Coulomb's Law
Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them, directed along the line joining them.
Curious
Charles-Augustin de Coulomb, using a delicate torsion balance in 1785, was the first to precisely measure how the electric force between two charged objects depends on their separation. He found a strikingly simple relationship: double the distance between two charges, and the force drops to a quarter of its original strength — the same inverse-square pattern Newton had found for gravity a century earlier, despite electricity and gravity being completely different forces.
This resemblance to gravity isn't a coincidence rooted in some deep unification (at the classical level, at least) — both forces simply happen to spread outward from a point source in three-dimensional space the same geometric way, causing their intensity to dilute following the same inverse-square pattern.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| F | Electrostatic force | newton (N) |
| q₁, q₂ | Point charges | coulomb (C) |
| r | Distance between charges | metre (m) |
| k | Coulomb constant | N·m²/C² |
Worked example: Two charges of +2 µC and −3 µC are separated by 0.5 m. F = (8.99×10⁹)(2×10⁻⁶)(3×10⁻⁶)/(0.5)² = (8.99×10⁹)(6×10⁻¹²)/0.25 ≈ 0.216 N, attractive (since the charges have opposite signs).
Deep Dive
Coulomb's law is mathematically equivalent to Gauss's law of electrostatics (∇·E = ρ/ε₀) for the special case of a point charge — Gauss's law can be derived from Coulomb's law by integrating the resulting field over a spherical surface, and conversely Coulomb's law follows from Gauss's law applied to a point charge's spherically symmetric field. Modern electrodynamics generally treats Gauss's law (part of Maxwell's equations) as the more fundamental statement, with Coulomb's law as its historically prior, experimentally-discovered special case.
Precision tests: The exponent in Coulomb's law's 1/r² dependence has been tested to extraordinary precision — modern experiments confirm the exponent equals 2 to better than 1 part in 10¹⁶, making it one of the most stringently verified relationships in physics. Any deviation from exactly 1/r² would imply the photon (the force-carrying particle of electromagnetism) has a nonzero rest mass, so these precision tests also serve as some of the tightest experimental bounds on the photon's mass, which is consistent with exactly zero.
Coulomb's original 1785 measurements used a torsion balance of his own design, adapted from the same basic technique Henry Cavendish would later use (1798) to measure the gravitational constant G — illustrating how the same experimental ingenuity, applied to different forces, helped establish quantitative laws for both electricity and gravity within a few decades of each other.
Concept Relationship Map
Requires: electric charge
Enables: electric field, Gauss's law
Commonly confused with: Gauss's law (mathematically equivalent for point charges, but Gauss's law is the more general and fundamental statement)
Sources
- Coulomb, C.A. de (1785). Histoire de l'Académie Royale des Sciences, 569–577.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 2.