I have seen the well known example of a charge $ Q $ placed in the center of a spherical cavity of radius $R $of a conductor. We can then say that the inner wall has a charge of $-Q $ and we can find the electric field $E$ by applying Gauss' law for a sphere of radius $r\lt R$.
So what if the charge Q is not in the center of the sphere but at some point of radius $a\lt R$ ? The charge of the inner wall will again be $-Q$ (we find this by applying Gauss' law for a sphere of radius $R' \gt R$ and noting that inside conductors $E=0$).
What is the best way to compute the electric field and the electric potential function though? Is it with respect to a position vector (x,y,z) or can we use other coordinates to simplify? I guess using the radius doesn't make sense as the problem is not symmetric anymore. Assume that everything outside the cavity is from the same conducting material, with potential $V_0=0$