Paradigms in Physics: Static Fields | 2024-Winter

- Course Name
- Paradigms in Physics: Static Fields

- Course Number
- ph422

- Year/Term
- Winter-2024

- 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.

Unit: Potentials Due to Discrete Charges

Learning Outcomes

1/8 Mon

Introduction to the Course

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

Electrostatic & Gravitational Potential

GSF: Electrostatic and Gravitational Potentials and Potential Energies

GEM 2.3.4

GSF: Dimensions

1/9 Tues

Dot Product

Calculating the Distance Between Two Points

Visualizing Potentials

1/10 Wed

1/11 Thurs

Superposition

Definition of Power Series

Derive Power Series Coefficients

Derive Power Series Coefficients

GMM: Definition of Power Series

GMM: Calculating Power Series Coefficients

Calculating Coefficients of Power Series

Power Series Approximations (Sine Example)

1/12 Fri

Potential Due to a Pair of Charges: Limiting Cases

Series Approximations

GMM: Discussion of Approximations Using Power Series

GMM: Using Technology to Explore Power Series Approximations

More Power Series Information

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

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

Unit: Integration in Curvilinear Coordinates

Learning Outcomes

1/17 Wed

1/18 Thurs

Snow Day

1/22 Mon

Scalar Line, Surface, Volume Elements

GSF: Scalar Surface Elements

GSF: Triple Integrals in Cylindrical and Spherical Coordinates

GEM 1.3.1, 1.4

GSF: Triple Integrals in Cylindrical and Spherical Coordinates

GEM 1.3.1, 1.4

Unit: Fields from Continuous Sources

1/23 Tues

1/24 Wed

Electrostatic Potential in Curvilinear Coordinates

GSF: Potentials from Continuous Charge Distributions

GSF: Potential Due to a Uniformly Charged Ring

GEM 2.3.4

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

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

Electric Field Due to a Point Charge

Vector Fields

Superposition for Electric Fields

Electric Field for Two Point Charges

1/26 Fri

Electric Fields from Continuous Charge Distributions

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

Learning Outcomes

1/29 Mon

Big Quiz Opens

Definition of 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

GSF: Using Technology to Visualize the Gradient

GEM 1.2.2-1.2.3

Taylor 4.3, 4.8

Gradient in Curvilinear Coordinates

Electric Field Due to a Point Charge as a Gradient

GEM 2.1.1-2.1.2

Unit: Gauss's Law (Integral)

1/30 Tues

Products of Vectors: Cross Product

Triple Product

Triple Product

GMM: Cross Product

GEM 1.1.1-1.1.3

GEM 1.1.1-1.1.3

Flux Calculation

1/31 Wed

Gauss's Law in Integral Form

Unit: Divergence and Curl

Learning Outcomes

2/1 Thurs

Derivatives of Vector Fields

Definition of Divergence

Circulation

2/2 Fri

Differential Form of Gauss's Law

Unit: Magnetic Fields

Learning Outcomes

2/5 Mon

Relationship of Fields

Lorentz Force Law

2/6 Tues

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

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

GSF: Current in a Wire

GSF: Ampère's Law and Symmetry

GSF: Ampère's Law on Cylinders

GEM 5.3.3

2/8 Thurs

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

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

2/9 Fri

2/12, 7-9pm