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Math Help - Stokes theorem trouble

  1. #1
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    Stokes theorem trouble

    Hi all,
    I have question that goes as follows:

    If f(\underline{r}) is a scalar field, use stokes theorem to deduce that

    \int\int_{S} grad  f \wedge d\underline{S} = -\oint_{C}fd\underline{r}

    Where C is a space curve bounding a closed space S.
    When I look at the equations, I can see that -\oint_{C}fd\underline{r} = -\int\int_{S} curl \underline{f} * d\underline{S} , as by Stoke's theorem. However, I don't think that helps just yet. Apart from that, I'm not sure how to approach this question.

    Any points in the right direction is greatly appreciated. Thanks in advance!
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  2. #2
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    Quote Originally Posted by Silverflow View Post
    Hi all,
    I have question that goes as follows:

    If f(\underline{r}) is a scalar field, use stokes theorem to deduce that

    \int\int_{S} grad  f \wedge d\underline{S} = -\oint_{C}fd\underline{r}

    Where C is a space curve bounding a closed space S.
    When I look at the equations, I can see that -\oint_{C}fd\underline{r} = -\int\int_{S} curl \underline{f} * d\underline{S} , as by Stoke's theorem. However, I don't think that helps just yet. Apart from that, I'm not sure how to approach this question.

    Any points in the right direction is greatly appreciated. Thanks in advance!
    If f is a scalar field, that second equation makes no sense- neither curl f nor f*dS is defined.

    However, if you take \vec{n} to be the unit normal at each point on the surface, then f\vec{n} is a vector and curl f\vec{n}= grad f\times\vec{n}+ f curl \vec{n}. Try using Stoke's theorem on that.
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  3. #3
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    Thanks!
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