Coulomb's law

For two stationary point charges in vacuum, separated by distance r, the magnitude of the electrostatic force is F = kₑ q₁q₂ / r², where q₁ and q₂ are the charges and kₑ = 1/(4πε₀) is Coulomb's constant in vacuum. In a material medium, the permittivity of that medium replaces the vacuum permittivity in the corresponding expression. The force is directed along the line connecting the charges: charges with the same sign repel, while charges with opposite signs attract.

The inverse-square dependence means that, with the charges unchanged, doubling their separation reduces the force magnitude to one quarter; reducing the separation by a factor of ten increases it by a factor of one hundred. The force magnitude is also proportional to each charge, so changing either charge changes the force in direct proportion. This relationship applies to point charges, or to suitably symmetric charged objects when they can be treated as point-like for the calculation.

The law describes a vector force as well as a magnitude: its direction depends on whether the interacting charges have the same or opposite signs. For a collection of source charges, the net electrostatic force on a test charge is the vector sum of the forces contributed by each source charge. This superposition principle lets a complicated charge arrangement be analyzed by considering pairwise forces and then adding their vector components.

In the 1780s, French physicist Charles-Augustin de Coulomb used a torsion balance to investigate small electrical forces. In this instrument, the twisting of a suspended fibre provided a way to compare the force acting on a charged element at different separations. His experiments established an inverse-square relationship for the electric force, helping make the study of electricity quantitative. The SI unit of electric charge, the coulomb, is named after him.

Coulomb's law is the electrostatic interaction law for charges at rest. It resembles Newton's inverse-square law of gravitation mathematically, but electric forces depend on electric charge and can be attractive or repulsive, whereas gravity between ordinary masses is attractive. In classical electromagnetism, the law is a foundation for calculating electric fields and forces; for moving charges and time-varying fields, the broader framework of electromagnetism is needed.