Determine potential outside a sphere

[Mythbusters]

1. How do I determine the potential in the region outside a sphere, when I have a static charge distribution outside the sphere?

 

[CeltIntuition]

Consider internal charges inside the sphere that will produce fields that match the boundary conditions.

Cumulative effect of theoretical internal and actual external charges will give you the answer.

 

[glueball8]

Gauss's Law?