Electric field continuity at the surface of a uniformly charged sphere

[xxbigelxx]

Homework Statement

Please calculate the potential for a sphere that is uniformly charged with density ρ₀ and also has a radius of R.
a. r<R
b. r>R
c. Is there a discontinuity of Electric Field at the surface? Explain your reasoning.

Homework Equations

The Attempt at a Solution

I have attached my work for the first two parts, which I am pretty sure is correct. However, I need help with the last part. I want to say that it is continuous, because of the nature of uniformly charged spheres. However I don't know if this is right, or how to really explain it. This is due tomorrow, so any help (especially if it's quick) would be GREATLY appreciated. Thank you.

http://i53.tinypic.com/xpszo7.jpg

 

[MathematicalPhysicist]

The answer is no, if the electric field was discontinuous we will find a surface density, but it's obviously zero, cause E_in| r=R = E_out| r=R.

You can look at this:
http://scienceworld.wolfram.com/physics/SurfaceChargeDensity.html

 

[xxbigelxx]

Ok great. Thanks.