Problem about charge concentration

[Cetullah]

Hello people, I m quite new at this forum, and since I m not a native American, I may have some problems with translating the problem to English, but I will try my best.

There are some problems in the same type with that in my worksheet, and I can solve none of them. Here is the question:

Homework Statement

We have a conductive spherical shell with the inner radius 1 cm, and the outer radius 2 cm, with the charge -4 nC. At the center of the shell, there is a particle with charge 6 nC. Find the concentration of charge at the outer side of the shell.

Homework Equations

Since this question is under the subject "Gauss' law":

∫EdA= q/ε₀

The Attempt at a Solution

Well, I have asked this to a noob scholar, and he also failed to answer.

 

[NoPoke]

Can you solve the problem if the -4nC surface charge was not mentioned at all?

 

[Cetullah]

No, I absolutely have no idea about how to solve this...

 

[NoPoke]

ok, how about if the sphere is very very thin?

 

[Cetullah]

Hmm, have never solved such a problem either, but I guess it can be about the equation:

ε₀E= q/∫dA

 

[NoPoke]

its all about that equation. or rather what that equation is telling you about how you can distribute charges and get the same electric field.

What do you get for the electric field if you eliminate the conducting sphere entirely?
What shape describes the equipotentials?
Does placing a thin wire along the equipotential change the electirc field?