Paradigms in Physics: Static Fields

Course name:
Paradigms in Physics: Static Fields
Course number:
PH 422
Course credits:
3
Class meeting times:
7 hours of lecture per week for five weeks
Prerequisites:
PH213, MTH255
Course description:
Theory of static electric, magnetic, and gravitational potentials and fields using the techniques of vector calculus in three dimensions.

Schedule from Winter 2023:

Day
Topic
Activities
Resources
Homework

Unit: Potentials Due to Discrete Charges
Introduction to the Unit
Learning Outcomes
  • face Unit Learning Outcomes: Potentials Due to Discrete Charges

1 1/9 Mon

IRB intake

Review on your own
(as necessary):
  Basic Calculus
  Exponentials & Logarithms
  Vectors
  • Basic Calculus: Practice Exercises
  • Derivative Rules
  • Exponential and Logarithm Identities
  • Properties of Logarithms and Exponents

The Distance Formula
GSF: The Distance Formula
GEM 1.1.2, 1.1.4
  • Graphs Involving the Distance Formula
  • Parameters in Trigonometric Functions

Position Vector

2 1/10 Tues

Dot Product
  • Tetrahedron
  • Vectors

Introduction to the Course
  • face Introduction to Static Fields
  • Introduction to Gradescope
  • Obtain Plotting Software
  • Syllabus and Schedule
  • Using Canvas Discussions

Dimensions
  • Dimensions

Electrostatic & Gravitational Potential
  • Potential vs. Potential Energy

Visualization of Potentials

Superposition
  • Linear Quadrupole (w/o series)



  • Exponential Rules A

  • Exponential Rules B

3 1/11 Wed

Definition of Power Series
Derive Power Series Coefficients

Calculating Coefficients of Power Series

Power Series Approximations

Power Series Notation
  • Power Series Practice
  • Series Convergence
  • Series Notation 1
  • Series Notation 2

Power Series Approximations
  • group Using Technology to Explore Power Series Approximations
  • Approximating Functions with Taylor Series

More Power Series Information

Power Series Sensemaking
  • assignment_ind Sensemaking from Graphs of Power Series I
  • assignment_ind Sensemaking from Graphs of Power Series II



4 1/12 Thurs

Potential Due to a Pair of Charges: Limiting Cases
  • Linear Quadrupole (w/ series)

Compare Series and Visualization

Unit: Integration in Curvilinear Coordinates
Introduction to the Unit
Learning Outcomes
  • group Unit Learning Outcomes: Integration in Curvilinear Coordinates

5 1/13 Fri

Zapping with d
  • face Differentials



6 1/16 Mon
MLK (No Class)

7 1/17 Tues

Curvilinear Coordinates
  • Distance Formula in Curvilinear Coordinates

Curvilinear Basis Vectors

Representations of Vectors
  • assignment_ind Representations of Vectors

Vector Differential

Scalar Line, Surface, Volume Elements

  • Memorize Power Series
  • Power Series Coefficients

  • Memorization A, Power Series
  • Power Series Coefficients A

  • Memorization B, Power Series
  • Power Series Coefficients B

8 1/18 Wed

Step Functions
  • Spherical Shell Step Functions
  • Theta Parameters
  • Triangle Parameters B

Delta Functions
  • Approximating a Delta Function with Isoceles Triangles
  • Linear Charge Density
  • Mass of a Slab
  • Volume Charge Density
  • Volume Charge Density, Version 2



9 1/19 Thurs

Densities
GSF: Densities
GEM 2.1.4

Total Charge
  • Cube Charge
  • Total Charge

Proportional Reasoning
  • Mass Density

Use What You Know
  • assignment_ind Introduction to Use What You Know
  • face Charge on a Parabola
  • group Surface Area of a Paraboloid
  • Charge on a Spiral
  • Cone Surface
  • Helix
  • Icecream Mass
  • Sphere in Cylindrical Coordinates

Unit: Fields from Continuous Sources
Introduction to the Unit
Learning Outcomes
  • face Unit Learning Outcomes: Fields from Continuous Sources

10 1/20 Fri

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

Vector Fields
  • group Draw Vector Fields
  • Vector Field Fit
  • Vector Sketch (Curvilinear Coordinates)
  • Vector Sketch (Rectangular Coordinates)

Electric Field Due to a Point Charge
  • assignment_ind Electric Field of a Point Charge

Superposition for Electric Fields
  • group Drawing Electric Field Vectors for Discrete Charges

11 1/23 Mon

Multipole Expansion
  • assignment_ind Linear Quadrupole Follow-up

Electrostatic Potential in Curvilinear Coordinates
  • Potential from a Cone
  • Potential from a Finite Disk



12 1/24 Tues

Electric Fields from Continuous Charge Distributions
  • Electric Field from a Rod LO1 LO4 LO10 LO8

Limiting Cases
  • Potential Due to a Ring of Charge--Limiting Cases

Other Continuous Sources
  • Line Sources Using Coulomb's Law
  • Potential for an Infinite Disk

  • Differentials of One Variable
  • Differentials of Two Variables
  • Find Area/Volume from \(d\vec{r}\)
  • Memorize \(d\vec{r}\)

  • Differentials Quiz A
  • Memorization A, \(d\vec{r}\)

  • Differentials Quiz B
  • Memorization B, \(d\vec{r}\)

Unit: $\vec{E}$ as a Gradient
Introduction to the Unit
Learning Outcomes
  • face Unit Learning Outcomes: \(\vec{E}\) as a Gradient

13 1/25 Wed

Review of Derivatives

Partial Derivatives
GEM 1.2.1

The Multivariable Differential
  • Differentials of Two Variables

Definition of Gradient

Properties of Gradient

Visualizing Gradient
  • Contours

Directional Derivatives
  • Directional Derivative
  • The puddle

Gradient in Curvilinear Coordinates
  • Gradient Practice

Electric Field Due to a Point Charge as a Gradient
GEM 2.1.1-2.1.2
  • Line Sources Using the Gradient
  • The Gradient for a Point Charge



Unit: Gauss's Law (Integral)
Introduction to the Unit
Learning Outcomes
  • face Unit Learning Outcomes: Gauss's Law (Integral Form)

14 1/26 Thurs

Products of Vectors
Cross Product
Triple Product
  • assignment_ind Cross Product Review
GMM: Cross Product
GEM 1.1.1-1.1.3
  • Cross Triangle

Vector Surface Elements
  • Flux through a Cylinder

Flux Definition
  • Flux I
  • Flux II
  • Flux III
  • Flux through a Plane

Flux Calculation
  • group Flux through a Paraboloid
  • Flux through a cone

15 1/27 Fri

Visualizing Flux



16 1/30 Mon

Gauss's Law in Integral Form
  • group Gauss's Law in Symmetric Situations
  • Gauss's Law
  • Gauss's Law for a Rod inside a Cube
  • Gauss's Law on a Cylindrical Shell
  • Symmetry Arguments for Gauss's Law

Electric Field Lines

Big Quiz Opens

Unit: Divergence and Curl
Introduction to the Unit
Learning Outcomes
  • face Unit Learning Outcomes: Divergence and Curl

17 1/31 Tues

Derivatives of Vector Fields
  • assignment_ind Derivatives of Vector Fields

Definition of Divergence
  • Divergence
  • Divergence Estimate
  • Redo

Visualization of Divergence

  • Use What You Know on the Helix

  • Use What You Know A

  • Use What You Know B

18 2/1 Wed

Divergence Theorem
GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7
  • Divergence Theorem on a Paraboloid (CAM Version)
  • Divergence through a Prism
  • Electric Field and Charge
  • Gravitational Field and Mass

Differential Form of Gauss's Law
  • Differential Form of Gauss's Law



19 2/2 Thurs

Circulation
  • Circulation I
  • Circulation II
  • Vector Line Integrals

Curl
  • group Visualization of Curl
  • Curl
  • Curl Estimate
  • The Bathtub

Work
  • Path Independence

Curl-Free Vector Fields
GSF: Curl-Free Vector Fields
GEM 1.6.2
Taylor 4.4

20 2/3 Fri

Electrostatic Energy Due to Discrete Charges
  • group Electrostatic Energy of Discrete Charges
  • Energy of Four Charges

Relationship of Fields
  • group V, \(\vec{E}\), U, \(\vec{F}\)




Unit: Magnetic Fields
Introduction to the Unit
Learning Outcomes
Learning Outcomes
  • face Unit Learning Outcomes: Magnetostatic Fields

21 2/6 Mon

Current Density
Total Current
GSF: Current
GEM 5.1.3, 5.2.2
  • Current in a Wire
  • Total Current, Circular Cross Section
  • Total Current, Square Cross-Section

Lorentz Force Law
  • group Lorentz Force and Work Done on a Rectangular Loop
  • Force and Torque on a Current Loop

22 2/7 Tues

Ampère's Law

Ampère's Law in Integral Form
  • group Ampère's Law in Symmetric Situations
  • Ampère's Law for a Cylinder
  • Symmetry Arguments for Ampère's Law

Stokes' Theorem
  • Paraboloid Sequence: Stokes' Theorem

Differential Form of Ampère's Law
  • Magnetic Field and Current
  • Magnetic Field and Current, Version II

  • Finding Gradient, Divergence, and Curl in Curvilinear Coordinates

  • Finding Gradient, Divergence, and Curl in Curvilinear Coordinates, A

  • Finding Gradient, Divergence, and Curl in Curvilinear Coordinates, B

23 2/8 Wed

Magnetic Vector Potential

Product Rule
Integration by Parts
Second Derivatives
Laplace's Equation

Magnetic Field \(\vec{B}\) from Magnetic Vector Potential \(\vec{A}\)
GEM 5.4.1



24 2/9 Thurs

Biot Savart Law
  • Square Sheet of Current

25 2/10 Fri

Conductors
  • group Conductors
  • Electric Field for a Capacitor

Review
  • face Introduction to Static Fields
  • face Static Fields Review
GSF: Review
GEM 2.3.5, 5.4.2
GEM 5.3.4



26 ??
FINAL EXAM 7 PM
Exam Equation Sheet