This is an excellent and brilliantly done video. The visualizations made things immediately clear that I have been working to understand for many years. I have recently explored a text from James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field" available in print or PDF from many sources. It summarizes Maxwell's Original 20 Equations that are frequently taught in the Integral or Differential form as 4 Equations. From what I can tell this simplification was done as a special case where the Vector Potential has zero value of the original equations. Heaviside and others assumed that since the "Potential Component" used in the equations could not be observed or measured, assuming it was zero (0) greatly simplified the equations and since all calculations were manually done, it would allow for ease of use and more rapid development of technology - which it did. Can 3Blue1Brown explore the original 20 equations and possibly produce a series of videos to help visualize and utilize the original forms and explore what may be lost in the simplification process. I have read that the original equations assume a medium of transmission (ether) that disappears as the Vector Potential Component is dropped. My math is weak, you may be my only hope.

This is an excellent and brilliantly done video. The visualizations made things immediately clear that I have been working to understand for many years. I have recently explored a text from James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field" available in print or PDF from many sources. It summarizes Maxwell's Original 20 Equations that are frequently taught in the Integral or Differential form as 4 Equations. From what I can tell this simplification was done as a special case where the Vector Potential has zero value of the original equations. Heaviside and others assumed that since the "Potential Component" used in the equations could not be observed or measured, assuming it was zero (0) greatly simplified the equations and since all calculations were manually done, it would allow for ease of use and more rapid development of technology - which it did. Can 3Blue1Brown explore the original 20 equations and possibly produce a series of videos to help visualize and utilize the original forms and explore what may be lost in the simplification process. I have read that the original equations assume a medium of transmission (ether) that disappears as the Vector Potential Component is dropped. My math is weak, you may be my only hope.