Electrostatic boundary conditions at a conductor
= Electrostatic boundary conditions at a conductor
= Electrostatic boundary condition
{synonym}
A Gaussian pillbox gives
$$
(E_{\rm out}-E_{\rm in})\cdot n=\frac\sigma{\epsilon_0}.
$$
Since $E_{\rm in}=0$, the surface charge density is $\sigma=\epsilon_0E_{\rm out}\cdot n$.