The definition of current is flow of electric charge. But recently I have heard that the electrons cannot move, that they just transmit energy to the other electrons and so on.
[Physics] Does an electron move in a conductor
electricityelectrons
Related Solutions
You've asked some really good questions here. Before starting, I want to first mention that the traditional picture of particles moving through a wire in electostatics is missing some physics; for instance, it ignores the quantum mechanical nature of electrons. The reason we still teach this model is because it captures the main effects (the phenomenon of current) without dealing with microscopic details, but I wanted to warn you that some of the answers will involve physics that is probably not contained in your readings in electrostatics.
To put things in perspective, we now know Newtonian physics is "wrong" (or perhaps more accurately, incomplete), and doesn't give the right answers if, for instance, an object is very small or moving very fast. But we still teach Newtonian physics because it's "good enough" for describing macroscopic objects like cars and baseballs.
Now, to answer your questions,
When electrons start moving through the wire to the positive terminal, do they all move at once? Because otherwise, while they are moving, they will still exert repulsive forces on each other? Does this repulsive force affect their movement?
The microscopic picture of a metal is (crudely) a collection of negative charges, aka electrons, moving through a lattice of positive ions. Indeed, there will be an attraction between these ions and the electrons, and repulsion between any two electrons. Surprisingly, there is also an attractive force between the electrons. The origin of this attractive force is that the electrons attract positive charges around them, and can in some cases lead to the formation of a bound state called a Cooper pair, which are relevant for explaining the phenomenon of super-conductivity, a phase of metals where the resistance is exactly zero. Note, this requires quantum mechanics to do properly, and is extremely subtle.
Shouldn't some of the electrons stay in the wire itself? If, at some point of the wire, there is not enough repulsive force present, will they stop at all, or will they reach the positive terminal?
Again, we need a more refined model, in this case statistical mechanics. Before connecting the terminals, the electrons all have a random distribution of energy which manifests itself as temperature. The presence of an electrostatic field causes a net flow of charge, but at the micro level, electrons are colliding and moving in a variety of directions. Often times you will see electrostatics books speak of drift velocity of the electrons, which is a statistical representation of the net flow. A single electron is probably moving much faster than the drift velocity, even perhaps in the opposite direction of the current flow, due to the random thermal energy and the collisions between particles.
Will the shape effect the movement of current? Does it have any effect on the electric field?
In electrostatics, no, but in reality, yes. In mechanics, one has statics and dynamics. In electromagnetism, one has electrostatics and electrodynamics. If you keep learning about electromagnetism, you will soon encounter another field, the magnetic field, and you will learn that the electric fields and magnetic fields are intertwined in such a way that lead you to reconsider the two fields as components of a single entity (hence, "electromagnetism"). In particular, you will learn that current carrying wires produce magnetic fields (Ampère's Law) and that changing magnetic fields can produce EMFs (Faraday's Law). This is a legitimate concern for building real world circuits, and the quantity associated with this effect is called impedance. Impedance is measured in Ohms, like resistance, and depends on the geometry of the circuit.
Will the length of the wire effect the speed of the flow of charges? If we have an infinite length of wire, will charges flow at all?
You're definitely on to something here. The resistance of the wire is proportional to the length of the wire. By Ohm's Law, the current is inversely proportional. The current is proportional to the drift velocity, so the current is inversely proportional to the length of the wire. See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c1 for a derivation.
One Coulomb is defined as the charge transported by a current of 1 Ampere during 1 s. The Coulomb has nothing to do with the electric field generated by electrons.
As one electron has the negative charge of $1.602·10^{-19}C$, this means that 1 Coulomb has $6.24·10^{18}$ absolute values of electron, i.e. elementary charges. The Coulomb has thus a $6.24$ times a billion billion elementary charges
Best Answer
Classically, electrons do move in a conductor that is passing direct current – but much more slowly than you might think. Let's break this down:
Current in a wire is defined as the amount of charge that passes through a cross-section of that wire in a single second. By this definition alone, it is clear that a current relies on the motion of some charged particle. It is possible that there could be a system where electrons transfer energy to each other, but in classical terms this would not be considered a "current." However, as I mentioned before, electrons actually move pretty slowly, even in very high-power currents. This might be what you're thinking of – how even very slow-moving electrons transfer a lot of power.
As a matter of interest, let's look at exactly how quickly electrons move. We need a common identity, $I = qnA\overline{v},$ where $q$ is the charge of the charge carrier, $n$ is the number of those particles per unit volume, $A$ is the cross-sectional area of the wire, and $\overline{v}$ is the average speed of these particles. This identity is fairly simple to derive – $q n$ is the charge density per unit volume, and $A \overline{v}$ is the average volume of particles that passes through a cross-section of the wire in a given second, so $q n A \overline{v}$ is the total charge that passes through a cross-section of a wire in a given second, or equivalently the current $I$.
Now, suppose we have a copper wire. Let's make it pretty thick – say, 1cm in diameter. Classically, a current in a copper wire is transmitted by electrons. So the charge of the charge carrier is $q = e = 1.6 \cdot 10^{-19}$ C.
To find $n$, we note that, from Wikipedia, "Copper has a density of $8.94$ g/cm$^3$, and an atomic weight of $63.546$ g/mol, so there are $140685.5$ mol/m$^3$. In 1 mole of any element there are $6.02\cdot 10^{23}$ atoms (Avogadro's constant). Therefore in $1$ m$^3$ of copper there are about $8.5 \cdot 10^{28}$ atoms ($6.02 \cdot 10^{23} \cdot 140685.5$ mol/m$^3$). Copper has one free electron per atom, so $n$ is equal to $8.5 \cdot 10^{28}$ electrons per m$^3$."
For $A$, our wire is circular and has diameter $1 cm$, so its cross-sectional area in square meters is $A = \pi r^2 = \pi (0.5 \cdot 10^{-2})^2 = 7.85 \cdot 10^{-5}$ m$^2$
Now let's suppose we have a current of $1$ ampere – a fairly strong current by most standards. The velocity of the moving electrons in the wire is
$$ \overline{v} = \frac{I}{q n A} = \frac{1 \text{ C/s}}{1.6 \cdot 10^{-19} \text{ C} \cdot 8.5 \cdot 10^{28} \text{ m}^{-3} \cdot 7.85 \cdot 10^{-5} \text{ m}^2} \approx 9.37 \cdot 10^{-7} \text{m/s}. $$
So a centimeter-thick copper wire carrying an ampere of current only requires its electrons to move $9.37 \cdot 10^{-7}$ m/s on average. That's very slow! You'll note from the relation $\overline{v} = I / q n A$ that the thicker the wire becomes, the smaller the velocity of the electrons is – that is, as $A$ grows larger, $\overline{v}$ grows smaller. Obviously, the wider a wire is, the more electrons can move through it. The more electrons moving through a wire, the slower they have to go to move the same total net charge.
The point is, power transferred in a wire is a result of massive numbers of electrons moving very, very slowly. They are moving, though.
Of course, this all only holds for direct current – as some other users have mentioned, alternating current is another common current in which electrons move back and forth with some predetermined frequency. In this case, the current is constantly switching directions, hence the name "alternating." This also could be what you're thinking of – as the electrons are moving back and forth but staying in essentially the same place. It is not the individual electrons that are transferring energy to each other, however, but the electric field pervading the wire which is constantly switching direction and forcing the electrons in the wire to change their direction of motion.