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Suppose I have two 1 F capacitors, each with potential difference 1
V. What physical difference between the capacitors makes one of
them "store" 1 J while the other "stores" 0.5 J?
A stronger electric field due to closer plate spacing or a good
dielectric insulator would do it. A larger plate surface would too.
Do I understand that two identical capacitors are supposed to have
the same potential difference across them while having different
charges? Since the charge on the plates is the source of the
electric field between them, how is this possible?