Electrostatic equilibrium and Gauss' law

[Kenny Lee]

A conducting spherical shell of ineer radius a and outer radius b carries a net charge Q. A point charge q is placed at the center of this shell. Determine the surface charge densit on (a) the ineer surface of the shell and (b) the outer surface of the shell.

I'm not sure of my reasoning. For part (a), I argued that at the inner surface
E = q/ (4*pi*a^2*epsilon) from Gauss' law.

And equated that to the formula for electric field, right outside a conductor in electro-static equilibrium i.e.
E = (surface charge density)/ epsilon.

So I get q/ (4*pi*a^2). Is that correct? If not, what would the correct method be.

Any advice pls. Thanks.

PS I apologize for the ugly equations. Still learning how to use the equation editor...

[phucnv87]

http://photo-origin.tickle.com/image/69/3/6/O/69362752O719777534.jpg

[Astronuc]

A charge q would induced an equal and opposite charge on the inner surface of a 'conducting' sphere, and the same charge on the outer surface. The areas are different.

However, the sphere also has a net charge Q. How would this be distributed.

And then think of superposition.

[Kenny Lee]

Thanks. So my answer was wrong? Yea, come to think of it, I only accounted for the charge q and not the sphere...I'll have another go at it.