Coulomb's law

Relate the electrostatic force between ideal point charges to the product of their charges and the inverse square of their separation, directed along the line joining them and modified by the medium.

Version

v2 · 2026-09-19 · History

Domain-specific #

3938

Domain group

Natural Sciences

Origin domain

Physics

Subdomains

Electromagnetism, Electrostatics → Physics

Aliases

Coulomb inverse-square law

Core Idea

Coulomb's law gives F=(¼πε)q1q2(r1−r2)/|r1−r2|³ for ideal point charges, with sign determining attraction or repulsion; extended distributions require integration. A charge produces an inverse-square electric field in three-dimensional space. A second charge experiences qE, and vector superposition combines contributions from multiple charges within linear electrostatics. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

How would you explain it like I'm…

The Push-and-Pull Rule

Some tiny things have an electric charge. Charges that are the same push each other away, and opposite ones pull together. Coulomb's law says how hard: the bigger the charges, the stronger the push or pull, and when they move farther apart it gets weaker very fast.

The Electric Force Rule

Electric charges come in two kinds, positive and negative. Coulomb's law says that like charges push apart and unlike charges pull together, and it tells you exactly how strong that push or pull is. The force gets bigger when the charges are bigger, and it gets weaker fast as they move apart: twice as far means only one quarter as strong. The push or pull acts along the straight line between the two charges. If there are many charges, you work out each push or pull separately and add them up.

Inverse-Square Electric Force Law

Coulomb's law gives the electric force between two point charges at rest. Its size is proportional to the product of the charges, q₁q₂, and inversely proportional to the square of the distance between them, and it points along the line joining them. The sign of q₁q₂ decides whether the force is repulsive (same signs) or attractive (opposite signs). A constant involving the permittivity ε of the medium sets the strength. Equivalently, one charge creates an electric field that falls off as 1/r², and a second charge q feels force qE. For more than two charges, the forces add as vectors (superposition), and for spread-out charge you integrate over the distribution.

 

Coulomb's law states that for ideal point charges at rest, the force on charge 1 due to charge 2 is F = (1/(4 pi epsilon)) q1 q2 (r1 - r2) / |r1 - r2|^3. The force is central, directed along the line of separation, proportional to q1 q2, and inversely proportional to the square of the distance, with the sign of the product determining attraction or repulsion. Equivalently, a point charge produces an inverse-square electric field in three-dimensional space, and a second charge q experiences force qE. Within linear electrostatics, fields and forces from multiple charges combine by vector superposition, and extended charge distributions are handled by integration. The permittivity epsilon encodes the medium, reducing to epsilon_0 in vacuum. The law's validity rests on its point-charge, static and medium assumptions and on consistent units and signs.

Scope of Application

Coulomb's law belongs to electromagnetism and is useful where the analyst can specify two stationary point charges, their signed charge values, a separation vector, and a homogeneous medium or vacuum permittivity, then evaluate under the point-charge, static, and medium assumptions, force is central, proportional to q1q2, and inversely proportional to squared separation with consistent units and sign. The scope is broad within that domain but bounded by the need for under the point-charge, static, and medium assumptions, force is central, proportional to q1q2, and inversely proportional to squared separation with consistent units and sign. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making under the point-charge, static, and medium assumptions, force is central, proportional to q1q2, and inversely proportional to squared separation with consistent units and sign the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Coulomb's law can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Coulomb's law. Coulomb's law compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: two stationary point charges, their signed charge values, a separation vector, and a homogeneous medium or vacuum permittivity. Reject examples whose alleged carrier belongs to a different problem.
2. Lock the constitutive rule. Express under the point-charge, static, and medium assumptions, force is central, proportional to q1q2, and inversely proportional to squared separation with consistent units and sign independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of electromagnetism because they reuse two stationary point charges, their signed charge values, a separation vector, and a homogeneous medium or vacuum permittivity, A charge produces an inverse-square electric field in three-dimensional space. A second charge experiences qE, and vector superposition combines contributions from multiple charges within linear electrostatics., and type the carrier, state every parameter and convention in the definition, test that under the point-charge, static, and medium assumptions, force is central, proportional to q1q2, and inversely proportional to squared separation with consistent units and sign, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Coulomb's law Domain-specific

Parents (1) — outgoing typed relations

• Coulomb's law is a kind of Scaling and Scale Dependence Prime

  Coulomb interaction scales exactly with inverse squared separation.

Hierarchy path (1) — routes to 1 parentless root

• Coulomb's law → is a kind of Scaling and Scale Dependence → is a decomposition of Scale

Neighborhood in Abstraction Space

Coulomb's law sits in a crowded region of the domain-specific corpus (37^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Molecular & Atomic Electronic Structure (12 abstractions)

Nearest neighbors

• Charge number — 0.89
• Method of image charges — 0.89
• Relativistic electromagnetism — 0.88
• Faraday paradox — 0.88
• Casimir effect — 0.87

Computed from structural-signature embeddings · 2026-10-25