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I read in a book that if both the plates of a parallel plate capacitor are given equal positive charges $q$, then the charges on the facing surfaces will be zero and the charge on the outer surfaces is $q$ for each plate. How is this possible? Shouldn't the charge distribute uniformly on both the surfaces of each plate?

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In a perfect the conductor the charges are free to move wherever they "want". Where they "want" to be is as far away as possible from other charges of the same sign (positive, in this case). After all, like charges repel each other. Consequently, they move to the outer surfaces of the plates, maximizing the distance between them.

Here's another way of saying the same thing: the charges are moving in order to minimize the total potential energy of the system.

Note that that is not the whole story, because it doesn't quite explain why the charges have to be right on the surface. Couldn't potential energy be minimized by some distribution that leaves some charges within the bulk? The answer is no, this cannot happen. A perfect conductor cannot maintain an electric field inside the bulk of the conductor. Otherwise charges within the bulk would feel this field and move in response. The only steady state condition that can be reached is the one where there is no electric field in the bulk.

In the parallel plate capacitor, the field due to the charges on the left side of the left plate exactly cancels the field due to the charges on the right side of the right place, with the result that the field in both conductors is zero (and all the charges are on the outside surfaces).

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Well, first you would need to know how a charge is created: Charge is created due to the excess or lack of electrons on a surface.

Key thing to remember, only electrons can move.

When the inside sides of both capacitors are positive, what happens is that here is a net positive charge on both sides, due to the absence of electrons.

The charges on both sides of the capacitors are due to the lack/excess of electrons. On the positive surfaces, it is due to their absence, while on the negative sides, it is due to the excess of electrons.

What happens is that the net positive charge on the insides of each capacitors attract the excess electrons from the outside side of the other capacitor. The electrons move in towards the inside, neutralizing the net positive charge. However, in the process, they leave behind a net positive charge on the outsides.

To repeat, the electrons get attracted by the net positive charge (on the insides of the capacitors), neutralizing the charge on the inside, however, leaving a net positive charge on the outsides.

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