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Paradigms in Physics: Static Fields | 2025-Winter
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Syllabus
Course Name
Paradigms in Physics: Static Fields
Course Number
PH 422 / PH 522
Year/Term
2025
Display other available years here.
Course Credits
4
Class meeting times
7 hours of lecture/discussion per week for five weeks.
Prerequisites
PH 213, MTH 255 (may be taken concurrently), PH 335 recommended
Course description
Theory of static electric, magnetic, and gravitational potentials and fields using the techniques of vector calculus in three dimensions.
Topic/Day
Activities
Resources
Homework Due
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
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
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
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
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