Surface Charge of Uniformly charged sphere

[teroenza]

Homework Statement

In the section on the discontinuity of the electric field (Griffiths introduction to electrodynamics) there is the following.

"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.

This is as opposed to being discontinuous, by σ/ε_0 when a surface charge exists

Homework Equations

The Attempt at a Solution

If it was a conducting sphere, I would understand that if it was neutral, there would be no net charge on the surface, but I do not see why it has to be the case here.

 

[Dick]

It doesn't say the sphere is conducting. A "uniformly charged sphere" means the charge density in each part of the sphere is the same. A conducting sphere can't be that. All of the charge would move to the surface.

 

[teroenza]

Ok. But because it is uniformly charged, there is presumably a nonzero charge density on the surface (as elsewhere) and thus charge on the surface.

I just don't understand why the surface of a uniformly charged solid sphere has no charge on it. That is contradictory. I'm not sure if I am not understanding the physics or the words.

Why is "...surface of a uniformly charged solid sphere." and example of a place ""Where there is no surface charge'''?

 

[Dick]

Ok. But because it is uniformly charged, there is presumably a nonzero charge density on the surface (as elsewhere) and thus charge on the surface.

I just don't understand why the surface of a uniformly charged solid sphere has no charge on it. That is contradictory. I'm not sure if I am not understanding the physics or the words.

Why is "...surface of a uniformly charged solid sphere." and example of a place ""Where there is no surface charge'''?

You misunderstand what 'surface charge' is. Surface charge is (ideally) a finite amount of charge contained in an infinitely thin layer, the surface. It's a useful idealization to make for a conducting sphere which has no charge in the interior and all of its charge very close to the surface. Very different from a 'uniformly charged sphere'.

 

[ehild]

Ok. But because it is uniformly charged, there is presumably a nonzero charge density on the surface (as elsewhere) and thus charge on the surface.

I just don't understand why the surface of a uniformly charged solid sphere has no charge on it. That is contradictory. I'm not sure if I am not understanding the physics or the words.

Why is "...surface of a uniformly charged solid sphere." and example of a place ""Where there is no surface charge'''?

Imagine the surface as a shell of one atom (molecule) thick. The radius of an atom is about 10^-10 m. How much is the charge of the shell compared to the charge of a sphere of radius R=0.1 m?

In case of a metal, all charge accumulates in that surface shell.

ehild