No actually not, they transmit a particular wiggle. Same as doing the wave at the stadium, nobody moves outside of their own space they might get hot and sweaty but they are not moving
So the electrons literally being shoved into a conductor don’t go anywhere, and just wiggle? You’re mistaken my friend, electricity flows 1/16th inch every minute, I wouldn’t pull that out of my ass.
In a capacitor is something like they are all positioned in such a way that they cannot move as easily. Imagine a line of people packed together all of them raise their left hand over the shoulder of the person in front. There's an interesting video about this on youtube go check it out
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