Difference between revisions of "Conservative vector"

Latest revision as of 16:58, December 26, 2009

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-A '''conservative field''' or '''conservative vector''' has a [[curl]] of zero:
+#REDIRECT [[conservative vector field]]
-:<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]]