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Conservative vector field (view source)
Revision as of 17:00, February 13, 2010
, 17:00, February 13, 2010Add historical info, include solenoidal field
It gets its name from the fact that, if a force field, such as the gravitational or electric field, has a curl of zero, the principle of conservation of energy will hold. This follows from the fact that the accumulated force around any closed loop is zero, so no energy is gained or lost.
It gets its name from the fact that, if a force field, such as the gravitational or electric field, has a curl of zero, the principle of conservation of energy will hold. This follows from the fact that the accumulated force around any closed loop is zero, so no energy is gained or lost.
An older name for such a field is ''irrotational''. This refers to the fact that such a field lacks "vortices" that go around in circles.
==Irrotational and Solenoidal Vector Fields==
An older name for a conservative field is ''irrotational''. This refers to the fact that such a field lacks "vortices" that go around in circles.
An older name for a field with a [[divergence]] of zero is ''solenoidal''. This refers to the fact that, according to [[Maxwell's equations]], the divergence of the magnetic field is zero, and "solenoid" is a traditional term for an electromagnet.
Both of these terms seem to have fallen out of use around 1960. <ref>Page, Leigh, ''Introduction to Theoretical Physics'', Van Nostrand, 1952</ref><ref>Constant, F.W., ''Theoretical Physics'', Addison-Wesley, 1958</ref><ref>Schwartz, M., S. Green, W.A.Rutledge, ''Vector Analysis'', Harper, 1960</ref>
==References==
<References/>
[[Category:vector analysis]]
[[Category:vector analysis]]
[[Category:calculus]]
[[Category:calculus]]
[[Category:mathematics]]
[[Category:mathematics]]