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Scalar and vector fields

  1. Aug 9, 2010 #1
    What is the relation between the flux through a given surface by a vector field? And how does stokes theorem relate to the line integral around a surface in that field
     
  2. jcsd
  3. Aug 10, 2010 #2

    HallsofIvy

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    The flux of a vector field [itex]\vec{F}[/itex] through surface S is, by definition,
    [tex]\int\int_S \vec{F}\cdot d\vec{S}[/tex]

    And Stokes' theorem say, specifically, that that is equal to
    [tex]\int_{c} \nabla\times\vec{F}\cdot d\vec{r}[/tex]
    Where c is the closed path bounding surface S.
     
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