A metallic vessel is placed on a non-conducting stand. The inner and outer surfaces of the vessel are connected to two gold leaf electroscopes A and B respectively. A charged sphere suspended by a non-conducting string is slowly lowered in to the vessel. How do the leaves of the electroscopes A and B behave? How will the behaviour change if the sphere makes contact with the inner surface of the vessel?

PLACEHOLDER ANSWER - the answer is a description. If the sphere carries charge $$+q$$, it induces $$-q$$ on the inner surface and $$+q$$ on the outer surface of the vessel. The vessel and both electroscopes form one conductor at a single potential, and the electroscopes lie outside the cavity, so both sets of leaves diverge, by the same amount, increasing as the sphere goes deeper and becoming steady once it is well inside. When the sphere touches the inner surface, its charge cancels the induced $$-q$$, leaving $$+q$$ on the outside, so the divergence of both electroscopes stays unchanged (Faraday's ice-pail experiment).