In the section on the discontinuity of the electric field (Griffiths Introduction to electrodynamics), there is the following statement:
Where there is no surface charge, the perpendicular component of the electric field (to the surface) is continuous, as for instance at the surface of a uniformly charged solid sphere.
Why does the surface of a uniformly charged solid sphere have no charge on it?
Best Answer
Surface charge refers to a thin layer of charge at a surface. For example, an ideal charged conducting sphere would have a layer of charge on the surface whose thickness would be infinitesimal. It would be represented by a delta function.
In the case of an idealized non-conducting uniformly charged sphere whose boundary is discreet, the charge density simply goes from a finite value to zero. No surface charge.
If we relax the restriction to ideal spheres, the conducting sphere has a charge density that spikes at the surface, while for a "uniformly charged" sphere, the charge density would drop smoothly to zero without a spike. (But it might have some structure depending on what model you use for the material and the electrons.)