Coulomb pressure and concentric spheres

[MarkL]

Suppose you have a sphere of radius a of positive charge, and a concentric shell from a to b of negative charge. The positive charge is equal to the negative charge. (non-conducting, uniform density)
Is there an outward pressure at a of kqq/a²/(4πa²) - with pressure decreasing with radius, becoming P = 0 at b.
Or, is there an attraction between the sphere and the shell --> P = 0 everywhere. The thickness of the shell does not matter. What if b was infinity?
Thanks

 

[ergospherical]

Do you know how to solve the problem for the field strength? Because it's the same as a hydrostatics problem with $\nabla p(r) = -\rho \mathbf{E}(r)$. Equivalently $\nabla(p - \rho \phi) = 0$.