Gauss’s Law

1773 Joseph Louis Lagrange

• 1785 Charles-Augustin de Coulomb - Coulomb’s experiments demonstrated the inverse‑square interaction and introduced quantitative electrostatics using the torsion balance. Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest.

• Poisson contribution produced the potential V and the Poisson differential relation ΔV + 4πρ = 0, connecting distributed charges to potentials and thus to field divergence.

1835 Carl Friedrich Gauss - attraction of ellipsoids

Gauss’s Law can be used to derive Coulomb’s las and vice versa

Gauss's law grew from Coulomb’s late‑18th‑century measurements and Poisson’s early‑19th‑century potential theory, was recast as a flux/divergence statement and then absorbed into Maxwell’s field equations by formalizing Faraday’s field ideas mathematically, and today is a foundational Maxwell equation with wide theoretical and practical uses.