Definition · Plain-language
Coulomb’s law
Coulomb’s law describes the electrostatic force between two point charges, which grows with the size of the charges and falls off with the square of the distance between them.
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The force between charges
Coulomb’s law, established by Charles-Augustin de Coulomb in the 1780s, gives the force between two stationary electric charges. The force is proportional to the product of the two charges and inversely proportional to the square of the distance separating them: F = k·q₁·q₂ ÷ r², where k is Coulomb’s constant. Two consequences follow immediately. Bigger charges feel a stronger force, and the force weakens rapidly as the charges move apart — doubling the distance cuts the force to a quarter. The direction depends on the signs: like charges (both positive or both negative) repel, while opposite charges attract.
An inverse-square law
The 1 ÷ r² dependence makes Coulomb’s law an inverse-square law, the same mathematical form as Newton’s law of universal gravitation. This shared form is no accident — both describe forces that spread out from a point through three-dimensional space. The crucial difference is strength and sign: the electrostatic force is vastly stronger than gravity between the same particles, and it can both attract and repel, whereas gravity only ever attracts. Coulomb’s law strictly describes point charges or uniformly charged spheres; for extended or moving charges the fuller framework of electromagnetism is needed.
Why it matters
Coulomb’s law underpins the structure of matter. It is the attraction between positively charged nuclei and negatively charged electrons that holds atoms together, and the same force, between atoms, that forms chemical bonds and gives materials their strength. It governs static electricity — why a charged balloon sticks to a wall — and is the starting point for understanding electric fields, capacitors and the behaviour of charged particles in everything from photocopiers to particle accelerators. In short, almost all of chemistry and everyday electricity rests on the electrostatic force this law describes.
Key facts
At a glance
- Definition: the electrostatic force between two point charges
- Equation: F = k·q₁·q₂ ÷ r² (k is Coulomb’s constant)
- Proportional to: the product of the two charges
- Falls off as: the square of the distance (an inverse-square law)
- Direction: like charges repel, opposite charges attract
- Relation: same mathematical form as Newton’s law of gravitation, but far stronger
Common misconceptions
What people often get wrong
Often heard: The electrostatic force decreases in proportion to the distance.
Actually: It decreases with the square of the distance. Doubling the separation cuts the force to one quarter, not one half, because it is an inverse-square law.
Often heard: Coulomb’s law only describes attraction.
Actually: It describes both attraction and repulsion. Opposite charges attract, but like charges repel — unlike gravity, which only ever attracts.
Often heard: Gravity and the electric force are roughly equal in strength.
Actually: Between the same two particles the electrostatic force is enormously stronger than gravity. Gravity dominates on astronomical scales only because large bodies are electrically neutral.
Going deeper
