Fall 2022 Static Fields

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1 1/3 Mon

Introduction

IRB intake
Qualtrics Version of Consent Form

Review on your own
(as necessary):
Basic Calculus
Exponentials & Logarithms
GVC: Review of Single Variable Differentiation

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

Vectors
GSF: Vectors
GSF: Bases
GSF: Unit Vectors
GEM 1.1.1-1.1.2
Taylor 1.2

2 1/4 Tues

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

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





3 1/5 Wed

Position Vector
GSF: The Position Vector
GEM 1.1.4

The Distance Formula
GSF: The Distance Formula
GEM 1.1.2, 1.1.4



4 1/6 Thurs

Dot Product
GSF: The Dot Product
GEM 1.1.1

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

Power Series Review
Notation
GMM: Power Series
GMM: Dimensions in Power Series

Guessing Power Series
GMM: Power Series: Exploration

Power Series Approximations
GMM: Approximations Using Power Series

More Power Series Information
GMM: Common Power Series
GMM: Convergence of Power Series
GMM: Theorems about Power Series

Limiting Cases
GSF: Power Series for Two Point Charges

5 1/7 Fri

Compare Series and Visualization



6 1/10 Mon

Curvilinear Coordinates
GSF: Curvilinear Coordinates
GSF: Change of Coordinates
GEM 1.4

Curvilinear Basis Vectors
GSF: Orthonormal Basis Vectors
GEM 1.4

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

7 1/11 Tues

Vector Differential
GSF: The Vector Differential
GSF: Other Coordinate Systems
GSF: Calculating Line Elements in Cylindrical and Spherical Coordinates

Scalar Line, Surface, Volume Elements
GEM 1.3.1, 1.4

Densities
GSF: Densities
GEM 2.1.4

Total Charge
GSF: Total Charge




8 1/12 Wed

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



9 1/13 Thurs

Proportional Reasoning

Use What You Know
GSF: Using \(d\vec{r}\) in Non-Rectangular Coordinate Systems
GVC: Use What You Know
GVC: Parametric Curves
GVC: Line Integrals on Parametric Curves

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

10 1/14 Fri

Limiting Cases



11 1/17 Mon

MLK (No Class)

12 1/18 Tues

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

Review of Derivatives

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




13 1/19 Wed

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



14 1/20 Thurs

Electric Field Due to a Point Charge
GEM 2.1.1-2.1.2

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 1/21 Fri

Visualizing Flux
GSF: Flux through a Cube

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



16 1/24 Mon

More Gauss's Law

17 1/25 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: Visualizing the Divergence
GSF: Exploring the Divergence




18 1/26 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 1/27 Thurs

Circulation

Curl
GSF: Curl
GSF: Visualizing the Curl
GSF: Visualizing Divergence and Curl
GSF: Exploring the Curl II
GEM 1.2.5

20 1/28 Fri

Step Functions
GMM: Step Functions
GEM 1.5.2

Delta Functions
GMM: Delta Functions
GEM 1.5



21 1/31 Mon

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
GSF: Electrostatic Energy
GSF: Electrostatic Energy
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

Divergence and Curl in Curvilinear Coordinates

22 2/1 Tues

Current Density
Total Current
GSF: Current
GEM 5.1.3, 5.2.2

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

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




23 2/2 Wed

Lorentz Force Law



24 2/3 Thurs

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

25 2/4 Fri

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

Review
GSF: Review
GEM 2.3.5, 5.4.2
GEM 5.3.4



26 2/7 Mon
FINAL EXAM 7 PM
Exam Equation Sheet