Potential Due to a Pair of Charges (without Series)

Read After Class:
GSF: Superpositions from Discrete Sources
GSF: Two Point Charges
GEM 2.3.4

Visualizing Potentials (with Technology)

Using Technology to Visualize Potentials

Read After Class:
GSF: Using Technology to Visualize Potentials

W2 D3

Veterans Day (No Class)

W2 D4

Potential Due to a Pair of Charges: Limiting Cases

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

Read After Class:
GSF: Power Series for Two Point Charges

Series for Multipoles

Multipole Expansions

Read After Class:
GSF: Using Technology to Visualize Power Series

Multipole Expansion

Linear Quadrupole Follow-up

Unit: Potentials from Continuous Sources

Unit Learning Outcomes: Potential from Continuous Sources
Constants, Variables, and Parameters
Electrostatic Potential Due to a Ring of Charge
Potential Due to a Ring of Charge--Limiting Cases

Electrostatic Potential in Curvilinear Coordinates

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

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

W2 D5

Limiting Cases (V Ring)

HW 03 Practice w/Solution
HW 03 w/Solution
HW 04 Practice w/Solution
HW 04 w/Solution

Constants, Variables, and Parameters

Other Continuous Sources

Read After Class:
GSF: Potential Due to a Finite Line of Charge
GSF: Potential Due to an Infinite Line of Charge
GEM 2.3.2

W3 D1

Unit: Electric Field

Unit Learning Outcomes: Electric Fields, $\vec{E}(\vec{r})$
Electric Field of a Line Source From Potential
Drawing Electric Field Vectors for Discrete Charges
Electric Field Due to a Ring of Charge

Quiz 2

Electric Field Due to a Point Charge

Electric Field of a Point Charge

GSF: Electric Field of a Point Charge

Superposition for Electric Fields

Drawing Electric Field Vectors for Discrete Charges

Read After Class:
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 (without Series)

Electric Field Lines

GSF: Electric Field Lines
GEM 2.2.1

W3 D2

Electric Fields from Continuous Charge Distributions

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

Read After Class:
GSF: Electric Field from Continuous Charge Distributions
GSF: Electric Field Due to a Uniformly Charged Ring
GSF: The Electric Field of a Uniform Disk
GEM 2.1

Definition of Gradient

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

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

Gradient in Curvilinear Coordinates

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

W3 D3

Electric Field Due to a Point Charge as a Gradient

GSF: Electric Field
GEM 2.1.1-2.1.2

HW 05 Practice w/Solution
HW 05 w/Solution

W3 D4

Unit: Gauss's Law

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

Flux Definition

Acting Out Flux

Read After Class:
GSF: Flux
GSF: Flux of the Electric Field
GEM 1.3.1, 2.2.1

Visualizing Flux

Visualizing Flux through a Cube

Read After Class:
GSF: Flux through a Cube

Flux Calculation

Flux through a Paraboloid

Read After Class:
GSF: Highly Symmetric Surfaces
GSF: Less Symmetric Surfaces

W3 D5

Gauss's Law in Integral Form

Gauss's Law in Symmetric Situations

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

HW 06 Practice w/Solution
HW 06 w/Solution

W4 D1

Unit: Maxwell's Equations in Differential Form

Unit Learning Outcomes: Maxwell's Equations in Differential Form

Quiz 3

Derivatives of Vector Fields

Definition of Divergence

Read After Class:
GSF: The Definition of Divergence
GEM 1.2.4

Visualization of Divergence

Read After Class:
GSF: Exploring the Divergence
GSF: Visualizing the Divergence

W4 D2

Divergence Theorem

GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7

Divergence in Curvilinear Coordinates

Read After Class:
GSF: The Divergence in Curvilinear Coordinates
GSF: Exploring the Divergence in Polar Coordinates

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

W4 D3

Unit: Magnetic Fields

Unit Learning Outcomes: Magnetic Fields

Current Density
Total Current

Acting Out Current Density

Read After Class:
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

Read After Class:
GSF: Magnetic Vector Potential
GEM 5.4.1

W4 D4

Thanksgiving (No Class)

W4 D5

Thanksgiving Break (No Class)

W5 D1

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

Quiz 4

Conductors

Read After Class:
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

W5 D2

Biot Savart Law

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

Read After Class:
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

Curl

Visualization of Curl

Read After Class:
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

W5 D3

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

GEM 5.4.1

W5 D4

Ampère's Law in Integral Form

Amp\`ere's Law in Symmetric Situations

Read After Class:
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

Curl-Free Vector Fields

Read After Class:
GSF: Curl-Free Vector Fields
GEM 1.6.2
Taylor 4.4

W5 D5

Relationship of Fields

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

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

Work

Read After Class:
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

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

Lorentz Force Law

Lorentz Force and Work Done on a Rectangular Loop

Electrostatic Energy Due to Discrete Charges

Electrostatic Energy of Discrete Charges

Read After Class:
GSF: Electrostatic Energy from Discrete Charges
GEM 2.4.1-2.4.2

Electrostatic Energy from a Continuous Charge Distributions

Read After Class:
GSF: Electrostatic Energy from Continuous Sources
GEM 2.4.3-2.4.4

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

More Paraboloids

12/10, noon

FINAL EXAM

Static Fields Equation Sheet

Topic/Day

Activities

Resources

Homework Due