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Meaning of Curl from stokes' theorem

  1. Oct 23, 2015 #1

    Titan97

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    Divergence can be defined as the net outward flux per unit volume and can be explained using Gauss' theorem. (I read this in Feynman lectures Vol. 2)
    IMG_20151023_184133_507.JPG

    In the next page, He derives Stokes' theorem using small squares.
    IMG_20151023_183636_615.JPG
    The left side of equation represents the total circulation of a vector field along a closed path S.
    The right side contains the component of Curl perpendicular to ##\Delta a##
    This only gives meaning to a particular component of Curl. How can I explain Curl using stokes' theorem just like how divergence is explained?
     
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  3. Oct 23, 2015 #2

    BvU

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  4. Oct 23, 2015 #3

    Titan97

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    So the total shear in a region R is related to the circulation of the field about the boundary of R.
     
  5. Oct 24, 2015 #4

    BvU

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    Yes, but be careful: no shear doesn't have to mean no curl. There is the viscosity somewhere in between and that can be zero (in theory).
     
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