1. If a vector field has zero curl, does it(adsbygoogle = window.adsbygoogle || []).push({}); alwaysmean that it is the gradient of some scalar (potential) field?

2. If the vector field is a force field and its curl is zero does that mean that the "potential" scalar field that it is the gradient of is always some form of "potential energy" (as in PE + KE = Constant). And, is that why they call vector fields like that (where the curl is zero) "conservative"? That is, are they called conservative fields because integratingF.dsaround any closed path equals zero and therefore they obey (??? - not the right word...) the conservation of energy? But... calculating the (closed loop) line integral ofF.dsfor someFvector field that has curl would not equal zero, would not be path independent, and would not be the gradient of some scalar potential field function; but it shouldNOTviolate the conservation of energy either... right? Anyway, I'm kind of confused.

3. Is there any physical significance to the term "potential field" if the zero curl vector field in question is a velocity field rather than a force field?

Thanks for any insights - (BTW - this isn't any assignment. I study stuff on my own.)

jf

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# Homework Help: Zero curl fields

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