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Singular vector fields

  1. Feb 6, 2014 #1

    ShayanJ

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    Gold Member

    You're probably familiar with Gauss's laws in electricity,magnetism and gravitation:
    [itex]
    \oint_{\partial V} \vec{D}\cdot \vec{d\sigma}=q_V \\
    \oint_{\partial V} \vec{g}\cdot\vec{d\sigma}=-4\pi G m_V\\
    \oint_{\partial V} \vec{B}\cdot\vec{d\sigma}=0 \\
    [/itex]
    It is also known that the first two integrals are non-zero because of the contributions from their singularities and the last one is zero because it is thought that it never gets singular.
    Now I just feel there is something more fundamental than these from the mathematical point of view.I mean,it seems to me that there is something mathematical about singularities in vector fields that I don't know but I just can't find it or understand it myself.
    I know,maybe there is nothing but my experience with mathematics tells me that it can't ignore such a...you know...mmm...anyway...just can't ignore it!!!
    I'll appreciate any idea
    thanks
     
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