Principles of Electricity and Magnetism

Theory and Applications

Vector Review

Lesson 0 – Before You Begin

0.0 Introduction
0.1 Notation

Lesson 1 – Stationary Point Charges and Their Forces

1.0 Introduction
1.1 Basic Rules of Electrostatics
1.2 Our Understanding of Conductors
1.3 Electrostatic Induction
1.4 Fundamental Interactions, Virtual Particles, and Geometric Theories
1.5 Physical Models
1.6 The Thread Model in Electrostatics
1.7 Obtaining Coulomb’s Law from the Thread Model
1.8 Using Coulomb’s Law
1.9 Force, Energy, and Work
1.10 Using Potential Energy

2.0 Introduction
2.1 How Motion Modifies Threads
2.2 Threads and Moving Train Cars
2.3 A Little Relativity
2.4 The Relativistic Train Car
2.5 Moving Source and Stationary Field Particle
2.6 Stubs and the Stub Force
2.7 Electric and Magnetic Forces and Fields
2.8 Visualizing Threads, Stubs, and Field Lines
2.9 Finding Forces of Moving Charges
2.10 The Magnetic Force and Relativity: An Intuitive Example

3.0 Introduction
3.1 The Electric Field of a Stationary Point Charge
3.2 The Fields of Uniformly-Moving Point Charges
3.3 Electric Potential and Voltage
3.4 Field Vectors, Field Lines, and Field Contours
3.5 Static Electric Fields and Potentials in Conductors
3.6 Force and Motion in Uniform Fields
3.7 Devices Using Electric and Magnetic Fields

4.0 Introduction
4.1 Electric Fields in Wires
4.2 Resistance, Ohm’s Law, and Power in Circuits
4.3 Resistivity and Resistors
4.4 Resistance Circuits
4.5 Resistors in Series and Parallel
4.6 Series-Parallel Reduction
4.7 Real Batteries
4.8 Kirchoff’s Laws
4.9 Drift Speed and Electron Velocity

5.0 Introduction
5.1 The Electric Field Lines of a Stationary Point Charge
5.2 Electric Field Contours of Point Charges
5.3 The Magnetic Field of a Current-Carrying Wire
5.4 Magnetic Field Contours
5.5 Comparing Electric and Magnetic Fields
5.6 Electric Field Lines of Multiple Point Charges
5.7 Drawing Fields of Multiple Point Sources
5.8 Symmetric Distributions of Charge
5.9 The Magnetic Field of Two Parallel Wires
5.10 Field Contours
5.11 A Summary of the Rules

6.0 Introduction
6.1 Defining Capacitors and Capacitance
6.2 Parallel-Plate Capacitors
6.3 Energy in a Parallel-Plate Capacitor
6.4 Dielectrics
6.5 Capacitors in DC Circuits
6.6 Charging and Discharging Capacitors: RC Circuits

7.0 Introduction
7.1 Gauss's Law of Electricity
7.2 Charge Density
7.3 The Fields of Charge Distributions with Radial Spherical Symmetry
7.4 Gauss’s Law and Conductors
7.5 Gauss's Law of Magnetism
7.6 Uniform and Non-uniform Densities
7.7 Two-dimensional Integration
7.8 Three-dimensional Integration
7.9 Gauss's Law and Electric Flux
7.10 The Integral Form of Gauss's Law
7.11 Applying Gauss's Law

8.0 Introduction
8.1 Ampère's Law
8.2 Current Density
8.3 The Fields of Current Distributions with Radial Cylindrical Symmetry
8.4 The Magnetic Line Integral
8.5 The Integral Form of Ampère's Law
8.6 Applying Ampère's Law
8.7 Finding Fields with Direct Integration
8.8 The Differential Form of Gauss’s Law and Ampère’s Law

9.0 Introduction
9.1 The Force on a Current-Carrying Wire
9.2 Magnetic Dipoles
9.3 Electric Dipoles
9.4 Atomic Dipoles, Domain Alignment, and Thermal Disalignment
9.5 Matter in External Magnetic Fields
9.6 Ferromagnetism

10.0 Introduction
10.1 The Fields of a Charge Accelerating from Rest
10.2 The Fields of Accelerating Point Charges
10.3 The Acceleration Fields for Slow Source Charges
10.4 Visualizing the Fields of Accelerating Charges
10.5 How Accelerating Charges Can Create Induced Currents
10.6 Displacement Current and the Magnetic Field in a Capacitor

11.0 Introduction
11.1 Electromotive Force
11.2 EMF without Acceleration.
11.3 Faraday’s Law
11.4 Induction Experimentally
11.5 Using Lenz’s Law
11.6 Using Faraday’s Law
11.7 Eddy Currents
11.8 Electric Motors.
11.9 Electric Generators

12.0 Introduction
12.1 An Inductor in a DC Circuit
12.2 An Inductor in an AC Circuit
12.3 Energy in Inductors and Magnetic Fields
12.4 LR Circuits
12.5 LC Circuits and Phases
12.6 Phasors
12.7 Rules for AC Circuits
12.8 Power in AC Circuits
12.9 The Series LRC Circuit
12.10 Resonance

13.0 Introduction
13.1 Transformers
13.2 Getting Electric Power to Your Home
13.3 Circuits and Circuit Breakers
13.4 Wires
13.5 Switches and Outlets
13.6 Safety Devices
13.7 Waves: A Review
13.8 Maxwell’s Equations and Radiation
13.9 Electromagnetic Radiation and Radio Waves
13.10 Carrying Information on Electromagnetic Waves
13.11 Polarization

A.0 Introduction
A.1 Stationary and Moving Train Cars
A.2 A Three-dimensional Train Car
A.3 Thread Length
A.4 Thread Density

B.0 Introduction
B.1 Definitions
B.2 Four Vectors
B.3 Lorentz Transformation
B.4 Invariants
B.5 Transformation of Velocity, Force, and Acceleration
B.6 Transformation of Threads
B.7 Transformation of Fields and the Field Strength Tensor

C.0 Introduction
C.1 Two Useful Mathematical Rules
C.2 Relations Involving Angles and Vector Lengths
C.3 Moving Source Charge, Stationary Field Charge
C.4 Moving Field Charge, Stationary Source Charge
C.5 Moving Field Charge, Moving Source Charge
C.6 Velocity and Acceleration Threads
C.7 Acceleration Threads and Fields
C.8. Exact Treatment of the Fields of a Wire with Constant Current
C.9 Fields of a Wire with Increasing Current

D.0 Introduction
D.1 A Tutorial on Linear Algebra
D.2 Rethinking Newton's Laws of Motion
D.3 The Lorentz transformation
D.4 Consequences of the Lorentz Transformation in Space and Time
D.A Propagating the World Line
D.B The Relativistic Transformation of Forces