Electricity| Electricity |
Basic Laws > s.a. Earnshaw's
Theorem; electromagnetism; maxwell's
field equations.
* Electric field:
In terms of potentials, E = –
+ 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: The electric
field created by a point charge q in a vacuum is
E = k qr / r3
, where k = 1/4
0
in the SI system, 1 in the cgs system .
Equivalent to Gauss' law, assuming linearity.
* Modifications:
If we paramerize F 
r^{–2+
},
the deviation
of the exponent from
2 is at most about 10–17 (Richard Crandall
1983); If we set r–1 exp{–
r}, = mc/
,
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
.
@ 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 about
10–22].
@ Solutions for simple situations: Rowley AJP(06)dec
[finite uniform 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]; Levin et al AJP(06)sep
[electromagnetic breaking, terminal speed]; Redzic EJP(08)
[derivations].
Electricity in Matter > s.a. earth [atmosphere and thunderstorms]; Insulators; particle
effects [creation]; technology [ferroelectrics].
* Permittivity: The second
rank tensor (usually
identified with a scalar) such that D = E.
* Dielectric constant:
* Dielectric strength:
The maximum value of the electric field before dielectric
breakdown occurs.
@ And life, health: Bastian PT(94)feb
[in fish]; Eisenberg SA(98)jun [defibrillation].
@ Dielectric
breakdown: Garroni et al PRS(01);
Arrayás & Trueba CP(05)
[pre-breakdown streamers].
@ Related topics: news PT(00)may,
news pw(07)mar
[ < 0];
Wesenberg & Molmer PRL(04)qp [random
dipole distribution].
Electric Current > s.a. detection
of gravitational radiation; electronic
technology.
* Conductivity: What
property of a solid determines whether electrons are free to move or not
is not clear; One model is the Hubbard model.
* Ohm's law: Can be expressed
as I = V/R or locally by J = 
E,
where R (the resistance) or (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 (
J)
= –B , (/t)(J)
= E (Gaussian units) .
@ Resistors: Romano & Price AJP(96)sep
[conical]; Wu JPA(04)mp [2-pt
resistance and network Laplacian].
@ Negative resistance:
Zudov et al PRL(06)
+ pn(06)jun;
+ Kaya & Eberl PRL(07)
+ pw(07)may
[in 2D electron gases].
@ 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]; > s.a. scattering [collision model].
@ Related topics: news pw(06)jun
[bi-directional single-electron ammeter]; news pw(08)apr
[memristors]; news pn(08)may [piezoresistance].
Other Concepts and Effects > s.a. Dipole
Moment; earth [atmospheric electricity]; electromagnetism;
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/
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: Generate 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].
@ Polarization: Maize & Williams AJP(04)may-mp/02
[polarizability of particle
in -potential]; Dereli
et al PLA-mp/06
[covariant description].
@ Capacitors: Jackson AJP(99)feb
[Thompson-Lampard theorem]; Parker AJP(02)may
[field outside]; > s.a. Trouton-Noble Paradox.
@ Related topics: Mahan et al PT(97)mar
[thermoelectricity]; Stahl AJP(03)nov,
Orton 04
[semiconductors, history]; Harpaz EJP(05)
[E field "falling" in gravity]; Saslow AJP(08)mar,
Abruña et al PT(08)dec
[batteries].
Electric Part of the Weyl Curvature > see weyl tensor.
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send feedback and suggestions to bombelli at olemiss.edu – modified 24
oct 2009