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Math Help - Find Flux Vector

  1. #1
    Junior Member
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    Find Flux Vector

    For \Phi (x,y,z) = x^{xy} \sin(x+z) + y \ln (z)

    find the flux vector \vec{J} = \triangledown \Phi

    and prove that curl \vec{J} = 0
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  2. #2
    Junior Member
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    Is this correct?

    \triangledown \Phi = \frac{\partial \Phi}{\partial x} i + \frac{\partial \Phi}{\partial y} j + \frac{\partial \Phi}{\partial z} k

    where

    \frac{\partial \Phi}{\partial x} = e^{xy} \cos(x+z) + \sin(x+z) y e^{xy}

    \frac{\partial \Phi}{\partial y} = \sin(x+z) x e^{xy} + \ln(z)

    and

    \frac{\partial \Phi}{\partial z} = e^{xy} \cos(x+z) + \frac{y}{x}

    and

    \triangledown \Phi = (e^{xy} \cos(x+z) + \sin(x+z) y e^{xy}) i + (\sin(x+z) x e^{xy} + \ln(z) ) j + (e^{xy} \cos(x+z) + \frac{y}{x})k

    Is there anything more I need to do with this?
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  3. #3
    Newbie
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    Oct 2008
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    In the k component it should be y/z, not y/x.

    Other than that, all you need to do is calculate the curl and it will cancel out nicely.

    Do you know how to find the general flux vector in the second part of question 1?
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