1) How do the electrons in a wire with 0 or negligible resistance arrange themselves in order to make the field in the wire 0?

2) The electric potential drop across a resistor is far more than compared to that in a wire. This means that the field in the resistor is greater than that in the wires. How does this happen inside a resistor?

I really like this paper for this topic: https://www.tu-braunschweig.de/Medien-DB/ifdn-physik/ajp000782.pdf

As the title says it is “A semiquantitative treatment of surface charges in DC circuits” (Rainer Mueller).

Surface charges accumulate wherever there is a sudden change in the direction of the electric field lines from inside the wire to outside. Overall, you tend to get positive charge accumulating near the positive terminal and negative charges accumulating near the negative terminal, and you have both positive and negative charges accumulate on opposite sides of the wire near bends.

Unfortunately, there is no one simple overall statement about the distribution. The charge distribution depends strongly on the geometry of the circuit layout. Circuit theory neglects the geometry of the circuit layout. So you need to use Maxwell’s equations which depend on the geometry.

1) Electons travel along the surface. Zero resistance of a superconductor not only rejects an electric field, it also ejects magnetic fields. It does the latter by responding diamagnetically via Eddie currents. Lenz's Law baby!

2) Resistance is proportional to length and a substance's resistivity, and inversely proportional to cross sectional area. So a resistor can be made of something with a high resistivity. Resistivity can vary by atom's capacity to shed free electrons. Geometric arrangement of atomic components can effect Mean Free Path.

$$I=nevA=\sigma EA=\frac{V}{R}$$

Also see Drude Model and Free Electron Mode l


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