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## Homework Statement

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.

## Homework Equations

Gauss's law for electric field (?):

E∫dA = (q in) / (ε

_{0})

E = ke q / r

^{2}

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.

So...

for r < a, the electric field is not 0 and so

E ∫ dA = q in / ε

_{0}

E (4πr

^{2}) = q in / ε

_{0}

E = q in / (4πr

^{2}ε

_{0})

which turns out wrong for r < a. It is still wrong even when I substitute q in as pV.