I had a search but couldn't find anything answering the specific situation, sorry if its come up before.
What can you do to investigate a charged item that has 0 charges? It's been all used up. The potions have been drank, the arrows have unleashed their payload, or whatever.
Can you investigate or Intellego Vim it and get a result that tells you that it used to be a charged item and/or what it was charged with? Or does the Quesitor spend a season looking at an empty bottle and write in his report that it is, indeed, an empty bottle with nothing special about it?
The guidelines for InVi and investigation stuff talk about magnitudes based on pawns of vis, and charged items don't use vis.
Are charged items the ultimate tool for the wizard that wants to leave no evidence?
Items still carry casting sigils, and the effect from the item should leave residue just like any other effect. So I don't see how there would be less evidence than could just be managed with spells alone.
There is a separate question about whether the used item itself should register residue for having held an effect, separate from the effect's actual residue. But I don't think you could do any non-residue analysis of a used up charged item since there is no magic left.
You have residue that you could, in theory, investigate more in depth, and the item's composition and shape and material bonus would also give hints. On the other hand there is clearly no longer an active enchantment to investigate.
The difficulty of investigating the remains of a Charged Item also depends on the individual item. If they can or can not be studied is a separate question for the SG to answer and can vary from saga to saga.
A potion for example, the Charged Item is the potion and not the bottle. After consumption the SG might rule that there was a drop of the potion left in the bottle. At that point you have environmental conditions which might destroy what little residue remains. Generally though unless it was exposed to water or flame something might remain to investigate.
Compare that to something like a blasting rod or arrows which use a non-self destructive effect, in which after all the charges are used you are left with a stick which bore the effect. This is a much more stable residue, unlikely to be wiped out by most environmental conditions. This will almost always leave something that can be studied.
As a final example we have the "bomb" items (which can include many types of enchanted arrows). These are items that create an effect on themselves or touch which is destructive and generally destroys themselves in the process. Effects which create shrapnel will generally have some remains which could be collected, while those which use fire can often be totally consumed. Gathering the ash afterwards and separating it from other ash would require fairly powerful magic if it could be done at all. Even if managed, the amount of useful information that could be extracted would be very dependent on the SG.