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* .

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**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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send feedback and suggestions to bombelli at olemiss.edu – modified 16 feb 2018