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I'm stuck thinking about this situation. I imagine that there are two oppositely charged objects at short distance $r$, put inside an insulator (Can I say air?). They generate a net elctric field, but since they're apart there's no electrons flowing. Then I connect them with a bizzare conductive wire and electrons start flowing till balance is reached.
I wonder:

  • How and why the electron flow will follow the shape of the wire?

  • Is it beacause the net electric field?

  • Can we say that they prefer to follow a strange path through a conductor than a straighter ,shorter one thorugh an insulator?

I tried to make a picture of the situation I describe. Since for my understanding it's easier to picture electrons flowing, I drew a reverse electric field so that charge will move from low to to high potential (hope I can do that!).

enter image description here

I hope it doesn't seem a too awkward question. If there is any problem with this question please make a comment and I will try to edit it. If there's any problem you want address don't hesitate.

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Not awkward question at all. I've had the same doubt and such details are important.

The thing is that electrons by all means won't cross an insulator. That takes immense energy or voltage (happens in lightning strikes).

  • When an electron reaches an edge of the conductor, it is therefore stopped.
  • Then the next electron arrives. They repel each other and will move anywhere where there is room. (They can't move forward, because the insulator prevents motion more than the repulsion pushes. And they can't move backwards, from where more electrons arrive. So they move sideways along the curved wire.

Everytime it reaches a corner or edge, this happens. This guides the electrons along the conducting path nomatter the shape.

If you cut the wire, so the electrons reach an end having nowhere to go, they have no choice but to stop and fight back against the incoming electrons. Soon several electrons gather at this dead end and the accumulated electric field becomes large enough to counteract the voltage that makes them move in the first place. The forces balance and everything stops moving. This is an open circuit.

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The key here is to realize that it takes some amount of energy to remove and electron from a solid into vacuum. This energy is given by the work function. The work function is a result of the fact that a metal contains, besides electrons, also positively charged nucleons which keep the electrons trapped to the solid.

For two oppositely charged objects, as in your example, the objects themselves would start moving towards each other (if they were free to move), but electrons would be confined to the objects because of the work function. For large enough potential difference, the work function can be overcome can the electrons can indeed go through the air; the threshold is called breakdown voltage. This is how lightning works.

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