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| {{Electromagnetism|cTopic=[[Classical electromagnetism|Electrodynamics]]}}
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| '''Weber electrodynamics''' is an alternative to [[Maxwell's Equations|Maxwell electrodynamics]] developed by [[Wilhelm Eduard Weber]]. In this theory, [[Coulomb's Law]] becomes velocity dependent. The theory is widely rejected and ignored by contemporary physicists, and is not even mentioned in mainstream textbooks on [[classical electromagnetism]].
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| ==Mathematical Description==
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| According to Weber electrodynamics, the force (F) acting simultaneously on point charges <math>q_1</math> and <math>q_2</math>, is given by
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| <math> \mathbf{F} = \frac{q_1 q_2 \mathbf{\hat{r}}}{4 \pi \epsilon_0 r^2}(1-\frac{\dot{r}^2}{2 c^2}+\frac{r\ddot{r}}{c^2}) </math>
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| where <math>\mathbf{r}</math> is the vector connecting <math>q_1</math> and <math>q_2</math>, the dot denotes a time [[derivative]] and <math>c</math> is the [[speed of light]]. In the limit that speeds and accelerations are small (i.e. <math>\dot{r}<<c</math>), this reduces to the usual Coulomb's law.<ref name=assis>{{cite journal|last=Assis|first=AKT|coauthors=HT Silva|title=Comparison between Weber’s electrodynamics and classical electrodynamics|journal=Pramana - journal of physics|date=September 2000|volume=55|issue=3|pages=393–404}}</ref>
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| This can be derived from the [[potential energy]]
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| <math> U_{Web} = \frac{q_1 q_2}{4 \pi \epsilon_0 r}(1-\frac{\dot{r}^2}{2 c^2}) </math>
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| This can be contrasted with the approximate potential energy from Maxwellian electrodynamics (where <math>v_1</math> and <math>v_2</math> are the velocities of <math>q_1</math> and <math>q_2</math>, respectively):<ref name=assis/>
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| <math> U_{Max} =\frac{q_1 q_2}{4 \pi \epsilon_0 r}(1-\frac{\mathbf{v_1}\cdot\mathbf{v_2}+(\mathbf{v_1}\cdot\mathbf{\hat{r}})(\mathbf{v_2}\cdot\mathbf{\hat{r}})}{2 c^2}) </math>
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| (This only includes terms up to order <math>(v/c)^2</math> and therefore neglects relativistic and retardation effects; see [[Darwin Lagrangian]].)
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| Using these expressions, the regular form of [[Ampere's law]] and [[Faraday's law of induction|Faraday's law]] can be derived. Importantly, this theory does not predict an expression like the [[Biot-Savart law]] and testing differences between Ampere's law and the Biot-Savart law is one way to test Weber electrodynamics.<ref>{{cite journal|last=Assis|first=AKT|coauthors=JJ Caluzi|title=A limitation of Weber's law|journal=Physics Letters A|year=1991|volume=160|issue=1|pages=25–30|bibcode = 1991PhLA..160...25A |doi = 10.1016/0375-9601(91)90200-R }}</ref>
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| ==Newton's third law versus Maxwell and Weber electrodynamics==
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| In [[Maxwell's equations|Maxwell electrodynamics]], [[Newton's third law]] does not hold for particles. Instead, particles exert forces on electromagnetic fields, and fields exert forces on particles, but particles do not ''directly'' exert forces on other particles. Therefore, two nearby particles need not experience equal and opposite forces. Related to this, Maxwell electrodynamics predicts that the laws of [[conservation of momentum]] and [[conservation of angular momentum]] are valid ''only'' if
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| *the momentum of particles ''and''
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| *the momentum of surrounding electromagnetic fields
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| are taken into account. Particles, if isolated from any electromagnetic field, will not satisfy these laws necessarily, because the particles may transfer some of their momentum to electromagnetic fields or vice-versa. The well-known phenomenon of [[radiation pressure]] can demonstrate that electromagnetic waves are able to "push" on matter. See [[Maxwell stress tensor]] and [[Poynting vector]] for further details.
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| The Weber force law is quite different: All particles, regardless of size and mass, will exactly follow [[Newton's third law]]. Therefore, Weber electrodynamics, unlike Maxwell electrodynamics, has conservation of ''particle'' momentum and conservation of ''particle'' angular momentum.
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| ==Predictions==
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| When applied to gravitation, it has been claimed to predict the [[perihelion precession of Mercury]], and has been used to explain various phenomena such as wires exploding when exposed to high [[Electric current|current]]s.<ref>{{cite journal|last=Wesley|first=JP|title=Weber electrodynamics, part I. general theory, steady current effects|journal=Foundations of Physics Letters|year=1990|volume=3|issue=5|pages=443–469|doi=10.1007/BF00665929|bibcode = 1990FoPhL...3..443W }}</ref>
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| ==Limitations==
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| Despite various efforts, a velocity and/or acceleration dependent correction to Coulomb's law has never been [[Tests of electromagnetism|observed]], as described in the next section. Moreover, [[Helmholtz]] observed that Weber electrodynamics predicted that under certain configurations charges can act as if they had negative [[inertial mass]], which has also never been observed.
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| ==Experimental tests==
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| ===Velocity Dependent Tests===
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| [[Velocity]] and [[acceleration]] dependent corrections to Maxwell's equations arise in Weber electrodynamics. The strongest limits on a new velocity dependent term come from evacuating gasses from containers and observing whether the [[electrons]] become [[Electric charge|charge]]d. However, because the electrons used to set these limits are [[atom|Coulomb bound]], [[renormalization]] effects may cancel the velocity dependent corrections. Other searches have spun current-carrying [[solenoids]], observed metals as they cooled, and used [[superconductors]] to obtain a large drift velocity.<ref>{{cite journal|last=Lemon|first=DK|coauthors=WF Edwards, CS Kenyon|title=Electric potentials associated with steady currents in superconducting coils|journal=Physics Letters A|year=1992|volume=162|issue=2|pages=105–114|bibcode = 1992PhLA..162..105L |doi = 10.1016/0375-9601(92)90985-U }}</ref> None of these searches have observed any discrepancy from Coulomb's law. Observing the charge of [[particle beams]] provides weaker bounds, but tests the velocity dependent corrections to Maxwell's equations for particles with higher velocities.<ref>{{cite journal|last=Walz|first=DR|coauthors=HR Noyes|title=Calorimetric test of special relativity|journal=Physical Review A|date=April 1984|volume=29|issue=1|pages=2110–2114|bibcode = 1984PhRvA..29.2110W |doi = 10.1103/PhysRevA.29.2110 }}</ref><ref>{{cite journal|last=Bartlett|first=DF|coauthors=BFL Ward|title=Is an electron's charge independent of its velocity?|journal=Physical Review D|date=15 December 1997|volume=16|issue=12|pages=3453–3458}}</ref> | |
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| ===Acceleration Dependent Tests===
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| Test charges inside a spherical conducting shell will experience different behaviors depending on the force law the test charge is subject to.<ref>{{cite journal|last=Junginger|first=JE|coauthors=ZD Popovic|title=An experimental investigation of the influence of an electrostatic potential on electron mass as predicted by Weber’s force law|journal=Can. J. Phys.|year=2004|volume=82|pages=731–735|doi=10.1139/p04-046|bibcode = 2004CaJPh..82..731J }}</ref> By measuring the [[oscillation frequency]] of a [[neon lamp]] inside a spherical conductor biased to a high voltage, this can be tested. Again, no significant deviations from the Maxwell theory have been observed.
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| ==References==
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| {{Reflist}}
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| [[Category:Electrodynamics]]
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| [[Category:Electromagnetism]]
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There is not any doubt...
Even though a lot of carpet maintenance might seem like a lot of additional work, you"ll certainly find that it"s worth it whenever you get many more years out of the carpets in the house. Additionally, correct carpet care will keep your home looking beautiful provided that you reside there. It"s recommended to make sure the long life of the carpet people should contact the carpet cleaning company San Jose California for the manipulation life of the carpet in way.
There"s undoubtedly about the health benefit that individuals might get while choosing the carpet cleaning practices or even the sources, as there is nothing such as the feel of walking barefoot over a freshly cleaned carpet. When a carpet is installed for the very first time, it exaggerate the look of the walls and the home floor.
Whether it is from stains, holes, or perhaps normal wear and tear over a carpet, you will start to notice symptoms of aging as your carpet ages. Nevertheless, this does not need to be the case! With proper carpet care and preservation, you"ll be able to keep your carpet seeking newer for longer by selecting reliable and professional carpet cleansing Orange County, and you"ll also be able to extend the lifetime of your carpet.
The most important things that you need to consider regarding rug treatment may also be the simplest things to accomplish. Firstly, you need to cleanup any spills as soon as they happen. Learn further on our affiliated link by navigating to office cleaning service. This will decrease the likelihood of spots, and will also keep the spots from soaking too far to the carpet. Be taught more on the affiliated web resource - Click here: Members - Daytime Confidential. You must also ensure that you carpet dry cleaning regularly - one or more times per week if you can handle it. That way, you will be able to keep the dirt that gets monitored on your carpet from getting ground too far into it. You"ll also decrease the mess occurring when there are leaks.
You must be sure that you get your carpet absolutely cleaned once everybody to three years according to how much wear and tear it sees all through those years. For children"s rooms and other areas of the home that see a lot of wear, you might want to think about best carpet products for cleaning the carpet at least once a year. Clicking cleaning company vancouver likely provides aids you should use with your girlfriend. For other locations of the house, you may only need to perform a full cleaning once every couple of years..Techniclean Industries Corp
Unit # 211-7184-120 Street,
Surrey, BC
V3W 0M6
(604) 265-5577
www.technicleanindustries.org
info@technicleanindustries.com
For those who have virtually any queries about where by as well as the best way to make use of children s health (Get the facts), you can e mail us from the website.