Electrostatics problem concerning induction by a point charge inside a conducting shell Consider two independent conducting shells (not thin shells! i.e., their internal and external surfaces do not overlap.)  whose shapes of external surfaces are identical but internal surfaces are not necessarily identical. They both enclose a point charge $q$ with the same quantity and sign but they may be stationed in different positions as to the two shells. See below.
Note that in fact the two systems are completely independent (i.e., far apart), although they look "close" shown in my drawing. And of course, there is nothing else in the surroundings! 
Obviously, on both shells' internal surface there will be the same quantity of induced charge $-q$, which, in turn, will induce charge $q$ on both external surfaces. Subsequently, the induced charge distributed on their external surfaces will give rise to the electric field exterior to the external surfaces. 
For the two systems the only things they have in common are the shape of the external surface and the quantity and sign of the enclosed point charge. Now the question is, do they necessarily share the same electric field exterior to their external surfaces?
I know if the shells are connected to the ground the answer will be yes. But what if they are NOT connected to the ground?  
 A: If they are conducting shells then they charge distribution on the outer shell will be absolutely independent of the position/shape of the inner surface. 
There is a similar question and answer here which is about the position of a single charge inside a sphere - the reasoning is exactly the same here, though the problem is slightly different.
First point is that free electrons in the shell will move so that there is no electric field inside the material the shell is made out of. 
Next point is that the charge on the inside of the shell will move depending on the shape of the inner shell. 
Final point is that the charge on the exterior of the shell will move just to minimize its energy on the external surface - it will not be effected by the inside because there is no electric field that passes through the conducting material from the inner surface to the exterior. 
I am not sure about connection to ground - but if the shells are isolated and they have no net charge and the total charge inside each of them is the same then the external electric fields will be the same. I guess if the shells were connected to ground then the potentials of the outside of the shells would be the same (I guess $0 V$) and any charge on the exterior would be distributed in the same way.
