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I understand that this happens due to Kirchhoff's law. Any current entering one side of the capacitor must have come from another part of the circuit connected to the other side.

But is there an alternative explanation for the above phenomenon which doesn't involve Kirchhoff's law?

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Conservation of electric charge

If your capacitor starts out uncharged, then unless you add or remove charge to it, it will always remain net neutral. Charging a capacitor simply applies a voltage to both sides (i.e. it doesn't add or remove charge), so the capacitor must remain net neutral. In other words, the two plates must store equal amounts of charge.

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If the amount(magnitude) of charge on both plates in a parallel plate capacitor is different , then there will be a net electric field present inside the conducting plates .Since we know the electric field inside a conductor is 0 , the charges have to be of equal magnitude.

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