Unit: Potentials Due to Discrete Charges

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Potentials Due to Discrete Charges

1/8 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

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
Rules for Differentials

Electrostatic & Gravitational Potential

Electrostatic Potential Due to a Point Charge

Read After Class:
GSF: Electrostatic and Gravitational Potentials and Potential Energies
GEM 2.3.4
GSF: Dimensions

Position Vector

Read After Class:
GSF: The Position Vector
GEM 1.1.4

1/9 Tues

Dot Product

Dot Product Review

Read After Class:
GSF: The Dot Product
GEM 1.1.1

Quiz 1 Prep
HW 01 Practice (w/ Solution)
HW 01

Calculating the Distance Between Two Points

The Distance Formula (Star Trek)

Read After Class:
GSF: The Distance Formula
GEM 1.1.2, 1.1.4

Visualizing Potentials

Drawing Equipotential Surfaces

Read After Class:
GSF: Visualization of Potentials

1/10 Wed

Visualizing Potentials

Using Technology to Visualize Potentials

Visualizing Potentials Mathematica
GSF: Using Technology to Visualize Potentials

1/11 Thurs

Superposition

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

Definition of Power Series
Derive Power Series Coefficients

Adding Functions Pointwise

Review Reading:
Read Before Class:
GMM: Definition of Power Series
GMM: Calculating Power Series Coefficients

Calculating Coefficients of Power Series

Calculating Coefficients for a Power Series

Read After Class:
GMM: Calculating Power Series Coefficients

Guessing Power Series

Read After Class:
GMM: Guessing Power Series from Graphs

Power Series Approximations (Sine Example)

Visualization of Power Series Approximations

Read After Class:
GMM: Visualization of Power Series Approximations

1/12 Fri

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

HW 02 Practice (w/ Solution)
HW 02

Series Approximations

Using Technology to Explore Power Series Approximations

Read After Class:
GMM: Discussion of Approximations Using Power Series
GMM: Using Technology to Explore Power Series Approximations

More Power Series Information

Read After Class:
GMM: Common Power Series
GMM: Dimensions in Power Series
GMM: Convergence of Power Series
GMM: Theorems about Power Series

Power Series Sensemaking

1/15 Mon

MLK (No Class)

1/16 Tues

Zapping with d

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

Quiz 2 Prep (w/ Solution)
Quiz 2a
Quiz 2b
HW 03 Practice (w/ Solution)
HW 03

The Multivariable Differential

GMM: The Multivariable Differential

Unit: Integration in Curvilinear Coordinates

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Integration in Curvilinear Coordinates

1/17 Wed

Step Functions

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

Delta Functions

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

1/18 Thurs

Snow Day

1/19 Fri

Densities

Acting Out Charge Densities

GSF: Densities
GEM 2.1.4

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

Modeling Nonuniform Densities

Modeling Nonuniform Density

Curvilinear Coordinates

Curvilinear Coordinates Introduction

GSF: Curvilinear Coordinates
GSF: Change of Coordinates
GEM 1.4

1/22 Mon

Scalar Line, Surface, Volume Elements

Total Charge of a Rod
Scalar Surface and Volume Elements

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

Unit: Fields from Continuous Sources

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Fields from Continuous Sources

1/23 Tues

Total Charge

GSF: Total Charge

Quiz 3 Prep (w/ Solution)

Representations of Vectors

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

Curvilinear Basis Vectors

GSF: Orthonormal Basis Vectors
GEM 1.4

Use What You Know

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

1/24 Wed

Electrostatic Potential in Curvilinear Coordinates

Electrostatic Potential Due to a Ring of Charge

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

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

1/25 Thurs

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

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 Lines

GSF: Electric Field Lines
GEM 2.2.1

1/26 Fri

Electric Fields from Continuous Charge Distributions

Electric Field Due to a Ring of Charge

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

HW 05
HW 06

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

Introduction to the Unit
Learning Outcomes

1/29 Mon

Big Quiz Opens

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

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

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

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

1/30 Tues

Products of Vectors: Cross Product
Triple Product

Cross Product Review

GMM: Cross Product
GEM 1.1.1-1.1.3

Quiz 4 Prep (w/ Solution)
Quiz 4a
HW 07

Vector Surface 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

Flux Calculation

Flux through a Paraboloid

GSF: Highly Symmetric Surfaces
GSF: Less Symmetric Surfaces

Visualizing Flux

Visualizing Flux through a Cube

GSF: Flux through a Cube

1/31 Wed

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

Unit: Divergence and Curl

Introduction to the Unit
Learning Outcomes

2/1 Thurs

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

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

2/2 Fri

Divergence Theorem

GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7

HW 08

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

Unit: Magnetic Fields

Introduction to the Unit
Learning Outcomes Learning Outcomes

2/5 Mon

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

Current Density
Total Current

GSF: Current
GEM 5.1.3, 5.2.2

Lorentz Force Law

2/6 Tues

Magnetic Vector Potential

GSF: Magnetic Vector Potential
GEM 5.4.1

Quiz 5 Prep (w/ Solution)
HW 09

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

Ampère's Law in Integral Form

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

2/8 Thurs

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

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

GEM 5.4.1

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

2/9 Fri

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

HW 10

2/12, 7-9pm

FINAL EXAM

Static Fields Equation Sheet

Topic/Day

Activities

Resources

Homework Due