Divergence and curl: Maxwell’s Equations, fluid flow and more

Maxwell’s equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. … Maxwell first used the equations to propose that light is an electromagnetic phenomenon.

Introduction to Maxwell’s Equations

James Clerk Maxwell [1831-1879] was an Einstein/Newton-level genius who took a set of known experimental laws (Faraday’s Law, Ampere’s Law) and unified them into a symmetric coherent set of Equations known as Maxwell’s Equations. Maxwell was one of the first to determine the propagation speed of electromagnetic (EM) waves was the same as the speed of light – and hence to conclude that EM waves and visible light were really the same thing.

maxwell's equations


(See below for small-but-important error correction) More thoughts from the end: https://www.patreon.com/posts/19586800 Special thanks: http://3b1b.co/divcurl-thanks Error: At 4:55, the narration should say “counterclockwise rotation gives positive curl, clockwise rotation gives negative curl”. The diagram is correct, though. My former work on divergence and curl at Khan Academy: https://www.khanacademy.org/math/mult… For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you’ll really enjoy this site: https://anvaka.github.io/fieldplay/ Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/a…

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