# Electric field outside a conductor and its surface charge

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1. Apr 30, 2015

### Happiness

Imagine a surface charge $\sigma$. The boundary condition on $E$ is

$E_{above}-E_{below}=\frac{\sigma}{\epsilon_0}\hat{n}$, where $\hat{n}$ points outwards perpendicularly to the surface.

Because the field inside a conductor is zero, it requires that the field immediately outside is $E=\frac{\sigma}{\epsilon_0}\hat{n}$.

But if the conductor is a large, flat plane with a uniform surface charge $\sigma$, shouldn't the field be $E=\frac{\sigma}{2\epsilon_0}\hat{n}$?

2. Apr 30, 2015