## Paradigms in Physics: Static Fields

Course name:
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:

##### 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

(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
• Obtain Plotting Software
• Syllabus and Schedule
• Using Canvas Discussions

Dimensions
• Dimensions

Electrostatic & Gravitational Potential
• Potential vs. Potential Energy

Visualization of Potentials

Superposition

• 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

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

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

• Contours

Directional Derivatives
• Directional Derivative
• The puddle

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