Siteadmin, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators
125,790
edits
Changes
Jump to navigation
Jump to search
Conservative vector (view source)
Revision as of 01:05, December 26, 2009
, 01:05, December 26, 2009a start
A '''conservative field''' or '''conservative vector''' has a [[curl]] of zero:
:<math>\nabla \times \vec V = (\ \ \frac{\partial V_z}{\partial y} - \frac{\partial V_y}{\partial z},\ \ \ \ \frac{\partial V_x}{\partial z} - \frac{\partial V_z}{\partial x},\ \ \ \ \frac{\partial V_y}{\partial x} - \frac{\partial V_x}{\partial y}\ \ ) = 0</math>
Its significance is that the line integral of a conservative field, such as a physical force, is independent of the path chosen. In physics, this means that the potential energy (which is determined by a conservative force field) of a particle at a given position is independent of how a particle was moved to its position.
[[Category:vector analysis]]
[[Category:mathematics]]
:<math>\nabla \times \vec V = (\ \ \frac{\partial V_z}{\partial y} - \frac{\partial V_y}{\partial z},\ \ \ \ \frac{\partial V_x}{\partial z} - \frac{\partial V_z}{\partial x},\ \ \ \ \frac{\partial V_y}{\partial x} - \frac{\partial V_x}{\partial y}\ \ ) = 0</math>
Its significance is that the line integral of a conservative field, such as a physical force, is independent of the path chosen. In physics, this means that the potential energy (which is determined by a conservative force field) of a particle at a given position is independent of how a particle was moved to its position.
[[Category:vector analysis]]
[[Category:mathematics]]