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The | {{Other uses|Force field (disambiguation)}} | ||
[[Image:GravityPotential.jpg|thumb|300px|Plot of a two-dimensional slice of the gravitational potential in and around a uniform spherical body. The [[inflection point]]s of the cross-section are at the surface of the body.]] | |||
In [[physics]] a '''force field''' is a [[vector field]] that describes a [[non-contact force]] acting on a particle at various positions in [[space]]. Specifically, a force field is a vector field <math>\vec{F}(\vec{x})</math>, where <math>\vec{F}</math> is the force that a particle would feel if it were at the point <math>\vec{x}</math>.<ref>[http://books.google.com/books?id=akbi_iLSMa4C&pg=PA211 Mathematical methods in chemical engineering, by V. G. Jenson and G. V. Jeffreys, p211]</ref> | |||
==Examples of force fields== | |||
*In [[Newtonian gravity]], a particle of mass ''M'' creates a [[gravitational field]] <math>\vec{g}=\frac{-G M}{r^2}\hat{r}</math>, where the radial unit vector <math>\hat{r}</math> points away from the particle. The gravitational force experienced by a particle of mass ''m'' is given by <math>\vec{F} = m \vec{g}</math>. This field <math>\vec{F}</math> is the force field for gravity.<ref>[http://books.google.com/books?id=LiRLJf2m_dwC&pg=PA288 Vector calculus, by Marsden and Tromba, p288]</ref><ref>[http://books.google.com/books?id=bCP68dm49OkC&pg=PA104 Engineering mechanics, by Kumar, p104]</ref> | |||
*An [[electric field]] <math>\vec{E}</math> is a vector field. It exerts a force on a [[point charge]] ''q'' given by <math>\vec{F} = q\vec{E}</math>. This field <math>\vec{F}</math> is the electric force field.<ref>[http://books.google.com/books?id=9ue4xAjkU2oC&pg=PA1055 Calculus: Early Transcendental Functions, by Larson, Hostetler, Edwards, p1055]</ref> | |||
==Restriction to position-dependent forces== | |||
Some forces, including [[friction]], [[air drag]], and the [[Lorentz force|magnetic force]] on a charged particle, depend on the particle's velocity as well as its position. Therefore these forces are not characterized by a force field. | |||
==Work done by a force field== | |||
As a particle moves through a force field along a path ''C'', the work done by the force is a [[line integral]] | |||
:<math> W = \int_C \vec{F} \cdot d\vec{r}</math> | |||
This value is independent of the velocity/momentum that the particle travels along the path. For a [[conservative force|conservative force field]], it is also independent of the path itself, but depends only on the starting and ending points. Therefore, if the starting and ending points are the same, the work is zero for a conservative force field. | |||
==See also== | |||
* [[Field line]] | |||
* [[Force]] | |||
==References== | |||
{{Reflist}} | |||
{{DEFAULTSORT:Force Field (Physics)}} | |||
[[Category:Force]] | |||
{{Classicalmechanics-stub}} | |||
{{Electromagnetism-stub}} | |||
Revision as of 03:47, 13 December 2013
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In physics a force field is a vector field that describes a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field , where is the force that a particle would feel if it were at the point .[1]
Examples of force fields
- In Newtonian gravity, a particle of mass M creates a gravitational field , where the radial unit vector points away from the particle. The gravitational force experienced by a particle of mass m is given by . This field is the force field for gravity.[2][3]
- An electric field is a vector field. It exerts a force on a point charge q given by . This field is the electric force field.[4]
Restriction to position-dependent forces
Some forces, including friction, air drag, and the magnetic force on a charged particle, depend on the particle's velocity as well as its position. Therefore these forces are not characterized by a force field.
Work done by a force field
As a particle moves through a force field along a path C, the work done by the force is a line integral
This value is independent of the velocity/momentum that the particle travels along the path. For a conservative force field, it is also independent of the path itself, but depends only on the starting and ending points. Therefore, if the starting and ending points are the same, the work is zero for a conservative force field.
See also
References
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