Unit 1

Unit 1

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From Coulomb to Maxwell - A Review of Maxwell's Equations

August 25 to September 9

You should review the notes and videos below by Thursday, September 9.
Questions on the material in Unit 1 may be posted to the Unit 1 Discussion Board, or the Unit 1 Slack channel.

Your response to Discussion Question 0 is due Tuesday, August 31, at 5pm.
Your response to Discussion Question 1 is due Tudesday, September 7, at 5pm.
Your solutions to Problem Set 1 are due Thursday, September 9, at 5pm.

In this unit we will review the development of Maxwell's Equations for classical electrodynamcis, expressing them in terms of both fields and potentials. We will discuss the different sets of physical units that are used for electrodynamics. We will see how gauge invariance leads to different representions of Maxwell's equations in terms of the potentials. We will see that waves are a solution. We will review Fourier transforms, that will be extensively used throughout the course.

Below is a list of links to course notes for each topic in this unit, followed by links to recorded video lectures.

Notes and Video Lectures

Notes 1-1 - Electrostatics
- Video 1-1.1 - Coulomb's Law, superposition, charge density [16 min]
- Video 1-1.2 - Electric field and Maxwell's equations for electrostatics [28 min]
- Video 1-1.3 - Helmholtz's Theorem [18 min]
Notes 1-2 - Magnetostatics
- Video 1-2.1 - Magnetic fields, current density, charge conservation [22 min]
- Video 1-2.2 - Maxwell's equations for magnetostatics [20 min]
Notes 1-3 - Faraday's Law and Maxwell's Correction to Ampere's Law, Systems of Units
- Video 1-3.1 - Faraday's Law, Maxwell's correction to Ampere's Law, waves, systems of units [30 min]
Notes 1-3-supp - Faraday's Law Revisited: Motional emf and special relativity
Notes 1-4 - Electromagnetic Potentials and Gauge Invariance
- Video 1-4.1 - Electrostatic potential, magnetostatic vector potential [18 min]
- Video 1-4.2 - Scalar and vector potentials for dynamics, gauge invariance [12 min]
- Video 1-4.3 - Lorenz gauge, Coulomb gauge [26 min]
- Video 1-4.4 - Transverse and longitudinal parts of a vector field, Helmholtz's Theorem revisited [17 min]
Notes 1-5 - Review of Fourier Transforms
- Video 1-5.1 - Fourier transforms, transform of the Dirac delta function, transform of the Coulomb potential [17 min]
Notes 1-5-supp - Review of Fourier Series and derivation of Fourier Transforms
Notes 1-supp - Review of Vector Calculus and Math Methods: surface and line integrals; rectangular, spherical and cylindrical coordinates; vector differential operators and their expression in different coordinate systems; integral vector calculus: Gauss' Theorem and Stoke's Theorem; the Dirac delta function