The four fundamental equations governing electromagnetism — visualized
Gauss's Law
∇·E = ρ/ε₀
Gauss's Magnetism
∇·B = 0
Faraday's Law
∇×E = −∂B/∂t
Ampère-Maxwell
∇×B = μ₀J + μ₀ε₀∂E/∂t
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About: Maxwell's four equations (1865) unified electricity, magnetism, and light. Gauss's law (∇·E=ρ/ε₀) states electric field lines diverge from charges. No magnetic monopoles exist (∇·B=0) — field lines always close on themselves. Faraday's law (∇×E=−∂B/∂t) shows changing magnetic fields induce electric fields, powering generators. The Ampère-Maxwell law adds displacement current ε₀∂E/∂t, predicting electromagnetic waves traveling at c=1/√(μ₀ε₀)≈3×10⁸ m/s.