 Quote by K^2
Yes, you are correct. The external field cannot be exactly zero. It is only exactly zero for a capacitor with infinite plates. For a real capacitor, keep in mind that the integral of electric field along any path gives you a potential difference. So if you have a potential difference across a capacitor, wire leading around a capacitor will certainly have electric field in it. That's the source of electromotive force resulting in the current.
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Thank you for the complete explanation.
I have one more question about the external electric field of a capacitor: Let the potential difference across the plates of the capacitor be V. So, if we calculate the integral of the electric field along a path
outside the capacitor from one plate to the other, we must also get (in absolute value) V, is this correct?
Since the electric field outside the capacitor is taken to be negligible in most calculations, does it mean that the external electric field very near each plate of the capacitor must be very strong, in order for the integral of the electric field along the external path to sum up to V?