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Lets say I have two spheres of equal dimensions, one charged and one uncharged. Now I connect them with a conducting wire. They will now very quickly reach equal potential. Can it be said that the total charge on each sphere remains almost unchanged?

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You haven't specified if the spheres are conducting or dielectric. If it's the former, charges will flow from the first sphere to the second until they are of equal potential. How much charge flows will depend on their capacitances. Actually the final amount of charge will be proportional to their capacitance. However, if the spheres are dielctric, only the surface charge of the first sphere will be shared between the two spheres, because the volume charge of the first sphere cannot flow to the surface.

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  • $\begingroup$ The spheres are conductors. Since the spheres are large compared to the wire I thought it might be "easier" for them to reach equipotential by moving their charges around internally, without passing through the wire $\endgroup$ – fibo11235 Aug 7 '18 at 2:36
  • $\begingroup$ Either way, the charges must be in proportion to their capacitances in order to make the potential equal. And since they are identical spheres, they must have equal dimensions so the capacitances and hence charges must be equal. $\endgroup$ – Abhirup Mukherjee Aug 7 '18 at 2:39
  • $\begingroup$ But doesnt the relationship potential=charge/capacitance only work when there are no external charges involved? $\endgroup$ – fibo11235 Aug 7 '18 at 2:47
  • $\begingroup$ I understand now that the charges must be equal. $\endgroup$ – fibo11235 Aug 7 '18 at 3:02

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