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Math Help - Potential theory?

  1. #1
    Super Member craig's Avatar
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    Potential theory?

    Tricky one here, just not sure where to start.

    \displaystyle \mathbf{u} = \nabla \phi, with

    \displaystyle \phi = \mathbf{U} \cdot \mathbf{r} + \frac{a^3}{2r^3}\left(\mathbf{U} \cdot \mathbf{r} \right)

    With \displaystyle \mathbf{U} = U\mathbf{k}.

    Show that:

    \displaystyle u_i = U_i + \frac{a^3}{2}\left\{\frac{U_i}{r^3} - \frac{3U_j x_j x_i}{r^5} \right\}

    Now I presume that we have to work out \displaystyle \nabla \phi first? Just not got a clue where to start.

    Any pointers in the right direction would be much appreciated.

    Thanks in advance
    Last edited by CaptainBlack; April 5th 2011 at 07:05 PM.
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  2. #2
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    Start by determining \phi. What's \mathbf{U}\cdot\mathbf{r}?
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  3. #3
    Super Member craig's Avatar
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    Ohh sorry I managed to sort this out, meant to mark as solved.

    Cheers for the reply though
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