Electricity |

**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 *E*_{i}
= –∂_{i}* A*_{0}
+ ∂_{0} *A*_{i},
or *E*_{a} = *F*_{ab}
*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* *q***r** /* r*^{3}
, where *k* = 1/4π*ε*_{0}
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{–*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** · d**s** = –(d/d*t*)
∫_{}_{S}** B** · d**A** , 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 Current**s > 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__: Can be expressed
as *I* = *V*/*R* or locally by *J* = *σ**E*,
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* ∇(*λ***J**)
= –**B** , (∂/∂*t*)(*λ***J**)
= **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].

@ __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*:= *V*/Δ*T* (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]; > 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.

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