Coulomb's law
(E1.2.1) E1.2 · Coulomb's Law →How hard two point charges push or pull each other. The force lies along the line joining them and weakens with the square of the distance.
| force between the charges | N | |
| the two charges | C | |
| separation | m | |
| Coulomb constant | 8.99×10⁹ N·m²/C² (=1/4πε₀) |
Applies to point charges at rest, and to uniformly charged spherical distributions with the separation measured between their centres.
Coulomb measured the force with a torsion balance: a charged sphere sits at the end of a light rod, suspended by its centre from a thin fibre. Bringing a second charged sphere close to it twists the rod, and the angle of twist is proportional to the force between the spheres. Halving the distance between the spheres made the twist four times larger:
Touching two identical spheres together splits the charge on them equally, giving a way to halve a charge at will. Doing that halved the twist, and so the force:
Combining the two proportionalities and naming the constant of proportionality k_e gives Coulomb's law:
Two charges q₁, q₂ at r = 3.0 cm apart:
Doubling the separation to 6.0 cm — with the charges unchanged:
Doubling r always cuts the force to a quarter, whatever the charges are — the inverse-square dependence, not any particular pair of numbers.
At the separation between proton and electron, 5.3 × 10⁻¹¹ m:
A ratio of about 2 × 10³⁹. The electric force dominates at atomic scale and is undetectable at astronomical scale, because charge cancels in bulk matter and mass does not.
Valid for point charges, and for uniformly charged spheres if you measure r centre to centre. The absolute-value bars give only the magnitude — read the direction off the signs.