This question already has an answer here:
In the classic example of a charging capacitor I can see how an Amperian loop with a surface going between the capacitor's plates would feel a changing electric flux, as the electric field between the plates changes with time.
However, considering the same Amperian loop but with a flat surface crossed by the wire leading to the capacitor, there is no displacement current, only conducting current.
The fact that there is no displacement current tell us that there is no change in the electric field across that flat surface.
Can someone elaborate more to me why there is no changing electric field across the flat surface too? I can't understand it...