Theory of Images or Gauss's Law for Concentric Conducting Spheres?

[atomicpedals]

Homework Statement

Two conducting spheres are concentric, the radius of the inner being a and the outer being b. One sphere is grounded & the other is at a potential V₀. Find the charge on each when the grounded sphere is a) the outer, b) the inner.

2. The attempt at a solution

Is this an appropriate application for theory of images? Or is it a far more straightforward application of Gauss's Law?

I'm tempted to use image charges from one sphere to the other, but fear that's making life harder than it needs to be.

 

[atomicpedals]

Ok, I've become comfortably certain that images are the way to go.

 

[kloptok]

Out of curiosity, what is your image system?