# Coulomb pressure and concentric spheres

• B
• MarkL
In summary, the conversation discusses a scenario of a sphere with a positive charge of radius a and a concentric shell with negative charge from a to b. The two charges are equal and the shell has uniform density. The question is whether there is an outward pressure at a with decreasing pressure at larger radii, reaching 0 at b, or if there is attraction between the sphere and the shell with pressure being 0 everywhere. The thickness of the shell is not relevant and the conversation also considers the case where b is infinity. The conversation also mentions using the hydrostatics equation to solve for the field strength, which can be expressed as ∇p(r) = -ρE(r) or ∇(p - ρφ)

#### 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

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##.