Coefficients of capacitance with spherical shell problem

[reaper929]

Homework Statement

Metal sphere of radius R1 is surrounded by a concentric metal shell of inner radius R2 and outer radius R3. The dielectric is air. Calculate coefficients of capacitance for the given setup.

Homework Equations

Picture of the problem:

The Attempt at a Solution

I have tried arriving to the solution by using coefficients of potential. I have done the following:

$\varphi_{1}=Q_{1}/4\pi\epsilon_{0}R_{1}+Q_{2}/4\pi\epsilon_{0}R_{3} \\\varphi_{2}=Q_{1}/4\pi\epsilon_{0}R_{3}+Q_{2}/4\pi\epsilon_{0}R_{3}$


But it looks errorneous to me. Can anybody clarify the matter for me?

 

[haruspex]

$\varphi_{1}=Q_{1}/4\pi\epsilon_{0}R_{1}+Q_{2}/4\pi\epsilon_{0}R_{3} \\\varphi_{2}=Q_{1}/4\pi\epsilon_{0}R_{3}+Q_{2}/4\pi\epsilon_{0}R_{3}$

Pls define these variables.
Bear in mind that the charge on the shell will consist of a distribution on its inner surface and another on its outer surface.

 

[reaper929]

Can you give me a hint about how it will look?

 

[haruspex]

Can you give me a hint about how it will look?

There will be a uniform spherical charge distribution at each of the three radii. I would take there to be equal and opposite charges on the central sphere and the enclosing shell, so the total charge is zero.
Can you develop the equations to determine how the charge is split between R2 and R3?

 

[reaper929]

I have succeeded. I'll put the solution here tomorrow. I'm in a bit of an exam hurry right now. Thx for the hint :)