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Math Help - Flux

  1. #1
    Super Member
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    Flux

    Please it is correct ?

    \int \int_S F.N.ds

    N = \frac{\frac{d(r)}{d(u)} X \frac{d(r)}{d(v)}}{|\frac{d(r)}{d(u)} X \frac{d(r)}{d(v)}|}

    ds = |\frac{d(r)}{d(u)} X \frac{d(r)}{d(v)}|dudv

    Flux:

    \int \int_S F. \frac{d(r)}{d(u)} X \frac{d(r)}{d(v)} dudv
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  2. #2
    MHF Contributor Amer's Avatar
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    Jordan
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    that is correct

    \int\int F.n dS = \int\int F.\left(\frac{\partial r}{\partial u} \times \frac{\partial r}{\partial v} \right) dA
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  3. #3
    Super Member Random Variable's Avatar
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    I always write it like the following:


    Let  \Phi (u,v) be a parametrization of the surface S

    then flux =  \int \int_{S} F \cdot dS = \int \int_{D} F \cdot (T_{u} \times T_{v}) \ du \ dv

    where  T_{u} = \frac {\partial \Phi}{\partial u}

    T_{v}= \frac {\partial \Phi}{\partial v}

    and D is an elementary region in the uv-plane


    There are other ways to write it, but I always stick with this definition.
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  4. #4
    Super Member
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    Quote Originally Posted by Random Variable View Post
    I always write it like the following:


    Let  \Phi (u,v) be a parametrization of the surface S

    then flux =  \int \int_{S} F \cdot dS = \int \int_{D} F \cdot (T_{u} \times T_{v}) \ du \ dv

    where  T_{u} = \frac {\partial \Phi}{\partial u}

    T_{v}= \frac {\partial \Phi}{\partial v}

    and D is an elementary region in the uv-plane


    There are other ways to write it, but I always stick with this definition.
    Ok. Thanks
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