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 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].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:= V/ΔT
(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.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 20 apr 2019