Potential of a conducting sphere with charge inside

[yarospo]

This is a general question:

What is the electric potential of a hollow neutral conducting sphere with radius R with a charge q placed inside it?
Intuitively I understand that it is the same - q/R, no matter where the charge is placed inside the sphere. Can anyone explain why it is so?

My thoughts: The potential on the surface of a conducting sphere is constant, and it seems implausible that I will be able to change the potential of the sphere just by moving the charge inside, and therefore, I may as well place it in the middle and then the potential is obviously q/R.

 

[gabbagabbahey]

Hint: What would you expect the charge distribution to "look like" when you are very far from the sphere? What is the total charge enclosed by a spherical, concentric Gaussian surface of radius r>>R? So, if the potential at r=infinity is zero, what must the potential be at any point outside the sphere?

 

[yarospo]

Thanks,

I've found a comprehensive and detailed explanation in Griffiths Intro to Electrodynamics. Should have known it'll be there - got to love that book!
:)