Day 321 · Nov 16

The Birthday of James Clerk Maxwell (1831) — Again?

Maxwell was born 13 June 1831, but 16 November is a good day to revisit his equations. Maxwell’s four equations unified electricity, magnetism, and light. They are written in vector calculus (divergence and curl) — a language invented largely by Gibbs and Heaviside after Maxwell’s death. Maxwell’s original work used 20 equations in quaternion form; the modern compact form (∇·E = ρ/ε₀, ∇×B = μ₀J + μ₀ε₀∂E/∂t) was refined by Oliver Heaviside. Every radio, smartphone, and fibre optic cable operates on principles described by Maxwell.

What is ‘displacement current’? Maxwell added it to fix a mathematical inconsistency in Ampère’s law; it predicted electromagnetic waves. Without it, light would not be an electromagnetic wave.

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