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Electric Potential...

Name: Anonymous 2009-10-21 20:59

Hey guys, i've got an EM problem i'm stuck with.  Maybe i can get some help with it.

Here goes:

The electric potential of a very large flat metal plate is V(sub 0).  It carries a uniform distribution of charge of surface density sigma (C/m^2).  Determine V at a distance X from the plate.  Consider the point x to be far from the edges and assume x is much smaller than the plate dimensions.

Name: Anonymous 2009-10-22 15:45

first, determine the electric field on both sides of the plate (assuming the plate lies in the x,y plane):

\oint \vec{E}\bullet \mathrm{d}\vec{a} = \frac{Q_{\mathrm{enclosed}}}{\epsilon_{0}}\\
2E \mathrm{d}a = \frac{\sigma\,\mathrm{d}a}{\epsilon_{0}}\\
\vec{E_{\mathrm{one side}} = \frac{\sigma}{2\epsilon_{0}}\hat{z}\\

V\left ( \vec{r} \right ) = -\int_{\vec{r}_{reference}}^{\vec{r}}\frac{\sigma}{2\epsilon_{0}}\hat{z}\bullet\mathrm{d}\vec{l}

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