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Charge flowing inside a wire:
Generally, electrons constitute the flow of charges in a circuit. When a conducting path (wire) is provided to a charged object, electrons begin to flow through the path from a higher electric potential to a lower electric potential.

Direction of current

The direction of the current is always from the positive terminal to the negative terminal of the battery through a conducting wire.

Electrons were not observed at the time of electricity invention. Initially, scientists believed that the positive charges generated electric current, and the direction of flow of positive charges were considered as the direction of the current.

Conventionally, the electric current's direction is opposite to the direction of negative charges (electrons).

Usually, electric wires are made of metals like copper, aluminium, etc. How do you think metal wires conduct electricity?

The atoms are tightly or closely packed together inside the solid substance, with very little space between them. However, it turns out that electrons move smoothly through a perfect solid crystal, almost as if they were in a vacuum. On the other hand, electrons in a conductor move differently from charges in empty space.

When a constant current flows through a conductor, the electrons also move at a constant speed called drift speed. This electron drift speed can even be calculated for a copper wire. The copper wire carries a small amount of current in the order of $$1\ mm s^{-1}$$.
The analogy of water flow and charge flow:
Charges do not flow freely in a copper wire on their own, just as water does in a perfectly horizontal tube. Imagine one end of a water pipe linked to the higher end of a tank and the other end at a lower level. Now, water flows out of the lower end of the tube, since a pressure difference is created between two ends of the tube.