A solid, insulating sphere of radius a has a uniform charge density of ρ and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c, as shown.
A). Find the magnitude of the electric field in the following regions:
r < a (Use the following as necessary: ρ, ε0, and r.)
a < r < b
b < r < c
r > c
B). Determine the induced charge per unit area on the inner and outer surfaces of the hollow sphere.
Gauss's law for electric field (?):
E∫dA = (q in) / (ε0)
E = ke q / r2
E = 0 inside a CONDUCTOR
q = σdA (surface area?)
q = ρdV (volume? )
The Attempt at a Solution
I'm just concerned about the first part r< a and hopefully I will understand the rest
This is just really tough for me... so many things I need to look out for and it is really confusing.
It is confusing when thinking about dimensions as the uniform charge is concerned with volume ( q = ρdV) yet I thought Gauss's Law ( flux = E ∫ dA ) was just concerned with 2D surface area only. Or am I missing something?
Also I am not sure how the inner sphere, being an insulator, has any affect on the electric field.
for r < a, the electric field is not 0 and so
E ∫ dA = q in / ε0
E (4πr2) = q in / ε0
E = q in / (4πr2ε0)
which turns out wrong for r < a. It is still wrong even when I substitute q in as pV.