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Demonstration that the electric potential is continuous over a surface

  1. Mar 4, 2013 #1

    fluidistic

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    Gold Member

    1. The problem statement, all variables and given/known data
    I'm asked to demonstrate that the electric potential is continuous over a surface with a charge density ##\sigma##.


    2. Relevant equations
    ##\Phi (\vec x )= \int _ S \frac{\sigma (\vec x' )}{|\vec x - \vec x '|}da'##


    3. The attempt at a solution
    I'm not sure what I must show mathematically. Is it that ##\Phi (\vec x )= \int _ S \frac{\sigma (\vec x' )}{|\vec x - \vec x '|}da'## remains integrable when x'=x? Or is it that (I believe it is), when I take the limit of when x tends to x', Phi must equate ##\Phi (\vec x')##? Either way I haven't figured out how to do it.
    Any tip is welcome. Thanks!
     
  2. jcsd
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