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enter image description hereenter image description here! When I see pictures like this and when my teacher explained to me how electrons flow inside a wire I imagined electrons to be moving inside the conductor where there are the atoms or jumping on the inner surface of it not in the empty space in the wire

But the thing is I then learned that the more the diameter of the wire is the less resistance there is

Which lead me to thinking that they're actually moving in the emptiness and the resistance is made when the electrons there bump into the atoms of the inner surface of the wire (the only way I could convince myself of the fact that the more emptiness there is the more they're free to move and less the resistance) However each time I see a video about how electrons move there are always atoms and the thing is the conductor atoms can't exist in the emptiness!

Note: please don't answer using high level physics I've seen a couple of answers about the movement of electrons but they either explain it in complicated words or they make it very simple by comparing them with other objects which wasn't good for me because I started making wrong assumption based on the characteristics of the object used in comparison. I want to imagine it right.

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    $\begingroup$ There is no "emptiness." The wire is made of solid metal. Picture one of those "ball pits" that kids play in. The atoms that constitute the metal wire are packed together like that. $\endgroup$ – Solomon Slow Jul 14 '20 at 17:15
  • $\begingroup$ Oh God! I imagined it to be sth like a tiny pipe: hollow from inside. And my teacher while explaining kept using the term 'empty wire' to describe a circuit without a resistor which enfrocred the idea to me that the wire is empty. Not a surprise now, she couldn't get me when I asked her if the electrons flow in the emptiness or not. $\endgroup$ – Manar Jul 15 '20 at 16:23
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To give you a little flavor of what the “high level” physics says, start by abandoning your notion of electrons as little balls of charge. Solid state physics (the relevant discipline) tells us that the electrons responsible for conductivity in a metal are delocalized. They are entities which are spread out over some large number of atoms. Moreover, they are waves with particular properties based on the positions of the atoms in the metal crystal. Thus, you might imagine the electrons as extended waves rippling amongst the atoms.

Now, there are many electrons in a metal, each going in a slightly different direction with a slightly different energy. In a wire with no applied electric field, the electrons are going in every which way such that the total current is zero. When there is an applied electric field, the whole population of electrons gets biased in the field’s direction such that there are slightly more electrons moving that way than the opposite way, and you get a net current.

This answer is inadequate. It glosses over a lot. But perhaps this helps you visualize things a little differently.

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In the beggining of electricity, it was sometimes treated as a kind of fluid.

When Millikan found that there is a minimum electric charge, that it can not be divided infinitely, as our idea of a fluid suggest, the intuition changes to little solid balls. But intuition is always a comparison, and that way misleading.

Unless we study solid state physics (what requires quantum mechanics), and the differences between conductors, semi-conductors and isolants based on its band structures, maybe the fluid analogy is better than the solid balls one for most of the electricity effects.

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Maybe this classical approximation will help:

Since electric charge is quantized in discrete multiples of the electron charge, it is instructive to look at electric current as the movement of multiple microscopic charge carriers with a drift velocity in a conductor.

current

So the charge carriers are in the volume of the wire.

Now for resistance , this makes the analogy with the flow of water in a hose:

How should resistance depend on length and area of a wire?

A narrow hose passes less water at a certain pressure difference than a large hose. A long hose passes less water at a certain pressure than a short hose.

$R≃1/A$

$R≃L$

A “frictiony” (rough on the inside) hose should carry less water than a smooth hose. Let's call“rho” the friction coefficient.Now put it all together.A long hose passes less water at a certain pressure than a short hose:

$R≃ρ$

$R=ρL/A$

That is the hand waving logic how resistance depends on the crossectional area

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  • $\begingroup$ Can I assume too that by thickening the wire we increase the number of atoms thus the number of free electrons so there are more electrons or couloms to move around in 1 second... Or this is wrong because by increasing current we also decrease voltage (ohm's law) and in the flow hose analogy the pressure of water which is supposedly the voltage stays the same???? $\endgroup$ – Manar Jul 15 '20 at 14:38
  • $\begingroup$ To increase the current you have to increase the voltage . The number of charge carriers per area depend on the material. In the classical picture charges are free to move,to really understand what is happening one has to go to the quantum mechanical model of solids . hyperphysics.phy-astr.gsu.edu/hbase/Solids/band.html $\endgroup$ – anna v Jul 15 '20 at 18:01

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