查看“︁力场 (物理)”︁的源代码

[[Image:GravityPotential.jpg|thumb|300px|均匀球体内部和周围引力势能的2维截面。截面[[拐点]]位于球体表面。]]

[[物理学]]中，'''力场'''是与作用于不同位置的[[质点]]上的[[非接触力]]对应的[[向量场]]。具体来说，力场是向量场<math>\vec{F}</math>，其中<math>\vec{F}(\vec{x})</math>是质点在<math>\vec{x}</math>处受到的力。<ref>[https://books.google.com/books?id=akbi_iLSMa4C&pg=PA211 Mathematical methods in chemical engineering, by V. G. Jenson and G. V. Jeffreys, p211]</ref>

==例子==
*[[引力]]是两个物体之间的吸引力。引力场模拟了大质量物体（或更广义地说，任何[[质能等价|能量]]量）对周围空间的影响。<ref>{{cite book
|title=General relativity from A to B
|first1=Robert
|last1=Geroch
|publisher=University of Chicago Press
|year=1981
|isbn=0-226-28864-1
|page=181
|url=https://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181
|access-date=2023-11-08
|archive-date=2023-01-25
|archive-url=https://web.archive.org/web/20230125211945/https://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181
|dead-url=no
}}, [https://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181 Chapter 7, page 181] {{Wayback|url=https://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181 |date=20230125211945 }}</ref>在[[牛顿万有引力定律]]中，质量为''M''的粒子会产生[[引力场]]<math>\vec{g}=\frac{-G M}{r^2}\hat{r}</math>，其中径单位向量<math>\hat{r}</math>指向远离粒子的方向。质量为''m''的轻质粒子在靠近[[地球]]表面时受到的引力由<math>\vec{F} = m \vec{g}</math>，其中''g''是[[地球引力]]。<ref>[https://books.google.com/books?id=LiRLJf2m_dwC&pg=PA288 Vector calculus, by Marsden and Tromba, p288]</ref><ref>[https://books.google.com/books?id=bCP68dm49OkC&pg=PA104 Engineering mechanics, by Kumar, p104]</ref>
*[[电场]]<math>\vec{E}</math>对点电荷''q''施加的力为<math>\vec{F} = q\vec{E}</math>。<ref>[https://books.google.com/books?id=9ue4xAjkU2oC&pg=PA1055 Calculus: Early Transcendental Functions, by Larson, Hostetler, Edwards, p1055]</ref>
*[[磁场]]<math>\vec{B}</math>中，在磁场中运动的点电荷会受到与速度和磁场方向垂直的力，其关系为<math>\vec{F} = q\vec{v}\times\vec{B}</math>。

== 功 ==
功取决于位移和作用在物体上的力。当质点沿路径''C''在力场中运动时，力做[[功]]为[[曲线积分]]：
:<math> W = \int_C \vec{F} \cdot d\vec{r}</math>

此值与粒子沿路径移动的[[速度]]/[[动量]]无关。

=== 保守场 ===
对[[保守力|保守场]]来说，它也与路径本身无关，只取决于始终点。因此，在起点与终点重合的闭合路径上运动的物体的功为0：

:<math> \oint_C \vec{F} \cdot d\vec{r} = 0</math>
认识到保守矢量场可以写成某个标量势函数的梯度，可以更容易地评估所做的功：

:<math> \vec{F} = -\nabla \phi</math>

功就是起点和终点的电势值之差。如果这两个点分别为''x'' = ''a''、''x'' = ''b''，则：

:<math> W = \phi(b) - \phi(a) </math>

==另见==
* [[经典力学]]
* [[场线]]
* [[力]]
* [[功]]

==参考文献==
{{Reflist}}

== 外部链接 ==
{{wikiquote}}
* [http://farside.ph.utexas.edu/teaching/301/lectures/node59.html Conservative and non-conservative force-fields] {{Wayback|url=http://farside.ph.utexas.edu/teaching/301/lectures/node59.html |date=20210419134703 }}, [http://farside.ph.utexas.edu/teaching/301/lectures/lectures.html Classical Mechanics] {{Wayback|url=http://farside.ph.utexas.edu/teaching/301/lectures/lectures.html |date=20220205083438 }}, University of Texas at Austin

{{Authority control}}

[[Category:力]]