I'm a beginner in E&M, and have just started to learn about current and Ohm's law.
According to this page there is a constant electric field everywhere in a DC circuit pointing against the direction that electrons flow. This is consistent with my textbook and general intuition thus far – a potential difference created by a battery causes charge carriers to flow because of an electric force, which can be represented by having an electric field everywhere in the circuit.
My question is then this – if the charge carriers in a circuit are motivated by an electric force, then how can current be a constant value? I am assuming current to be a measurement of how much charge crosses a cross-sectional area perpendicular to the direction of flow, per time; furthermore, shouldn't the velocity components of the charge carriers in the direction of flow, which is proportional to current, increase because of the electric force that is motivating them in that direction?
In thinking about this question, I was led to a possible explanation related to Ohm's Law – my textbook compares resistance to a frictional force, caused by the accumulation of collisions undergone by a charge carrier (which result in changes in velocity against flow direction). So to answer my initial question, I was thinking that perhaps a reason why current was constant was because in each circuit, resistance provided an effective equal and opposite force to the battery, resulting in a net force of 0 on charge carriers, thus resulting in a constant velocity component in the direction of flow. This explanation also seemed to line up with the concept of 'voltage drops' – take a circuit with a battery and a resistor – the charge carriers before the resistor are motivated by the electric field, then in moving through a bumpy resistor they do work per charge equivalent to the voltage, and thus exit the resistor with their potential gone; the key here being that the resistor provides the exact amount of work needed to counteract the voltage, going with my idea that the resistance in a circuit provides an effective opposite to the electric field at each point (I'm assuming that the resistor affects the entire circuit acting like a plug in a pipe; and, simultaneously, does exist as a physical point in the circuit across which charges do work – potential does change within the resistor, but also the resistor can only let through a constant amount of charge per time, which somehow affects the entire circuit just as the electric field does (?)). Continuing, I would then assume that with a given voltage and given resistance, current changes so that the two exert equal effective forces on charge carriers – this is implying that a resistor would only be able to apply a specific amount of total force (work) at a time, and thus the charge per time must be changed to ensure that the work per charge is equivalent to voltage (this last bit seems the most questionable to me).
Is the idea that resistance provides an equal and opposite force valid reasoning to explain constant current? If not, why is constant current? If yes, is my reasoning above coherent, or what am I missing/misunderstanding?
*Please note: when I refer to 'the direction of flow' above, I am referring to the direction that the charge carriers would flow.
Best Answer
It is a analogic useful way to understand the resistive circuit, in the meaning that the electric expression $V = RI$ has the same form as the mechanical $F = kv$, in an environment where the drag force is proportional to the velocity.
In the case of a conductor, it is important to note that even whithout any applied field, the free electrons have momentum to all directions, and of different magnitudes. But there is no net flow without an E-field. The effect of the E-Field is to increase the fraction of electrons to one direction, and decrease the fraction to the opposite. The scattering with the lattice limits that net flow, and is responsible for the Joule effect of the electrical resistance.