Electromagnetism and Theoretical Physics
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In this live, I present classical electromagnetism and reformulate this theory by applying three simplifications, which allow to see more clearly: - A good choice of units allows to remove arbitrary constants - The formalism of differential forms allows to make the derivation operators more uniform - The relativistic unification of space and time allows to unify electric field and magnetic field into a single field. ------------------------------------------------------------------- My name is Antoine Bourget, I am a theoretical physicist, and I try to transmit in video what I find elegant in mathematics and physics. To follow the news of the channel, and contact me, you can join the Discord server or follow me on social networks. If you want to donate, I also have a Tipeee Discord account: / discord Twitter: / antoinebrgt My personal website: http://www.antoinebourget.org Tipeee: https://fr.tipeee.com/scientia-egregia/ ------------------------------------------------------------------- Video outline: 00:00 Start of the blabla 5:45 Start of the presentation Part 1: History 13:20 Birth of electrodynamics 17:00 Coulomb force and Gauss's law (Maxwell's first equation) 38:10 Ampere's law (Maxwell's second equation) 50:00 Magnetic induction, Faraday's law (Maxwell's third equation) 53:03 Absence of magnetic monopoles (Maxwell's fourth equation) 55:30 Lorentz force Part 2: Natural units 58:30 Unit deletions redundant 1:09:40 Natural units 1:16:50 Maxwell's 4 equations Part 3: Differential forms 1:24:45 Reminders on differential forms in R^3 1:39:35 Correspondences between vectors and forms in R^3 1:47:24 Contractions of forms 1:54:15 The fundamental scheme (differentials and differential operators) 2:00:30 Example: rotational in spherical coordinates 2:17:23 Vectors, pseudo-vectors and symmetry in a mirror 2:24:50 Electric and magnetic fields in terms of forms 2:31:50 Maxwell's equations in terms of forms Part 4: Relativity and electromagnetic unification 2:35:00 Electromagnetic tensor and space-time unification 2:42:40 Relativistic Maxwell's equations 2:52:05 Stokes' theorem 2:58:15 Poincaré's lemma and potentials 3:01:30 Gauge invariance Conclusion 3:05:50 Summary 3:08:40 Questions References: The subject is classic and treated in many books, but to my knowledge nowhere in the way presented here, in such a unified way and focused on Maxwell's equations. However, the elements that I give here can be found in the following books: - Theodore Frankel, The geometry of physics - Mikio Nakahara, Geometry, Topology and Physics Equipment used for the video: GIMP software + XP-Pen Star03 graphics tablet. Errata 2:45:27 There is a missing - sign on the Bx (thanks to Gwenilamalice) 35:00 I should have written integral of f(x), without the dx, because we integrate on the boundary only (thanks to Aymeric Melt)
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