If an electron is repelled by another electron how is it that we get an electric current? As we know that an electric current is a flow of electric charge in a circuit, and in electric circuits, the charge carriers are often electrons moving through a wire.
Now, since we know that like charges repel each other, then how do the electrons flow through a wire since they are like charges they should repel each other.
 A: They do indeed repel each other. But they are repelled from the point they are coming from even stronger.

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*Imagine having two charged metal balls where one has half the charge of the other. When you connect them with a wire, will charges flow?

Yes. Sure, each individual electron feels a strong repulsion from both of the balls, since there already is an accumuation of electrons on both.
But the electron feels a stronger repulsion from the ball with more charge. So it will want to move towards the ball of lower charge. Just like a car being pushed from either end by two strong men will drift towards the weaker of them. The total force is relevant.
In fact, this is the working principle behind any charging mechanism. In order to accumulate a lot of charge in one point you just have to apply a greater force on the charge-carriers than the repulsion force they feel from that point. Charging a battery for instance requires the internal electrochemical forces to "push" electrons to the negative terminal with a force that is greater than the repulsion from that negative terminal.
A: Electrons do repel each other but they also like to spread out. Quantum mechanics tells us that it costs a lot of energy to localize an electron in a small volume. These two tendencies compete. The quantum mechanical Hubbard model is based on these two effects. It has two parameters: on-site repulsion and transfer energy (transfer Hamiltonian matrix element). Depending on the ratio of these you either get an insulator with localized electron orbitals or a conductor with delocalized orbitals. Localized orbitals describe electrons that are bound to a position are require an activation energy to become mobile.  Delocalized orbitals describe electrons that permanently move throughout the material at high energy and velocity. If all mobile electrons move in all directions with equal probability there is no current. When an electric field is applied a net drift velocity results and there is a current.
Electrons are also able to avoid one another to a large extent in 3D. This is why the free electron model of conductors is not even so bad. In 1D they are not, which is why a true 1D system will always have localized orbitals and be an insulator.
A: The electrons in a conductor repel each other and are attracted by the nuclei. Both effects cancel out. The conductor is neutral, there is no excess of electrons.
So, without an applied emf their directions are random, and under an emf there is a net flow, breaking the symmetry of their momentum distribution.
A: Good question, but you're imagination of current is wrong. You are imaging current or flow of electrons like number of balls flowing side by side to each other. However, that's not the case. If I'm not wrong, they're hoping from one atom to another. So if we take a snapshot of a moment when current is flowing it'll look exactly like a stationary material viz.with atoms huddled together and electrons orbiting them, and not just electrons flowing. They'll be at same distance from each other when flowing as they are when stationary (not under an emf).
