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In physics and chemistry, charge is fundamentally related to fields and forces, and is a property of pieces of matter that leads to attraction to (or repulsion from) spatially separate pieces of matter that likewise manifest that particular property. There are a wide variety of such charges, including the electric charge underlying electric current that enters Maxwell's equations for the electromagnetic field, color charge that enters the chromodynamic forces, mass that enters gravitation and a number of others.[1]
These charges are conserved quantities and are related to currents describing their flux or motion. The conservation law relating the charge to its current is of the form:
where div is the vector divergence operator, J is the vector current density, and ρ is the charge density. For a volume enclosed by a surface, this equation can be expressed by the statement that any change in the charge contained inside the closed surface is due to a current of said charge either entering or exiting through that surface.
Such conservation laws are examples of Noether's theorem, which states that every symmetry of a physical theory is related to a conservation law of this kind. This theorem is closely related to Curie's principle:
- The symmetry of an isolated system cannot decrease as the system evolves with time.[2]
The best known of these conservation laws are the conservation of momentum (the current is momentum density, the charge is mass density), related to translational symmetry of the laws of mechanics, conservation of angular momentum, related to the rotational symmetry of the laws of mechanics, and conservation of energy, related to the time-independence of the laws of mechanics. Such symmetries are intuitive for point particle mechanics, but for the physics of general fields some symmetries are quite non-intuitive.
Electrodynamics
In electrodynamics, two types of charge are known, magnetic and electric. The distinguishing property of electric charge is that electric charges can be isolated, while while an isolated magnetic charge or magnetic monopole never has been observed.[3][4][5][6] Electric charges interact with magnetic charges only when in relative motion one to the other.
The conservation of electric charge follows directly from Maxwell's equations. It also can be derived from Noether's theorem as a result of a gauge invariance of Maxwell's theory when that theory is expressed in terms of a vector potential. Although this approach has continuity with much of modern field theory, it is somewhat unintuitive, as the "symmetry" of the recast Maxwell equations is simply due to introduction of a mathematical device that adds an unnecessary degree of freedom into the formulation thereby introducing this symmetry artificially.
Chromodynamics
In the physics of quantum chromodynamics, the successor to quantum elecrodynamics, color charge is recognized as a property of quarks.[7] Similar to magnetic charge, color is not seen directly, as all observable particles have no overall color.[8] Color charge causes interaction between charged entities via the chromoforce, also called the color force. As with electric and magnetic charge, color charge can be multiple valued, conventionally called red, green or blue. Color charge is not assigned a numerical value; however, a superposition in equal amounts of all three colors leads to a "neutral" color charge, a somewhat stretched analogy with the superposition of red, green and blue light to produce white light.[9] Thus, protons and neutrons, which consist of three quarks with all three colors are color-charge neutral. Quark combinations are held together by exchange of combinations of eight different gluons that also are color charged.[10][11][12][13]
The color charges of antiquarks are anticolors. The combination of a quark and an antiquark to form a meson, such as a pion, kaon and so forth, leads to a neutral color charge.
Other charges
The charges above are related to fields and forces and to a local (coordinate dependent) Noether's theorem. Other charges are known, however, that are connected to global symmetries (no coordinate dependence) and a global Noether's theorem, and have no relation to forces or fields.
One such charge in elementary particle theory is the baryonic charge, B, with value +1 for all baryons (notably, neutrons and protons, but also others like the Λ and Σ particles) and −1 for all antibaryons and zero for non-baryons. Quarks have a baryon number of 1/3. Unlike electric charge, which serves as a source for the electromagnetic field, baryon charge is not related to an associated "baryonic" field.[14]
Finally, we mention the leptonic charge carried by electrons and neutrinos.[9] Lepton charge also is referred to as a flavor[15] Le, Lμ, Lτ with values +1 for the electron, muon and tau meson, and −1 for their antiparticles.[14] The total lepton flavor L of a complex is:
Non-leptons have a total lepton flavor L of zero. Lepton charge is not necessarily conserved in particle reactions.[14]p. 38
References
- ↑ Mark Burgess (2004). “Chapter 12: Charge and current”, Classical covariant fields. Cambridge University Press, pp. 325 ff. ISBN 0521813638.
- ↑ Some care is needed in looking at this principle because of the phenomenon of spontaneous symmetry breaking. For example, as a cubic ferroelectric material like BaTiO3 is cooled below its Curie point, its cubic symmetry is replaced by a tetragonal ferroelectric symmetry. The overall cubic symmetry of the crystal is retained because the crystal breaks into finite domains, each with a differently oriented tetragonal axis, so that statistically the symmetry of an infinite crystal still is cubic. For a general discussion, see F. Strocchi (2008). Symmetry breaking, 2nd ed. Springer. ISBN 3540735925.
- ↑ Douglas C. Giancoli. Physics for scientists and engineers with modern physics, 4rth ed. Pearson Education, p. 708. ISBN 0132273594.
- ↑ Gibilisco S. (2005). “Chapter 2: Charge, current, voltage”, Electricity Demystified. McGraw-Hill. ISBN 0071439250. An entry level account by Stan Gibilisco, an electronics engineer and mathematician, author of numerous technical books on electronics and mathematics.
- ↑ Glenn Elert (1998-2010). The electric charge: Summary. The Physics Hypertextbook. Retrieved on 2011-07-27.
- ↑ Glenn Elert (1998-2010). The electric charge: Discussion. The Physics Hypertextbook. Retrieved on 2011-07-27.
- ↑ Stephen Webb (2004). Out of this world: colliding universes, branes, strings, and other wild ideas of modern physics. Springer, p. 190. ISBN 0387029303.
- ↑ Andrew Watson (2004). The quantum quark. Cambridge University Press, pp. 170 ff. ISBN 0521829070.
- ↑ 9.0 9.1 M. Y. Han (1999). Quarks and gluons: a century of particle charges. World Scientific, p. 116. ISBN 9810237456.
- ↑ Joe Rosen (2004). Encyclopedia of physics. Infobase Publishing, p. 85. ISBN 0816049742.
- ↑ Joe Rosen, Lisa Quinn Gothard (2009). Encyclopedia of Physical Science, Volume 1. Infobase Publishing, p. 278. ISBN 0816070113.
- ↑ (2009) “Quantum chromodynamics (QCD)”, Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert: Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy. Springer, pp. 524 ff. ISBN 3540706224.
- ↑ OW Greenberg (2008). "The color charge degree of freedom in particle physics". Chapter in Greenberger et al. below.
- ↑ 14.0 14.1 14.2 O. M. Boyarkin, Alfred L. Heinzerton (2007). Introduction to Physics of Elementary Particles. Nova Publishers, pp. 39-40. ISBN 160021200X.
- ↑ Paul Allen Tipler (2007). “Summary table”, Physics for scientists and engineers: Elementary modern physics, Volume 3, 6th ed. Macmillan, p. 1409. ISBN 1429201347.