Coulomb's law: the inverse-square law of electrostatic force

Mathematical expression

In scalar form the magnitude is commonly written as F = k |q1 q2| / r^2, where q1 and q2 are charges, r is the separation, and k is Coulomb's constant. The constant k can be expressed in terms of the vacuum permittivity ε0 as k = 1/(4π ε0). The full vector form gives direction: like charges repel and unlike charges attract, with the force acting along the line joining the charges. This electrostatic force follows an inverse‑square dependence similar to Newton's law of gravitation.

Assumptions and limitations

Coulomb's law applies exactly to point charges or to spherically symmetric charge distributions outside the objects. It assumes charges are stationary (no magnetic effects) and that the surrounding medium is linear and uniform; in a dielectric material the effective force is reduced by the material's permittivity. For systems of many charges the principle of superposition allows pairwise forces to be summed.

History and theoretical context

Charles‑Augustin de Coulomb established the empirical law using a torsion balance in the late 18th century. The law became a cornerstone of classical electrostatics and was later incorporated into Maxwell's equations, which place Coulomb's law in a broader dynamical theory of electric and magnetic fields.

Uses and notable facts

• Practical calculations: design of capacitors, high‑voltage engineering, particle separation and manipulation.
• Scientific applications: estimating forces at atomic and molecular scales, explaining ionic bonding trends and Coulomb barriers in nuclear physics.
• Distinction: Coulomb's law describes static electric interactions; moving charges require the full framework of electromagnetism.

Coulomb's law remains a fundamental, experimentally verified rule for electrostatics and a useful approximation in many physical and engineering contexts. For more detailed historical or mathematical treatments consult specialized texts or resources on the subject.