Gauss' Law Hollow Sphere with Charged Ball

[hy23]

Homework Statement

A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner raduis b and outer radius c. \The hollow sphere has net charge +2Q.

Determine the Electric Field Strength at r when r is,

r < a
a < r < b
b< r < c
r > c

Homework Equations

I'm struggling with the flux concepts in this case.

The Attempt at a Solution

I guess the main concepts I need clarification on is:
in the hollow sphere, there is flux pointing out from the metal spherical surface, but is there flux pointing into the hollow sphere? (in that case would there be a net flux into the small ball?)
Inside the actual shell of a charged metal sphere ( or inside a charged slab/puck/etc.), what is the flux, is it 0?



Here's my analysis for the problem

So when r < a , the net flux at r only depends on the charge inside the small ball.

When a < r < b, ok so this is where I'm struggling, please tell me if my analysis is wrong,
r is the hollow part, since all the charge gathers on the surface, r has no net charge, so it has no net flux, so its E field is 0?

when b < r < c, this is IN the shell of the charged outer sphere, now I know how to deal with the flux at the surfaces of conductors, so would this be the same thing?

when r > c, this is at a point outside the large sphere, so the flux is related to the net charge of the sphere and the ball

 

[supratim1]

first of all, flux depends on total charge enclosed. So total charge of hollow sphere + ball = Q. So net flux is outwards.

for r<a, use uniformity of charge on ball, by finding charge density.