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Trying to understand the concept of divergence

  1. Aug 17, 2010 #1
    [tex]\operatorname{div}\,\mathbf{F}(p) =
    \lim_{V \rightarrow \{p\}}
    \iint_{S(V)} {\mathbf{F}\cdot\mathbf{n} \over |V| } \; dS[/tex]

    This is the definition of divergence from wikipedia...

    The divergence is property of a point in space. Is that right?

    If the divergence is zero at a point, that means that such point does not contribute with the field as source nor a sink. Is that right?

    So, the divergence of a point measures how that point contributes as a source or a sink with the field?

    The surface integral in the equation above means a certain area, right? Is that area the area of the entire surface (like a gaussian surface in the gauss's law) or the area of the micro-surface that is "around" the point I'm measuring the divergence on?

    Usually I like to think in the dimensions of the conceps (units). I noticed that the unit of divergence will always be area/volume (m^-1). Does that have any meaning?

    If someone can help me with some of these questions I would be grateful...

    Thank you,
    Rafael Andreatta
  2. jcsd
  3. Aug 18, 2010 #2
    Nobody can help me?

    Either I asked some very noob questions or very hard questions haha
  4. Aug 19, 2010 #3


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    There is an alternate way of expressing divergence (which is the one I am used to).

    In Cartesian coordinates:
    divF=∂F/∂x + ∂F/∂y + ∂F/∂z

    This definition is for any point in space where the partials are defined.
  5. Aug 19, 2010 #4


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    It is, indeed.

    The divergence is a property of your vector field F.
    Then there is no net flux of F per unit volume centred about that point.
    Your limiting process consists computing the net flux of F across the surrounding surfaces of ever-shrinking volumes V, giving you, in the limit of V to 0, the divergence of F at that point.
    Units are: (area)*(unit of F)/volume.

    If, for example, F is (velocity field of some fluid), then (area)*F gives the net amount of fluid flowing out of V; dividing with V gives you the volume flux per unit volume.
    Ask more if you feel to.
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