W1 D1: Math Bits

Introduction to the Static Fields (Math Bits)

Course Lecture Notes
Key Request Form
Research Consent Form

Densities

Acting Out Charge Densities

GSF: Densities
GEM 2.1.4

Non-uniform Densities

Modeling Nonuniform Density

Unit: (Math Bits) Integration and Differentiation in Curvilinear Coordinates

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Integration and Differentiation in Curvilinear Coordinates

W1 D2: Math Bits

Review Curvilinear Coordinates

GSF: Curvilinear Coordinates
GSF: Change of Coordinates

Scalar Line, Surface, Volume Elements

Total Charge of a Rod
Curvilinear Volume Elements

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

Total Charge

Total Charge: Spheres \& Cylinders

GSF: Total Charge

W1 D3: Math Bits

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

HW 01 Practice (w/ Solution)
HW 01 Practice (pdf)
HW 01 (w/ Solution)
HW 01 (pdf)

Use What You Know

Introduction to Use What You Know
Charge on a Parabola

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

W1 D4: Math Bits

Vector Fields

Draw Vector Fields

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

Work and Vector Line Integrals

Vector Line Integrals (Contour Map)

Curvilinear Basis Vectors

GSF: Orthonormal Basis Vectors
GEM 1.4

W1 D5: Math Bits

Review The Multivariable Differential

GMM: The Multivariable Differential

HW 02 Practice (w/ Solution)
HW 02 Practice (pdf)
HW 02 (w/ Solution)
HW 02 (pdf)

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

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

Unit: Potentials Due to Discrete Charges

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Potentials Due to Discrete Charges

W2 D1

Introduction to Static Fields (Physics)

Introduction to Static Fields

Electrostatic & Gravitational Potential

Electrostatic Potential Due to a Point Charge

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

Review Distance Formula

Visualizing Potentials I

Drawing Equipotential Surfaces

Read After Class:
GSF: Visualization of Potentials

W2 D2

Veterans Day (No Class)

W2 D3

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

HW 03 Practice (w/ Solution)
HW 03 Practice (pdf)
HW 03 (w/ Solution)
HW 03 (pdf)

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

W2 D4

Visualizing Potentials (with Technology)

Using Technology to Visualize Potentials

Read After Class:
GSF: Using Technology to Visualize Potentials

Series for Multipoles

Multipole Expansions

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

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

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

Electrostatic Potential in Curvilinear Coordinates

Electrostatic Potential Due to a Ring of Charge

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 04 Practice (w/ Solution)
HW 04 Practice (pdf)
HW 04 (w/ Solution)
HW 04 (pdf)

Unit: Electric Fields

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Electric Fields, $\vec{E}(\vec{r})$

W3 D1

Constants, Variables, and Parameters

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 Lines

GSF: Electric Field Lines
GEM 2.2.1

W3 D2

Electric Field Due to a Point Charge as a Gradient

GSF: Electric Field
GEM 2.1.1-2.1.2

Electric Fields from Continuous Charge Distributions

Electric Field Due to a Ring of Charge

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

Unit: Gauss's Law (Integral)

Introduction to the Unit
Learning Outcomes

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

W3 D3

Products of Vectors: Cross Product
Triple Product

Cross Product Review

GMM: Cross Product
GEM 1.1.1-1.1.3

HW 05 Practice (w/ Solution)
HW 05 Practice (pdf)
HW 05 (w/ Solution)
HW 05 (pdf)

Vector Surface Elements

Vector Surface and Volume Elements

Read After Class:
GSF: Vector Surface Elements
GEM 1.3.1

Flux Definition

Acting Out Flux

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

W3 D4

Flux Calculation

Flux through a Paraboloid

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

Visualizing Flux

Visualizing Flux through a Cube

Read After Class:
GSF: Flux through a Cube

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

W3 D5

Step Functions

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

HW 06 Practice (w/ Solution)
HW 06 Practice (pdf)
HW 06 (w/ Solution)
HW 06 (pdf)

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

W4 D1

Big Quiz

Static Fields Equation Sheet

Gravity (w/ Solution)
Gravity (pdf)

Unit: Maxwell's Equations in Differential Form

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Divergence and Curl

W4 D2

More Gauss's Law

Derivatives of Vector Fields

W4 D3

Definition of Divergence

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

HW 07 Practice (w/ Solution)
HW 07 Practice (pdf)
HW 07 (w/ Solution)
HW 07 (pdf)

Visualization of Divergence

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

Divergence Theorem

GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7

W4 D4

Thanksgiving (No Class)

W4 D5

Thanksgiving Break (No Class)

HW 08 Practice
HW 08 Practice (pdf)
HW 08
HW 08 (pdf)

Unit: Magnetic Fields

Introduction to the Unit
Learning Outcomes Learning Outcomes

Unit Learning Outcomes: Magnetostatic Fields

W5 D1

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

Current Density

Acting Out Current Density

Read After Class:
GSF: Current
GEM 5.1.3, 5.2.2

W5 D2

Big Quiz Redux

Total Current

Current from a Spinning Cylinder

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

W5 D3

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

HW 09 Practice (w/ Solution)
HW 09 Practice (pdf)
HW 09 (w/ Solution)
HW 09 (pdf)
Proportional Reasoning Practice (w/ Solution)
Proportional Reasoning Practice (pdf)

W5 D4

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

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

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

Lorentz Force Law

Curl-Free Vector Fields

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

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

W5 D5

Biot Savart Law

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

HW 10 Practice (w/ Solution)
HW 10 Practice (pdf)
HW 10 (w/ Solution)
HW 10 (pdf)

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

12/10, noon

FINAL EXAM

Static Fields Equation Sheet

Topic/Day

Activities

Resources

Homework Due