Acapacitor with plates separated by distance d is charged to a potential difference δvc. all wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d. part a does the capacitor charge q change as the separation increases? if so, by what factor? if not, why not?

Yes, the capacitor's Q load varies inversely proportional to the distance between plates.

Explanation:

In the attached files you see the inverse relationship between capacity and distance between plates "d".

In the following formula we see its relationship with the "Q" load

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