I am studying EE and have (unfortunately) only found unsatisfactory answers to this question. Here is my understanding and confusion thus far.
When a battery is connected to a wire, the electric field of the battery is said to be "confined" or at least somewhat concentrated to/along the shape of the wire, no matter how many "loops" or whatever strange configuration the wire makes up.
I understand that the cause for current flow in a wire is from the impressed EMF of a voltage source (e.g a battery) forcing the electrons to accelerate, ultimately causing a net drift velocity. What I don't understand is how this electric field travels so well inside the conductor, compared to in the surrounding free space.
One of the puzzling things to me can be seen in this moment in a video which simulates a popular transmission line experiment (Ben Watson's YouTube video "Response to Veritasium - In Depth Explanation").
As can be seen, the electric field lines are strongly concentrated and parallel along the outside of the wire. I am presuming that they are even stronger within the wire, but the simulation seems to not show this (I guess this is due to the idealization of the conductors i.e. they are able to immediately re-arrange in such a way as to reach static equilibrium instantly, and therefore the software considers there to be no net electric field within them).
How does this "concentration" take place? How does the field propagate in such a "kind" manner? How would resistors come into play? Do they decrease this effect?