Electric Field and Basic Laws > s.a. Earnshaw's Theorem; electromagnetism; maxwell's field equations.
* Electric field: In terms of potentials, E = −∇φ + c−1 A,t, or Ei = −∂i A0 + ∂0 Ai, or Ea = Fab t b (with t a a unit timelike vector field).
$Coulomb's law: A formula for the electric field created by a point charge q in a vacuum, equivalent to Gauss' law (assuming linearity), E = k qr / r3 , where k = 1/4πε0 in the SI system, 1 in the cgs system . * Modifications: If we paramerize F ~ r−2+δ, the deviation δ of the exponent from 2 is at most about 10−17 (Richard Crandall 1983); If we set φ ~ r−1 exp{−em>μr}, μ = mc/$$\hbar$$, m can be interpreted as the photon mass (> see Proca Theory).$ Faraday's law of induction: Gives the electric field produced by a changing magnetic field, in the SI

C E · ds = −(d/dt) S B · dA ,   or   ∇ × E = −∂B/∂t .

@ Electric field: Ivezić PS(10) [Lorentz transformations].
@ Coulomb's law: Deser AJP(05)aug-gq/04 [from field theory]; Pinto IJMPD(05) [modification in a gravitational field, tests]; Neyenhuis et al PRL(07) + news pw(07)nov [proposed charged-particle matter-wave interferometry test down to δ about 10−22]; Pedram AJP(10)apr [in closed spaces]; Jaeckel & Roy PRD(10)-a1008 [spectroscopic tests]; Sheykhi & Hendi IJTP(11)-a1009 [entropic corrections]; Machet & Vysotsky PRD(11)-a1011 [in a superstrong magnetic field]; news APS(16)jun [history, Coulomb's work].
@ Solutions for simple situations: Rowley AJP(06)dec [finite uniform line of charge]; Zypman AJP(12)jan [charged ring and infinite line of charge].
@ Faraday's + Lenz's law: Wood et al AJP(04)mar [and conservation of energy]; Galili et al AJP(06)apr [teaching]; Redžić EJP(08) [derivations]; Giuliani EJP(10) [vector potential and physical meaning]; > s.a. phenomenology of magnetism [magnetic breaking].

Electric Currents > s.a. detection of gravitational waves; electronic technology; physics teaching [eddy currents]; units of measurement.
* Conductivity: What property of a solid determines whether electrons are free to move or not is not clear; One model is the Hubbard model; Atom-thick sheets of carbon, or graphene, conduct electricity better than any other known substance at room temperature.
* Ohm's law: It can be expressed as I = V/R or locally by J = σE, where R (the resistance) or σ (the conductivity) usually depend on the temperature; In superconductors, can be replaced by London's equations.
* London's equations: Equations relating E and J, that replace Ohm's law for superconductors,

c ∇(λJ) = −B ,   (∂/∂t)(λJ) = E   (in Gaussian units) .

@ Conductivity: Ahmedov & Ermanatov FPL(02)gq/06 [and gravitational effects]; Smolyaninov PRL(05) [metal-dielectric interface and fluctuations in n]; Vekilov & Isaev PLA(05) [T dependence near Anderson transition]; news ns(10)jul [mimicking graphene conductivity in silicon using lead]; news ieee(12)jan [validity of Ohm's law at the atomic level]; Bringuier EJP(13) [resistance of the vacuum]; Goodby Phy(14) [quantum fluctuations contribute to a metal's low-temperature resistance]; Bru & Pedra a1611-proc [microscopic explanation, and thermodynamics]; > s.a. Insulators; scattering [collision model].
@ Specific materials: news pt(18)dec [metal–insulator transition not accompanied by a structural change].
@ Resistors: Allen & Liu TPT(15)#2 [networks].

Other Concepts and Effects > s.a. electromagnetism and electromagnetism in matter; units.
* Thermoelectric effect: The fact that some materials conduct electricity when a temperature difference is established across them (Seebeck effect), or viceversa (Peltier effect); Basically, due to the fact that electron/hole flow carries heat; The effect is quantified by the Seebeck coefficient S:= VT (typically, for metals S ~ 10−6 V/K, and for semiconductors S ~ 10−3 V/K), but in practice the performance of a device built with a thermoelectric material needs to take into account its electric and thermal conductivity, and the temperature; Applications: Generating power in cars from waste heat instead of alternators; Late 1990s, Car makers are working on it.
* Biefeld-Brown effect: A force on an asymmetric capacitor [@ Bahder & Fazi ARL(03)phy/02].
* Ferroelectric materials: Materials exhibiting a spontaneous electric polarization that can be reversed by an applied electric field; This behavior is related to chemical composition and to the nanostructure of the material lattice.
@ Polarization: Maize & Williams AJP(04)may-mp/02 [polarizability of a particle in a δ-potential]; Dereli et al PLA(07)mp/06 [covariant description]; Silenko PPNL(14)-a1411 [polarizability of pointlike spin-1/2 particles].
@ Capacitors: Jackson AJP(99)feb [Thompson-Lampard theorem]; Parker AJP(02)may [field outside]; Bičák & Gürlebeck PRD(10)-a1008 [in general relativity]; news rd(12)jul [ultracapacitor delivers energy at a constant voltage]; Staunton AJP(14)sep [restoring force]; news pw(19)jan [negative capacitance in ferroelectric materials]; > s.a. Trouton-Noble Paradox.
@ Semiconductors: Stahl AJP(03)nov, Orton 04 [history]; Ridley 13 [quantum processes, r CP(14)]; Rammer 17 [quantum mechanics].
@ Thermoelectricity: Mahan et al PT(97)mar; Whitney PRL(14) [quantum effects on the operation of thermoelectric devices].
@ Related topics: Harpaz EJP(05) [electric field "falling" in gravity]; Saslow AJP(08)mar, Abruña et al PT(08)dec [batteries]; news nw(11)apr [neutral atoms made to act like charged particles in synthetic electric fields]; Williams AS(12)#4 [causes of static electricity]; news Phy(12)oct [promising candidates for ferroelectric materials]; > s.a. Continuous Media; Dipole Moment; earth [atmospheric electricity].

Electric Part of the Weyl Curvature > see weyl tensor.