Electrostatics
Electrostatics studies electric charges at rest and the time-independent electric fields, potentials, and forces they produce.
Definition
The study of the forces, fields, and potentials arising from electric charges that are static or in steady-state equilibrium, governed by Coulomb's law and, equivalently, by Gauss's law and the irrotational nature of the electrostatic field.
Scope
Electrostatics is the branch of electromagnetism concerned with stationary charge distributions and the fields, potentials, energies, and forces associated with them. It covers Coulomb's law, the electrostatic field and potential, Gauss's law, the behaviour of conductors and dielectrics in static fields, capacitance, and the solution of Laplace's and Poisson's equations under given boundary conditions. It excludes time-varying phenomena such as magnetic effects of currents and electromagnetic radiation, which require the full electrodynamic treatment.
Sub-topics
Core questions
- What force does one static charge distribution exert on another?
- How is the electric field determined from a given charge distribution, and vice versa?
- How do conductors and dielectrics rearrange charge in response to applied fields?
- How are the potential and field found when only boundary values are known?
Key concepts
- electric charge
- electric field
- electrostatic potential
- Gauss's law
- permittivity
- electric flux
- field lines
- electrostatic energy
Key theories
- Coulomb's law
- The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them, directed along the line joining them.
- Gauss's law
- The electric flux through any closed surface equals the enclosed charge divided by the permittivity, providing an integral form of the inverse-square law and a powerful tool for symmetric problems.
- Electrostatic potential theory
- Because the electrostatic field is irrotational, it derives from a scalar potential satisfying Poisson's equation (Laplace's equation in charge-free regions), reducing field problems to boundary-value problems.
Clinical relevance
Electrostatics underpins capacitor design, electrostatic precipitators, xerography and laser printing, electrostatic discharge protection in electronics, and the modelling of charged biological membranes and macromolecules.
History
Quantitative electrostatics began with Coulomb's torsion-balance measurements in the 1780s establishing the inverse-square force law. Poisson and Gauss developed the potential-theoretic formulation in the early nineteenth century, and Faraday introduced the intuitive picture of field lines and the role of the surrounding medium, which Maxwell later cast in field-theoretic terms.
Key figures
- Charles-Augustin de Coulomb
- Carl Friedrich Gauss
- Siméon Denis Poisson
- Michael Faraday
Related topics
Seminal works
- jackson1998
- griffiths2017
- purcell2013
Frequently asked questions
- How does Gauss's law relate to Coulomb's law?
- Gauss's law is mathematically equivalent to Coulomb's inverse-square law for static fields; it restates the same physics in terms of flux through closed surfaces and is especially convenient when the charge distribution has high symmetry.
- Why is the electric field zero inside a conductor in electrostatic equilibrium?
- Mobile charges in a conductor redistribute until the net field inside vanishes; any residual field would drive further current, contradicting the assumption of static equilibrium.