Motion of the electrons in a electric conductor when connected to a potential difference?

Question

(I am a beginner in physics, so please forgive me if this is stupid.) Normally, under static electric state there is no resultant electric field existing inside a conducting material. But, when a potential difference is applied an electric field (E) generates inside the conductor.

So, my questions are,

1. According to F=ma and F=EQ (Q- electric charge of the particle), shouldn't the electron accelerate. Nevertheless, where V=IR and I= Q/Δt, it shows that when potential difference is constant(V), I is constant too, so the flow of current has a constant speed. How can I clarify this?
2. Doesn't the above scenario make the term 'drift velocity' inappropriate, hence the travelling electrons have a acceleration?
3. If we consider a long, thin conductor or a conductor with higher resistance ( like, a wire with 1mm diameter and 10km length) what does it means that current doesn't flow? Is it because the electric field weakens in longer distances or because the flow of the current is negligible in such instances. Or is it because the work done against the resistance in the conductor by electrons is higher than the energy which electrons attain by the potential difference (being in an electric field) within two terminals?

(sorry if my English is bad. English is not my first language. Most of the scientific terms I used are directly translated from my language. If you need any clarifications on this question feel free to ask...Thank you)

Answer 1

Electrons do accelerate under the influence of the electric field, but not indefinitely. Electrons constantly undergo scattering events that disrupt their acceleration: they scatter due to imperfections in the crystal lattice of the metal, vibrations of the ions that make up this lattice, and due to other electrons. On the average, the effect of each scattering event is to set the velocity of the electron back to zero: see the Drude model of conduction. So electrons can be viewed as constantly accelerating, coming to a stop after a scattering event, and so on. On average, electrons thus have a certain finite velocity, called the drift velocity, which is proportional to the electric field.

I don't fully understand your third question. A glib answer would be that for a given potential difference, the current through a high resistance conductor will be low because resistance is defined as potential difference divided by current. Resistance is directly proportional to the conductor length, and inversely proportional to the cross section area, electron density and drift velocity. The resistance might therefore be high (and hence the current might be low) for different reasons: for example,

1. If the resistor is long, the electric field in the conductor is low, so the drift velocity is low.
2. Depending on the material, the resistor may not have many electrons per unit volume.
3. Again depending on the material as well as its purity and crystallinity, the scattering events may be more frequent, again causing the drift velocity to be low.