Field

Columbia Electronic Encyclopedia - Cite This Source

field, in algebra, set of elements (usually numbers) that may be combined under the operations of addition and multiplication so that it constitutes an additive group, the nonzero elements form a multiplicative group, and multiplication distributes over addition. The set of real numbers (see number) and the set of complex numbers are both examples of fields.

The Columbia Electronic Encyclopedia Copyright © 2004, Columbia University Press.
Licensed from Columbia University Press

30 More from Columbia Encyclopedia »

Field

Columbia Electronic Encyclopedia - Cite This Source

field, in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. The field concept was developed by M. Faraday based on his investigation of the lines of force that appear to leave and return to a magnet at its poles (see flux, magnetic). Fields are used to describe all cases where two bodies separated in space exert a force on each other. The alternative to postulating a field is to assume that physical influences can be transmitted through empty space without any material or physical agency. Such action-at-a-distance, especially if it occurs instantaneously, violates both common sense and certain modern theories, notably relativity, which posits that nothing can travel faster than light. In a field description, rather than body A directly exerting a force on body B, body A (the source) creates a field in every direction around it and body B (the detector) experiences the field that exists at its position. If a change occurs at the source, its effect propagates outward through the field at a constant speed and is felt at the detector only after a certain delay in time. The field is thus a kind of "middleman" for transmitting forces. Each type of force (electric, magnetic, nuclear, or gravitational) has its own appropriate field; a body experiences the force due to a given field only if the body itself it also a source of that kind of field. The reciprocity implied by Newton's third law of motion (equal action and reaction) is thus preserved. If two bodies exert a mutual force, they possess potential energy that depends on their relative positions; it is natural to regard this energy as residing in the field the bodies create.

The Columbia Electronic Encyclopedia Copyright © 2004, Columbia University Press.
Licensed from Columbia University Press

30 More from Columbia Encyclopedia »

Field

Wikipedia, the free encyclopedia - Cite This Source

Field or fields may refer to:

• Field (agriculture), an area of land used to cultivate crops for agricultural purposes
• Field of study, a branch of knowledge
• Playing field, in sports, the area in which the sport is played
• Visual field or field of view, the area visible from a point of view (it can be a camera or an eye)
• Depth of field, in photography, the distance in front of and beyond the subject that appears to be in focus

Science and mathematics

• Field (mathematics), an algebraic system with well-behaved addition, multiplication, and division
• Vector field, a field of vectors on a space, which is an example of a tensor field
• Field (physics), an assignment of a quantity to every point of space, especially a tensor field
• Field (geography), with a definition similar to that of physics but in a different context and using unique models and methods
• Field (computer science), a smaller piece of data from a larger collection (e.g., database fields)
• Field of sets, a mathematical structure of sets in an abstract space

Sociology and politics

• Field (Bourdieu), a sociological term coined by Pierre Bourdieu to describe the system of objective relations constituted by various species of capital
• Field Department, the division of political campaigns tasked with organizing local volunteers and directly contacting voters

Other technical uses

• Field (video), one half of a frame in an interlaced display
• Field (heraldry), the background of a shield
• In flag terminology, the background of a flag

Persons

• Totie Fields, an American comedian
• W.C. Fields, an American comedian
• John Charles Fields, a Canadian mathematician and founder of the Fields Medal
• John Field (composer), an Irish classical music composer
• Joshua Field, British civil engineer
• Todd Field, American film director
• The Field (musician), a.k.a. Axel Willner, a Swedish electronic musician

Place names

• Field, British Columbia
• Field, Minneapolis, Minnesota

Objects

• Field (sculpture), a sculpture by Anthony Gormley
• Murray Field Airport

Brand names

• Fields (department store), a chain of discount department stores operating in the Canadian provinces of Alberta and British Columbia
• Field's, a shopping centre in Denmark.
• Field and Stream, a US magazine featuring hunting, fishing, and other outdoor activities
• FIELD, a literary magazine http://www.oberlin.edu/ocpress/field.html
• Field Records, a record label
• Fields (band), an indie rock band.

See also

• The Field (disambiguation)
• Meadow
• Paddock
• Fielding
• Feld
• Fields Medal

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)
This article is licensed under the GNU Free Documentation License.
Last updated on Sunday March 02, 2008 at 07:56:09 PST (GMT -0800)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

4,242 More from Wikipedia »