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Conservative vector field (view source)
Revision as of 16:59, December 26, 2009
, 16:59, December 26, 2009better home for this
A '''conservative field''' or '''conservative vector field''' 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:calculus]]
[[Category:mathematics]]