How is Potential Difference Created across a Resistor?

[Dario56]

In a simple circuit consisted of a battery and a resistor, how is potential difference actually established on the resistor?

My understanding is that battery creates the electric field which propagates through space at the speed of light. Resistor is put inside this field and therefore potential difference exists on that resistor (as potential difference is just the line integral of the electric field), causing current according to Ohm's law.

However, I also know that potential difference on resistors are established through charges on the conductor surface.

I'm not sure how to connect these two views as in the former case it seems that potential difference is simply created by the electric field of the battery (in the same way how voltage exist between two points in the electric field of the single charge, supposing that two points have a different distance from that charge) while in the latter case there is a charge redistribution on the conductor surface creating that potential difference the resistor.

In another words, in the former case, potential difference has nothing to do with surface charges and their redistribution while in the latter case that holds.

Therefore, according to my understanding, these two views aren't supporting each other. What am I missing?

 

[Dale]

You are right, the connection between these two is not obvious at all. This is the best paper I know for addressing this concept

Rainer Muller. A semiquantitative treatment of surface charges in DC circuits.

https://www.tu-braunschweig.de/inde...oken=2cc8a71e4fdbf159121c6b8ef8348952a2e0c197

 

[vanhees71]

What a great paper! If now he'd also have added the full calculation with the magnetic field and drawing also the Poynting vector describing the energy flow! Then I'd force all my colleagues in the physics-didactics institute to read it carefully! May be they think over their nonsensical "water analogy" for circuit theory, which they hammer into the heads of the teacher students I try to teach Maxwell electrodynamics in their theoretical-physics lecture course :-(.

 

[Dario56]

You are right, the connection between these two is not obvious at all. This is the best paper I know for addressing this concept

Rainer Muller. A semiquantitative treatment of surface charges in DC circuits.

https://www.tu-braunschweig.de/inde...oken=2cc8a71e4fdbf159121c6b8ef8348952a2e0c197

Thank you, Dale. I remember when I first found this paper and how much I liked it. It seems that the gap is bridged by the non-stationary state where the initial electric field created by the battery is changed by the local charge redistribution on different interfaces. This redistribution changes the electric field as long as the charge accumulation at all points inside the conductor becomes zero, $\frac {\partial c}{\partial t} = - \nabla \cdot j =0$. Stationary state is reached, current inside the different conductors in serial connection (branch) is the same.

 

[Dale]

Yes. Note that during that non-stationary state you cannot use circuit theory as it violates the assumptions of circuit theory.