# Demonstration that the electric potential is continuous over a surface

1. Mar 4, 2013

### fluidistic

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!

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