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What does it mean When $Curl \ F = 0$ or $Div\ F = 0$ ?

F is a vector field

I am new in vector calculus;

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2 Answers 2

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Curl measures how much the field is rotating. If you enclose a region with (defined) curl of 0 everywhere, the line integral around that curve will be zero (Greens' Thm.)

Divergence measures how much the field is expanding. If you enclose a region with a (defined) divergence of 0 everywhere, the flux integral around the curve will be zero (normal form of Greens' Thm).

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I feel "rotating effect of field" is better than "field is rotating". –  007resu Dec 19 '12 at 4:45
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I like this set of videos covering grad, div, and curl. Just scroll down a little bit and you will see individual links to the three videos, one for each concept.

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