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Math Help - Vector Analysis

  1. #1
    Super Member Aryth's Avatar
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    Vector Analysis

    Evaluate

    \int\int_S \left[\frac{1}{R}\nabla{\phi} - \phi\nabla{\left(\frac{1}{R}\right)}\right]\cdot d\bold{S}

    over the surface of the sphere (x-3)^2 + y^2 + z^2 = 25, where \phi = xyz + 5
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  2. #2
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    I see a vector valued function dotted into the normal of a ball centered at (3,0,0). Can't you use the divergence theorem? So instead of evaluating
    <br />
\vec f \cdot n dS<br />
    you instead evaluate
    <br />
\nabla \cdot \vec f dV<br />
    It looks like the integrand was chosen so a couple of terms drop out. Then
    <br />
\nabla \cdot \nabla \frac{1}{r}<br />
    gives you a constant because the origin is in your ball, and the other
    <br />
\nabla \cdot \nabla (xyz+5)<br />
    should give you zero.
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