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Math Help - Divergence Help

  1. #1
    Junior Member
    Joined
    Mar 2009
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    Divergence Help

    Hello,

    I need some help with divergence



    {\bf{E}} = \frac{1}{\varepsilon }\left( {\frac{{\partial \phi }}{{\partial {z^{}}}}{\bf{i}} - \frac{{\partial \phi }}{{\partial x}}{\bf{k}}} \right)


    and



    \nabla  = {\bf{i}}\frac{\partial }{{\partial x}} + {\bf{j}}\frac{\partial }{{\partial y}} + {\bf{k}}\frac{\partial }{{\partial z}}

    Show that


    \nabla  \cdot {\bf{E}} = 0


    When I work with numbers, all is good but now I'm confused. Is the answer related to the fact that the i component only contains z and the k only contains x? So that these will become 0?

    Thanks for any help.
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  2. #2
    MHF Contributor
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    Re: Divergence Help

    Hey mark090480.

    You should use the fact that <i,j> = <i,k> = <j,k> = 0 and expand out the representation of E in terms of its components <a,b,c> = ai + bj + ck. where a,b,c are real valued variables.
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