Suppose we have a parallel plate capacitor with two plates of unequal areas. Now we connect them across a battery and both will get equal and opposite charges. But, will the charge be distributed uniformly over the two plates or will it be present only in the overlapping area of the two plates?

  • $\begingroup$ In the ideal case, where the distance between plates approaches zero, only the overlapping area of the two plates will be charged. A handwavy intuition(which can be made robust) to see this is that this configuration will make the least amount of electrical field in the space, which in turn minimizes the potential energy conserved in it, ergo it's the final configuration. $\endgroup$ – Ali Jun 3 '18 at 14:51
  • $\begingroup$ Ali, I like your reasoning about minimizing the field and potential energy in the final charge configuration. $\endgroup$ – Kevin Jan 17 '19 at 5:51

Even when the plates are of the same size, the charge is not uniformly distributed over the plates: closer to the edges, charge density is lower than in the middle and there are some charges on the outer surfaces as well.

If the plates are not of the same size, the density near the edges of a larger plate will be much lower, but it still won't be zero and there still will be charges on the outer surfaces.

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