It took Maxwell over 10 years and multiple papers to shape those equations in these final forms. The main difficulty was that Faraday’s field concept, on which his equations were based, was extremely hard to grasp. Maxwell had to rely on complicated mechanical models of molecular vortices in ether to come up with them. In this video, we will go through his heroic journey.
Timestamps:
0:00 - 0:42 Intro
0:43 - 3:47 Status of Electromagnetism at his time
3:48 - 5:06 Divergences and Flux
5:07 - 6:33 How did Maxwell derive the first two equations?
6:35 - 7:05 Limitations of hydrodynamics approach
7:06 - 7:49 Molecular's vortices theory
7:50 - 10:22 How did Maxwell derive the last two equations?
10:23 - 10:47 Speed of light
10:48 - 12:05 Maxwell's later abstract approach
12:06 - 13:49 Why was his theory discarded by colleagues?
13:50 - 14:48 Legacy of his equations
References:
1. 3blue1brown
2. https://www.tec-science.com/
3. The Man Who Changed Everything: The Life of James Clerk Maxwell by Basil Mahon
4. https://mathshistory.st-andrews.ac.uk/Biographies/Maxwell/