concept

electric field

An electric field is a region around charged particles where electric forces act on other charges.
14 related articles · 5 formulas · 1 who worked here

Description

An electric field is an invisible force around charged objects. Like water around a magnet creating circles, the electric field draws lines along which a charge will move. When you touch synthetic clothing and hear a crackle, you are feeling the electric field.

History

Michael Faraday in 1831 introduced the concept of lines of force to visualize electric and magnetic interactions. James Clerk Maxwell in 1864 generalized the discoveries into equations, predicting electromagnetic waves. Hendrik Lorentz introduced the concept of the electromagnetic field as a separate entity and the Lorentz force for moving charges. Henri Poincaré studied the symmetries of Maxwell's equations and pointed out relativistic effects. The development of quantum electrodynamics in the works of Dirac and others built a bridge to the microworld.

How it works

The electric field E is defined by the force per unit test charge and obeys superposition. Maxwell's equation ∇·E = ρ/ε₀ (Gauss's law) relates the field to charge density. For electrostatics, the field is conservative, and the potential φ satisfies Poisson's equation. In dynamics, the electric field is also generated by a changing magnetic field (Faraday's law). In the relativistic formulation, the electromagnetic tensor F^{μν} combines the fields E and B. The quantum limit is described by Feynman diagrams with the photon as the U(1) gauge boson. Coulomb's law for a point charge gives E = k q / r².

Fun fact

Lightning is a giant discharge that occurs due to the huge difference in electric fields between clouds and the ground.

Concept graph →

Formulas

$$\nabla^2 \phi = V'(\phi)$$
Field minimizes Euclidean action in scalar theory.
What is in the formula
φvariableScalar field configuration — scalar field
∇²operatorLaplacian (sum of second spatial derivatives) — laplacian operator
\frac{\partial^2φ_b}{\partialx^2}+\frac{1}{x}\frac{\partialφ_b}{\partialx}=v'(φ_b) · 2607.06680
$$V(z) = \phi - eFz - \frac{e^2}{4\pi\epsilon_0 z}$$
Potential energy for electron emission including work function and field.
What is in the formula
Vvariablepotential energy of electron — potential energy joule
zvariabledistance from the metal surface — position metre
φvariablework function of the metal — work function joule
Fvariableapplied electric field strength — electric field volt per metre
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
ε0constantability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre
$$\Delta n \propto r E$$
Refractive index change proportional to electric field.
What is in the formula
ΔnvariableChange in refractive index — refractive index change
EvariableApplied electric field — electric field volt per metre
rconstantPockels coefficient (linear electro-optic coefficient) — pockels coefficient = varies by material (e.g., 30.8e-12 for L metre per volt
$$\mathcal{L} = g_{a\gamma\gamma} a \mathbf{E} \cdot \mathbf{B}$$
Lagrangian term coupling axion to electromagnetic fields.
What is in the formula
avariableaxion field — axion field
Evariableelectric field — electric field volt per metre
Bvariablemagnetic field — magnetic field strength tesla
g_{aγγ}constantStrength of the interaction between axions and two photons. — axion photon coupling constant = model-dependent
$$a_0 = \frac{e E_0}{m_e c \omega}$$
Dimensionless parameter comparing electron oscillation energy to rest mass.
What is in the formula
a_0variablerelativistic intensity parameter (normalized vector potential) — relativistic parameter
E_0variablepeak electric field amplitude of the laser — electric field volt per metre
ωvariableangular frequency of the laser — angular frequency radian per second
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
m_econstantmass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
cconstantuniversal speed limit of light in vacuum — speed of light = 299792458 metre per second

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