# Proving continuity of potentials and fields due to a surface charge

Is there a way to show:

$$(1)\ \displaystyle \phi=\int_{S'} \dfrac{\sigma}{r} dS'$$ is continuous all over space

$$(2)\ \mathbf{E}=\displaystyle\int_{S'} \dfrac{\sigma}{r^2}\ \hat{\mathbf{r}}\ dS'$$ is continuous everywhere except at boundary $$S'$$

where $$\sigma$$ is the surface charge density

• Why is this site so inactive? I am only getting question likes but no answers. – Alfred Apr 15 at 8:19